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\author 194268660 "CIT-Labs" 
\author 270189200 "owner" 
\author 1750459017 "Rachel Whiteheart" 
\author 2090522031 "mw24" 
\end_header

\begin_body

\begin_layout Title
Village Source to Environment
\end_layout

\begin_layout Author
Diana Kelterborn, Sarah Levine, Nicholas Parisi, and Rachel Whiteheart
\end_layout

\begin_layout Date
May 16, 2014
\end_layout

\begin_layout Section*
Detailed Task List
\end_layout

\begin_layout Subsection*
Design a distributed storage system for a village water supply 
\end_layout

\begin_layout Subsubsection*
Design of distribution system 
\end_layout

\begin_layout Itemize
Review last semester's projects [Completed by Diana]
\end_layout

\begin_layout Itemize
Compile best strategies from previous projects into one comprehensive design
 [Completed by Diana]
\end_layout

\begin_layout Itemize
Revise capstone calculations to incorporate tubing [Completed by Sarah]
\end_layout

\begin_layout Itemize
Optimize design for cost efficiency and equity [Completed by Rachel]
\end_layout

\begin_layout Itemize
Optimize for convenience [Ongoing; Rachel]
\end_layout

\begin_layout Itemize
Incorporate solar code into distribution code [Completed by Diana]
\end_layout

\begin_layout Itemize
Change flow equations to reflect turbulent flow [Completed by Rachel]
\end_layout

\begin_layout Itemize
Incorporate well pump [Completed by Rachel]
\end_layout

\begin_layout Itemize
Optimize algorithm for varying tier/length [Completed by Sarah]
\end_layout

\begin_layout Subsubsection*
Design photovoltaic and pump system
\end_layout

\begin_layout Itemize
Obtain hourly solar insolation data for India [Completed by Nick]
\end_layout

\begin_layout Itemize
Obtain accurate cost and efficiency data for solar panels and pumps [Completed
 by Diana] 
\end_layout

\begin_layout Itemize
Design algorithm to determine how often the solar pumps will not receive
 enough power [Completed by Diana] 
\end_layout

\begin_layout Itemize
Design algorithm for solar power generated at a given location [Completed
 by Nick]
\end_layout

\begin_layout Itemize
Sizing PV array for pumps, optimized for cost and designed to accommodate
 future growth [Completed by 5/09; Diana]
\end_layout

\begin_layout Itemize
Change optimal angle for solar panels [Completed by Nick]
\end_layout

\begin_layout Itemize
Incorporate read data into solar calculations and incorporate pump efficiency
 as a function of panel power [Completed by Diana]
\end_layout

\begin_layout Itemize
Include pump efficiency curves and ensure they reflect desired head and
 flow rate [Completed by Diana]
\end_layout

\begin_layout Itemize
Comprehensive system diagram [Completed by Nick]
\end_layout

\begin_layout Subsection*
Individual roles
\end_layout

\begin_layout Subsubsection*
Team Coordinator: Diana 
\end_layout

\begin_layout Itemize
Responsible for facilitating Team meetings and keeping track of progress
 over the course of the semester to ensure that goals are completed in a
 timely manner.
 Point person for communication between the team and advisers, as well as
 between the team and the AguaClara leadership team.
\end_layout

\begin_layout Subsubsection*
Literature Coordinator: Rachel 
\end_layout

\begin_layout Itemize
Responsible for compiling all relevant information gathered from literature
 sources and ensuring all material is properly cited.
 
\end_layout

\begin_layout Subsubsection*
Report Proofreader: Sarah
\end_layout

\begin_layout Itemize
Responsible for checking reports for proper spelling and grammar.
 
\end_layout

\begin_layout Subsubsection*
Team Glue: Nick
\end_layout

\begin_layout Itemize
Responsible for ensuring team unity and productivity.
 
\end_layout

\begin_layout --Separator--

\end_layout

\begin_layout Section*
Introduction
\end_layout

\begin_layout Standard
The newly formed Village Source to Environment Team combines the design
 of a distribution storage plan and wastewater treatment system for rural
 villages in India.
 Current distribution infrastructure consists of an elevated tank that fills
 and dispenses twice daily, each time supplying half the village's water
 needs.
 This method is inefficient and inconvenient, since villagers can only obtain
 water when the tank dispenses and must carry it half a kilometer to their
 homes.
 This system also makes it impossible to ensure that each family receives
 their designated share of water.
 Furthermore, due to limited access to water, villages improvise unsanitary
 household storage.
 They obtain all water for washing, drinking and cooking from these open
 containers, meaning the entire source can be contaminated any time they
 use it.
 Our proposed distribution system will pump water directly into villagers'
 homes, replacing the elevated storage tank with smaller household tanks.
 Each tank will connect to a sink for sanitary use on demand.
 Additionally, the sink's drain will allow us to eventually integrate a
 wastewater treatment or irrigation system.
 Small villages with limited resources often lack sanitary solutions for
 handling greywater and blackwater; we hope future teams will investigate
 strategies for treating wastewater for irrigation.
\end_layout

\begin_layout Standard
Our work 
\change_deleted 1750459017 1400271081
will 
\change_unchanged
build
\change_inserted 1750459017 1400271084
s
\change_unchanged
 
\change_inserted 1750459017 1400271086
up
\change_unchanged
on capstone design projects from the Fall 2013 CEE 4540 class that focused
 on a distribution system for the village of Gufu, India.
 We 
\change_deleted 1750459017 1400271095
will
\change_unchanged
 revise
\change_inserted 1750459017 1400271099
d
\change_unchanged
 the distribution design and 
\change_inserted 1750459017 1400271105
planned to 
\change_unchanged
add household storage tanks
\change_inserted 1750459017 1400271123
, however the distribution system design took the majority of our focus
 this semester
\change_unchanged
.
 This new team was formed to facilitate AguaClara's expansion to India.
 The local infrastructure, community sizes, and therefore required flow
 rates, differ significantly from those in Honduras.
 As a result, the team must take a very different approach to the problem.
 The Village Source to Environment Team 
\change_deleted 1750459017 1400271138
will lay
\change_inserted 1750459017 1400271140
has laid
\change_unchanged
 the foundation for distribution design this semester.
 
\end_layout

\begin_layout Section*
Parameter Definitions 
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status open

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Variable
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Definition
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g
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Gravitational constant
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\begin_inset Formula $\nu$
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Kinematic viscosity constant for water
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Unit-less parameter that represents equity of flow throughout the system.
 Set equal to 20% to ensure that all flows are within 20% of each other.
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Unit-less parameter that describes minor losses through an orifice
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Area of the orifice
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\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252572
\begin_inset Formula $h_{LE}$
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\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252572
Head loss due to major losses.
 Maximum, minimum, and average major losses are given with subscripts
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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\begin_layout Plain Layout

\change_inserted 1750459017 1400252605
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\change_inserted 1750459017 1400252605
Head required to maintain equity throughout the distribution system
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\begin_layout Plain Layout
\begin_inset Formula $Q_{TargetHouse}$
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\begin_layout Plain Layout
Flow rate for each house throughout the system.
 Maximum, minimum, and average flow rates are given with subscripts
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\begin_layout Plain Layout

\change_inserted 1750459017 1400252327
\begin_inset Formula $Q_{TargetTotal}$
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\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252353
Total flow rate through the transmission line
\change_inserted 194268660 1400291196
,
\change_inserted 1750459017 1400252353
 i.e.
 flow rate that the pump must be able to handle
\end_layout

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\begin_layout Plain Layout
\begin_inset Formula $Q_{Capita}$
\end_inset


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Desired per capita flow rate of 100 L/day
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\begin_inset Text

\begin_layout Plain Layout
N
\begin_inset Formula $_{People}$
\end_inset


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\begin_inset Text

\begin_layout Plain Layout
Village population, estimated to be 240 for our model
\end_layout

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\begin_layout Plain Layout
\begin_inset Formula $D_{Tubing}$
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\begin_inset Text

\begin_layout Plain Layout
Diameter of the tubing
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\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253338
\begin_inset Formula $Q_{Tubing}$
\end_inset


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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253338
Real flow rate through the tubing at each house, given each house's accrued
 head loss
\end_layout

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</cell>
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<row>
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\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $h_{f.tubing}$
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\end_layout

\end_inset
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\begin_inset Text

\begin_layout Plain Layout
Requisite head loss through tubing to maintain equity.
 Maximum, minimum, and average tubing head losses are given with subscripts
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\begin_layout Plain Layout

\change_inserted 1750459017 1400252208
\begin_inset Formula $\Pi_{RatioAvgMin}$
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252558
Ratio of the average flow rate to the minimum flow rate through the tubing.
 Equals 1.1 for a 
\begin_inset Formula $\Pi_{Q}$
\end_inset

of 20%
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\begin_layout Plain Layout
\begin_inset Formula $h_{p}$
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\begin_layout Plain Layout
Head provided by pump
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\begin_inset Text

\begin_layout Plain Layout
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\end_layout

\end_inset
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\begin_inset Text

\begin_layout Plain Layout
Head losses (excluding minor losses)
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\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $L_{Tubing}$
\end_inset


\end_layout

\end_inset
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\begin_inset Text

\begin_layout Plain Layout
Length of tubing
\change_inserted 194268660 1400296629
 necessary to dissipate the average head for each house in the system,
\change_deleted 194268660 1400296628
 chosen
\change_unchanged
 given the flow rate and equity requirements
\change_inserted 1750459017 1400252892
 for
\change_deleted 194268660 1400296636
 any given
\change_inserted 194268660 1400296636
 each
\change_inserted 1750459017 1400252892
 iteration of the code
\change_unchanged

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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400296653
\begin_inset Formula $L_{Additional}$
\end_inset


\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400296707
Length of additional tubing required for a given house to achieve equitable
 head loss
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\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $Min{}_{DTubing}$
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\begin_inset Text

\begin_layout Plain Layout
Minimum diameter possible for tubing
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252523
\begin_inset Formula $\Pi_{RatioMaxAvg}$
\end_inset


\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252550
Ratio of maximum flow rate to average flow rate through the tubing.
 Equals 1.1 for a 
\begin_inset Formula $\Pi_{Q}$
\end_inset

of 20%
\change_unchanged

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\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252657
\begin_inset Formula $f_{factor}$
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\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252682
Friction factor used to estimate head loss through turbulent tubing
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252822
\begin_inset Formula $A_{Tubing}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252840
Area of the tubing given 
\change_inserted 194268660 1400292703
a 
\change_inserted 1750459017 1400252840
diameter 
\change_deleted 194268660 1400292709
chosen
\change_inserted 1750459017 1400252840
 for 
\change_deleted 194268660 1400292711
any
\change_inserted 194268660 1400292711
each
\change_inserted 1750459017 1400252840
 
\change_deleted 194268660 1400292719
given 
\change_inserted 1750459017 1400252840
iteration of code
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252844
\begin_inset Formula $D_{Tubing}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400252863
Diameter of tubing chosen for any given iteration of the code
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253007

\family roman
\series medium
\shape up
\size normal
\emph off
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\begin_inset Formula $\Delta h_{f.dist}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253089
Difference 
\change_deleted 194268660 1400292763
of 
\change_inserted 194268660 1400292765
between 
\change_inserted 1750459017 1400253089
minimum major losses through pipes in the distribution system 
\change_deleted 194268660 1400292770
from
\change_inserted 194268660 1400292771
and
\change_inserted 1750459017 1400253089
 maximum major losses through pipes.
\end_layout

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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253147
\begin_inset Formula $\alpha$
\end_inset


\end_layout

\end_inset
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 1750459017 1400253162
Constant employed in 
\change_inserted 194268660 1400292808
tubing 
\change_inserted 1750459017 1400253162
head loss 
\change_deleted 194268660 1400292812
through tubing 
\change_inserted 1750459017 1400253162
calculations
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 194268660 1400291821
Distribution 
\change_unchanged
Parameter Definitions
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

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wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Tabular
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<column alignment="center" valignment="top" width="5in">
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400292593
Variable
\change_unchanged

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400292595
Definition
\change_unchanged

\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\Pi_{SunHours}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Percentage of each day for which there is sufficient sunlight to operate
 the PV pump.
 For the Gufu Village, this is assumed to be 33% (8 hours/24 hours).
 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $N_{JD}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Number of Julian day, ranging from 1 to 365.
 One day was chosen for the 15th of each month (i.e.
 January 15 is the 15th Julian day) 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none
\begin_inset Formula $D_{\delta}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Declination angle relative to the equator
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $H_{d}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Diffuse component of daily insolation sum, thermal energy per square meter
 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\overline{H}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Global daily insolation sum, thermal energy per square meter 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $K_{T}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Monthly average clearness index
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R_{r}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Ratio of total insolation on a tilted surface to that on an equivalent horizonta
l surface
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $R_{Bbeta}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Ratio of beam insolation on a tilted surface to that on an equivalent horizontal
 surface
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $S_{M}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Optimum PV tilt angle for a month, measured from the horizontal
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\rho_{Ref}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Reflection coefficient, with 1 being the least reflective
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $H_{t}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Monthly average total daily insolation on a tilted surface, thermal energy
 per square meter 
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\beta$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Solar cell temperature coefficient of PV efficiency, 1/degree C
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\eta_{r}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Solar cell efficiency at rating conditions
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\eta$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Overall panel efficiency
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $T_{A}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Monthly average air temperature
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $T_{M}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Mean monthly ambient air temperature
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $T_{C}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Monthly average cell temperature
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $\beta_{tiltsim}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Optimal angle for solar panels
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400297247
\begin_inset Formula $\rho$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400297345
Density of water
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400297363
\begin_inset Formula $\epsilon$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400297373
Pump Efficiency
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Solar Parameter Definitions
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section*
Literature Review
\end_layout

\begin_layout Subsection*
Gufu Village
\end_layout

\begin_layout Standard
While the team ultimately plans to design a template applicable to any small
 village, we 
\change_deleted 1750459017 1400271159
will base
\change_inserted 1750459017 1400271161
base
\change_inserted 194268660 1400292850
d
\change_unchanged
 our design on Gufu Village, seen in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Map-of-Gufu"

\end_inset

 below.
 An electric pump powered by solar panels 
\change_deleted 1750459017 1400271169
will lift 
\change_inserted 1750459017 1400271171
lifts 
\change_unchanged
water from a well located just outside the village.
 The water will be treated by an AguaClara 
\change_deleted 1750459017 1400271308
filter 
\change_inserted 1750459017 1400271326
Low Flow 
\change_deleted 194268660 1400285208
Stakced
\change_inserted 194268660 1400285208
Stacked
\change_inserted 1750459017 1400271326
 Rapid Sand filter (LFSRSF) 
\change_unchanged
and piped to each household.
 We 
\change_deleted 1750459017 1400271335
will 
\change_unchanged
assume a total population of 240 people, 5 people per household, and per
 capita demand of 100 liters per day.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename ../../Village_Source_to_Environment_Report_3/Village_Source_to_Environment_Report_3/images/Gufu.PNG
	lyxscale 30
	scale 50

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Map of Gufu Village in India
\begin_inset CommandInset label
LatexCommand label
name "fig:Map-of-Gufu"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
The 2canzzzz' Capstone Design
\end_layout

\begin_layout Standard
The design for this project
\change_deleted 1750459017 1400271356
 will be
\change_inserted 1750459017 1400271357
 is
\change_unchanged
 based primarily on The 2canzzzz’ capstone design project for CEE 4540 in
 Fall 2013.
 There were several recurring ideas that this group, and others who focused
 on the village distribution system, used that will be maintained in the
 ongoing design.
 Some of these ideas include:
\end_layout

\begin_layout Itemize
Use of a dimensionless parameter, 
\begin_inset Formula $\Pi_{Q}$
\end_inset

, shown in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:ΠQ"

\end_inset

 below.
 
\begin_inset Formula $\Pi_{Q}$
\end_inset

 represents equity in flow between houses in the village, and in The 2canzzzz'
 design was forced to be no greater than 0.1.
 Therefore, all household flows are within 10% of each other.

\change_deleted 2090522031 1399986142
 
\change_unchanged
 
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\Pi_{Q}=\frac{Q_{max}-Q_{Min}}{Q_{Avg}}\label{eq:ΠQ}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
The equation can be rewritten in terms of head loss using an orifice, as
 seen in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:ΠQ for Orifice"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\Pi_{Q}=\frac{\left[\Pi_{VC}A_{Orifice}\sqrt{2g\left(h_{Equity}-h_{LEMinimum}\right)}-\Pi_{VC}A_{Orifice}\sqrt{2g\left(h_{Equity}-h_{LEMaximum}\right)}\right]}{\Pi_{VC}A_{Orifice}\sqrt{2g\left(h_{Equity}-h_{LEAverage}\right)}}\label{eq:ΠQ for Orifice}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Since every house has the same size orifice, we can reduce the equation
 and solve for equity, as reflected in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Equity Equation"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
F_{hEq}(h_{Equity})=(\sqrt{h_{Equity}-h_{LEMinimum}}-\sqrt{h_{Equity}-h_{LEMaximum}})-\Pi_{Q}\sqrt{h_{Equity}-h_{LEAverage}}\label{eq:Equity Equation}
\end{equation}

\end_inset


\end_layout

\begin_layout Itemize
Use of different tiers of pipe that carry water from a main transmission
 pipe, originating at the well and ending in the center of the village,
 to each household.
 
\end_layout

\begin_layout Itemize
Iterating pipe diameter for each tier based on each tier's flow rate.
 Options will be narrowed down based on which pipe diameters maintain equity,
 and a final selection will be made by optimizing for cost.
 
\end_layout

\begin_layout Itemize
Use of a distribution system with one central pipe and a series of smaller
 pipes that branch outward from the central pipe, as shown in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Distribution-Layout"

\end_inset

.
\end_layout

\begin_layout Itemize
Separate designs for the transmission line (based on PV/PVC tradeoff) and
 for the distribution system (based on an initial guess as to the economic
 value of equity).
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename ../../Village_Source_to_Environment_Report_3/Village_Source_to_Environment_Report_3/images/Distribution Layout.PNG
	lyxscale 30
	scale 70

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Distribution Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Distribution-Layout"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
One significant difference between The 2canzzzz' design and the design that
 we will implement is our use of small diameter tubing to restrict the flow
 to each house.
 In The 2canzzzz' design, an orifice was used to control this flow and to
 maintain adequate pressure throughout the distribution system; however,
 we will utilize tubing as the 
\change_deleted 194268660 1400285219
headloss
\change_inserted 194268660 1400285219
head loss
\change_unchanged
 element.
 Tubing will be more readily available than small orifices and will be less
 prone to clogging because it will have a larger diameter than the orifices.
 It will also allow easy alteration of each household's flow rate by simply
 increasing or decreasing the length of the tubing for each house.
 
\change_inserted 1750459017 1400271451
Additionally, it will allow for easier monitoring of each house
\change_inserted 194268660 1400293125
'
\change_inserted 1750459017 1400271451
s flow rate, as the tubing will be placed in a small box at street level
 where flow meters can be 
\change_deleted 194268660 1400293140
placed
\change_inserted 194268660 1400293142
installed
\change_inserted 1750459017 1400271451
.
\change_unchanged

\end_layout

\begin_layout Standard
Another significant difference between The 2canzzzz' design and ours is
 that our design 
\change_deleted 1750459017 1400271473
will anticipate future growth
\change_inserted 1750459017 1400271619
accounts for weather variability during the year.
 This variability is key in determining the real performance of solar PV
 
\change_deleted 194268660 1400285222
paneels
\change_inserted 194268660 1400285222
panels
\change_inserted 1750459017 1400271619
 that power 
\change_deleted 194268660 1400293164
this
\change_inserted 194268660 1400293164
the
\change_inserted 1750459017 1400271619
 entire system.
 This weather variability will be discussed 
\change_deleted 194268660 1400293174
further 
\change_inserted 1750459017 1400271619
later in this document.
\change_deleted 1750459017 1400271473
.
 This will likely be accomplished by designing a pipe and pump system capable
 of accommodating increased load.
 Given that the actual location of new homes will not be known, the increased
 capacity can be designed by either multiplying each household node flow
 rate by a growth factor or by applying a growth node where each distribution
 pipe reaches the edge of the village.
\change_unchanged

\end_layout

\begin_layout Standard
Although our code is primarily modeled after The 2canzzzz' design, a few
 concepts were borrowed from another group who worked on distribution system
 design for CEE 4550 in Fall 2013.
 The use of tubing to restrict the flow rate to each house instead of an
 orifice was initially proposed by Mathcadre.
 
\end_layout

\begin_layout Subsection*
Additional resources
\end_layout

\begin_layout Standard

\shape italic
Design of Potable Water Supply Systems in Rural Honduras
\shape default
 
\begin_inset CommandInset citation
LatexCommand cite
key "RefWorks:284"

\end_inset

, a report published by Nathan Reents in fulfillment of his Masters thesis,
 details the design of a gravity-powered distribution system in rural Honduras.
 This system design is only slightly applicable to our design, as the flat
 topography of our site prohibits the use of gravity, so our design is driven
 entirely by pressure.
 However, Reents' design could be used in the future if the topography of
 the region in question changes.
 This system was designed using an Excel spreadsheet initially developed
 by the Peace Corps.
 Break-tanks were used to maintain a static head of less than 100 m and
 dynamic pressure greater than 0 m at all points throughout the system.
 This was controlled in order to eliminate the need for high-strength PVC
 pipes.
 
\end_layout

\begin_layout Section*
Methods
\end_layout

\begin_layout Subsection*
Distribution
\end_layout

\begin_layout Standard
We began by modifying The 2canzzzz' report to incorporate tubing into the
 distribution system.
 In the revised design, seen in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Distribution-Illustration"

\end_inset

, all three tiers of PVC pipe will remain, with tubing placed into each
 house's segment of tier three pipe.
 We selected three tiers of tubing and the system layout suggested by The
 2canzzzz', as this layout 
\change_deleted 1750459017 1400271640
seemed
\change_inserted 1750459017 1400271640
was
\change_unchanged
 most effective at minimizing elevation differences between houses throughout
 the system and minimizing the quantity of tubing, and thus cost, required.
 Ultimately the distribution system layout must be customized for each village
 to account for topography and placement of houses, and a method for optimizing
 the number of tiers must be determined.
 
\change_inserted 194268660 1400285062

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400285063
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400285094
\begin_inset Graphics
	filename images/HGL.png
	lyxscale 50
	scale 70

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400285097


\backslash
centering
\change_unchanged

\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 194268660 1400294235
Hydraulic gradient line (HGL) following energy throughout the entire distributio
n system.
\begin_inset CommandInset label
LatexCommand label
name "fig:HGL-following-energy"

\end_inset


\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard

\change_inserted 1750459017 1400273497
Our code is based primarily on an energy analysis that tracks the head throughou
t the system and determines the head available at each house
\change_inserted 194268660 1400293698
,
\change_deleted 194268660 1400293697
 
\change_inserted 194268660 1400293843
 
\change_deleted 194268660 1400293697
(
\change_inserted 1750459017 1400273497
shown as 
\change_inserted 194268660 1400293243

\begin_inset Formula $\Delta h$
\end_inset


\change_deleted 194268660 1400293224
Δ h
\change_inserted 1750459017 1400273497
 in
\change_deleted 194268660 1400293219
 the
\change_inserted 1750459017 1400273497
 Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:HGL-following-energy"

\end_inset


\change_inserted 194268660 1400297384
 of a Hydraulic gradient line (HGL
\change_inserted 1750459017 1400273497
).
 There is a submerged well pump that provides enough head to bring water
 up from the 
\change_deleted 194268660 1400293334
surface of the water in the 
\change_inserted 1750459017 1400273497
well and push it through the LFSRSF.
 Because these submerged pumps are already in place for most villages, calculati
ons were not included for the well pumps.
 However, future iterations of the code should include this submerged pump.
 The pump located at the AguaClara LFSRSF "plant" provides a certain head
 (hp) that increases the energy in the system by hp (seen by the rise in
 the HGL at the plant).
 During the transportation of 
\change_deleted 194268660 1400293570
the 
\change_inserted 1750459017 1400273497
water from the LFSRSF to the village, energy is lost due to major losses
 in the pipe and because the elevation of the village is higher than that
 of the pump.
 This is reflected 
\change_deleted 194268660 1400293885
by 
\change_inserted 194268660 1400293886
in 
\change_inserted 1750459017 1400273497
the downward slope of the HGL.
 The line 
\change_inserted 194268660 1400293751

\begin_inset Formula $h_{eq}$
\end_inset


\change_deleted 194268660 1400293747
h.eq
\change_inserted 1750459017 1400273497
 measures the total available head when
\change_deleted 194268660 1400293767
 the
\change_inserted 1750459017 1400273497
 water enters the distribution system in the village.
 The major losses after this point are determined by the diameters and flows
 of all of the relevant pipes leading up to each house.
 In The 2canzzzz' design, the head available at the orifice at each house
 is then converted to kinetic energy as 
\change_deleted 194268660 1400293787
the 
\change_inserted 1750459017 1400273497
water flows through the orifice and into the distribution tank.
 Because this available head drives the flow through the orifice, they found
 this available head at each house and then found
\change_deleted 194268660 1400293804
 what
\change_inserted 1750459017 1400273497
 the respective flow 
\change_deleted 194268660 1400293809
would be 
\change_inserted 1750459017 1400273497
for each house
\change_inserted 194268660 1400293834
.

\change_inserted 1750459017 1400273497
 
\change_unchanged

\end_layout

\begin_layout Standard
Instead of an orifice restricting flow at the household level, flow is restricte
d by a coil of tubing located at the street level.
 Tier 3 pipe carries water from the Tier 2 pipe to this tubing box and from
 the tubing box to each house, where it discharges directly into a household
 storage tank equipped with a float valve.
 The coil of tubing improves equity among the houses by increasing head
 loss to all houses.
 Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:EGL-Basic"

\end_inset

 shows a simplified energy gradient line (EGL) from the house closest to
 the transmission line to the house furthest from the line.
 This diagram neglects elevation differences between houses and changes
 in rate of head loss for each diameter of pipe and instead plots head loss
 as a linear trend.
 A more in-depth EGL that accounts for differences in pipe diameter is shown
 in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:EGL"

\end_inset

.
 
\change_deleted 194268660 1400294078
.
 
\change_unchanged

\begin_inset Formula $\Delta h_{f.dist}$
\end_inset

 represents the difference in major losses between the closest house and
 farthest house.
 The closest house to the transmission line will experience the least amount
 of head loss from pipes leading up to it and will consequently receive
 the highest flow.
 Since this house has the highest flow rate it will also have the highest
 head losses through tubing,
\change_inserted 194268660 1400294122
 
\change_unchanged

\begin_inset Formula $h_{f.tubing.max},$
\end_inset

 assuming that all head is dissipated through the tubing before entering
 the house.
 
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none

\begin_inset Formula $h_{f.tubing.min}$
\end_inset

 represents the head losses through the tubing for the house furthest from
 the transmission line, which would experience the most head loss from pipe
 length and receive the minimum flow.

\change_deleted 2090522031 1399986142
 
\change_unchanged
 Equity is centered around a target flow rate, ensuring all houses receive
 a flow within 20% of the target.
 The target flow rate 
\change_inserted 194268660 1400181615
per house 
\change_unchanged
is 
\change_inserted 1750459017 1400251891
1
\change_unchanged
500 L/day per house, calculated using Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Target Flow Rate"

\end_inset

 which uses the desired flow rate per capita of 100 L/day, 
\change_deleted 194268660 1400181467
the 240 people in the village
\change_inserted 194268660 1400181470
5 people per house
\change_unchanged
, and the 
\change_deleted 194268660 1400181485
number of hours th
\change_inserted 194268660 1400181494
percentage of the day that the
\change_deleted 194268660 1400181485
e
\change_unchanged
 pump is in operation
\change_inserted 194268660 1400181770
 based on 
\change_deleted 194268660 1400294189
er
\change_deleted 1750459017 1400251908
re
\change_inserted 194268660 1400294190
a viable amount of sunlight
\change_unchanged
.

\change_inserted 194268660 1400294216
 The target flow rate for the entire village (i.e.
 the flow rate that the pump must be able to supply) is calculated by multiplyin
g this target flow rate per house by the number of houses (48 houses) in
 the village.
\change_deleted 194268660 1400181621

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399989874

\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none
This sentence is confusing.
 Rewrite it! The target flow in the equation is NOT the household target
 flow.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/old Pi.Q EGL Diagram.jpg
	lyxscale 70
	scale 60

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Simplified EGL
\begin_inset CommandInset label
LatexCommand label
name "fig:EGL-Basic"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
Simplified EGL illustrating the difference in head loss experienced by the
 house closest to the transmission line and the house furthest from the
 line.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/FullHouse.PNG
	lyxscale 70
	scale 55

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Distribution Illustration
\begin_inset CommandInset label
LatexCommand label
name "fig:Distribution-Illustration"

\end_inset


\end_layout

\end_inset

Illustration of the three-tier distribution system.
 Tier 1 (yellow) is connected to the main transmission line and Tier 3 (blue)
 opens into a storage tank in each house.
 Tubing is placed into a small box located in each house's length of tier
 three pipe.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/Pi.Q EGL Diagram.jpg
	lyxscale 65
	scale 55

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
EGL 
\begin_inset CommandInset label
LatexCommand label
name "fig:EGL"

\end_inset


\end_layout

\end_inset

 Representative EGL for one house that reflects changes in head loss given
 different pipe and tubing diameters.
 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
Q_{TargetHouse}=\frac{Q_{capita}*N_{PeoplePerHouse}}{\Pi_{SunHours}}\label{eq:Target Flow Rate}
\end{equation}

\end_inset


\change_inserted 194268660 1400181514

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400181536
\begin_inset Formula 
\[
Q_{TargetTotal}=Q_{TargetHouse}*N_{Houses}
\]

\end_inset


\change_deleted 194268660 1400181526

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399995859
Is this household flow rate while pumping? Target isn't a very good subscript.
 Create a clearer name.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
We began the process by demonstrating that the flow through the tubing could
 be turbulent under certain conditions.
 Since we
\change_deleted 2090522031 1399986142
 
\change_unchanged
 already assumed that the remainder of the flow through our system (i.e.
 through the pipes) was turbulent, this simplified the design.
 Turbulent flow will also dissipate more head through the tubing, decreasing
 the amount of tubing required at each house.
 However, although this turbulent assumption will hold for some of the tubing
 diameter and flow rate combinations, future designs should account for
 the variability in flow regime and model the rest of the system accordingly.
\end_layout

\begin_layout Standard
We found the Reynolds number for the smallest tubing diameter we are considering
 given available adapters and pipe sizes, 0.25 in, and maximum flow through
 the system, as these conditions will result in the highest Reynolds number.
 As shown in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Reynold's number"

\end_inset

 below, we multiplied the target flow by 
\change_deleted 1750459017 1400252432
1.1
\change_inserted 1750459017 1400252433

\begin_inset Formula $\Pi_{RatioMaxAvg}$
\end_inset


\change_unchanged
, since this represents the maximum flow under the 20% equity constraint,
 and 1.5 to account for variability in solar power, which will result in
 variable flow.
 We found a Reynolds number of 5,744, which is well within the turbulent
 range.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
Re=\Pi_{RatioMaxAvg}*1.5*\frac{Q_{TargetHouse}}{\frac{\pi}{4}\nu Min_{DTubing}}=5,744\label{eq:Reynold's number}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Since tubing replaced orifices as the head loss element, we had to revise
 our 
\begin_inset Formula $\Pi_{Q}$
\end_inset

 equation to reflect this change.
 Assuming flow is always turbulent, we calculated the friction factor using
 the Swamee-Jain equation (
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Swamee-Jain Equation for Friction Factor"

\end_inset

).
 We used our maximum flow rate (not accounting for solar-induced flow variations
), minimum diameter of tubing, and the roughness coefficient for PVC pipe
 and tubing as inputs.
 The resulting friction factor of 0.06 represents the 
\change_deleted 194268660 1400181789
m
\change_deleted 2090522031 1399995973
a
\change_deleted 194268660 1400181789
i
\change_deleted 2090522031 1399995973
x
\change_deleted 194268660 1400181789
nimum
\change_inserted 194268660 1400181791
minimum
\change_deleted 194268660 1400181796

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399995954
Isn't this the minimum? Friction factor decreases as Re increases.
\change_unchanged

\end_layout

\end_inset


\change_inserted 194268660 1400294397
 
\change_deleted 194268660 1400181796
 
\change_unchanged
possible friction factor.
 
\change_inserted 194268660 1400285242
Using the minimum friction factor will result in the minimum estimated head
 loss, which equate
\change_inserted 1750459017 1400251995
s
\change_deleted 1750459017 1400251995
d
\change_inserted 194268660 1400182365
 to a conservative design.
\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
f_{factor}=\frac{0.25}{\left(\log\left(\frac{\varepsilon}{3.7Min_{DTubing}}+\frac{5.74}{Re_{Pipe}(Q_{Max},Min_{DTubing},\nu)^{0.9}}\right)^{2}\right)}\label{eq:Swamee-Jain Equation for Friction Factor}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We used the EGL shown in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:EGL-Basic"

\end_inset

 to determine relationships between head loss through tubing and head loss
 through the distribution system, as shown below.
 The first two equations were gleaned directly from the EGL diagram.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
h_{f.tubing.max}=\Delta h_{f.dist}+h_{f.tubing.min}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
\Delta h_{f.dist}=h_{LEMax}-h_{LEMin}
\]

\end_inset


\end_layout

\begin_layout Standard
Since flow through the tubing is assumed to be turbulent, Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Tubing Head Loss"

\end_inset

 below for head loss through tubing is related to turbulent flow through
 the tubing.
 It uses the diameter for the tubing for each iteration and assumes a
\change_deleted 194268660 1400294455
s
\change_unchanged
 fraction factor as calculated in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Swamee-Jain Equation for Friction Factor"

\end_inset

.

\change_inserted 1750459017 1400253296
 Each of these parameters represent the flow rate, diameter, and length
 chosen for each specific iteration of the code.
 They are used as general terms here.
\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
h_{f.tubing}=f_{factor}\left(\frac{L_{Tubing}}{D_{Tubing}}\right)\frac{\left(\frac{Q_{Tubing}}{A_{Tubing}}\right)^{2}}{2g}\label{eq:Tubing Head Loss}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
All constants from Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Tubing Head Loss"

\end_inset

 were compiled into one constant, 
\begin_inset Formula $\alpha$
\end_inset

, shown in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Alpha Constant"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\alpha=\frac{f_{factor}L_{Tubing}}{2gD_{Tubing}A_{Tubing}^{2}}\label{eq: Alpha Constant}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We then solved for the maximum, minimum, and average tubing flow rates in
 terms of their respective head losses.
 
\change_inserted 1750459017 1400252064

\end_layout

\begin_layout Standard

\change_inserted 1750459017 1400252073
\begin_inset Formula 
\begin{equation}
\Pi_{RatioAvgMin}=\frac{Q_{Avg}}{Q_{Min}}=1.1\label{eq:Pi.Ratio}
\end{equation}

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
Q_{Max}=\sqrt{\frac{h_{f.tubing.max}}{\alpha}}=\sqrt{\frac{\Delta h_{f.dist}+h_{f.tubing.min}}{\alpha}}
\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\[
Q_{Min}=\sqrt{\frac{h_{f.tubing.avg}}{\alpha}}=\Pi_{RatioAvgMin}\sqrt{\frac{h_{f.tubing.min}}{\alpha}}
\]

\end_inset


\change_deleted 1750459017 1400271778

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399996310
Why is Q.min a funtion of the average head loss? Also this factor of 1.1 shouldn't
 be given as a constant.
 Presumably this factor is related to 
\begin_inset Formula $\Pi_{Q}$
\end_inset

.
 Show that relationship and eliminate 1.1 in all subsequent equations.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
We solved 
\begin_inset Formula $Q_{Avg}$
\end_inset


\change_inserted 194268660 1400294496
 
\change_unchanged
in terms of 
\begin_inset Formula $h_{f.tubing.min}$
\end_inset


\change_inserted 194268660 1400294502
 
\change_unchanged
to minimize the number of variables in our calculations.
 Because we know that 
\begin_inset Formula $Q_{Avg}$
\end_inset


\change_inserted 194268660 1400294510
 
\change_unchanged
should be no more than 10% greater than the minimum, we multiplied the 
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\strikeout off
\uuline off
\uwave off
\noun off
\color none

\begin_inset Formula $Q_{Min}$
\end_inset


\change_inserted 194268660 1400294503
 
\change_unchanged
head loss term by
\change_inserted 194268660 1400294544
 
\change_deleted 1750459017 1400271796
 110% 
\change_inserted 1750459017 1400271818

\begin_inset Formula $\Pi_{RatioAvgMin}$
\end_inset

 
\change_unchanged
to put the 
\begin_inset Formula $Q_{Avg}$
\end_inset


\change_inserted 194268660 1400294508
 
\change_unchanged
term
\family default
\series default
\shape default
\size default
\emph default
\bar default
\strikeout default
\uuline default
\uwave default
\noun default
\color inherit
 in terms of 
\begin_inset Formula $h_{f.tubing.min}$
\end_inset

.
 From this equation, we could solve for our new 
\begin_inset Formula $\Pi_{Q}$
\end_inset


\change_inserted 194268660 1400294553
 
\change_unchanged
equation, illustrated in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:ΠQ for Tubing"

\end_inset

 below.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\Pi_{Q}=\frac{\sqrt{\frac{\Delta h_{f.dist}+h_{f.tubing.min}}{\alpha}}-\sqrt{\frac{h_{f.tubing.min}}{\alpha}}}{\Pi_{RatioAvgMin}\sqrt{\frac{h_{f.tubing.min}}{\alpha}}}=\frac{\sqrt{\Delta h_{f.dist}+h_{f.tubing.min}}-\sqrt{h_{f.tubing.min}}}{\Pi_{RatioAvgMin}\sqrt{h_{f.tubing.min}}}\label{eq:ΠQ for Tubing}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We rearranged this equation and found roots of the following function, Equation
 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:root function"

\end_inset

 (i.e.
 the values of 
\begin_inset Formula $h_{f.tubing.min}$
\end_inset


\change_inserted 194268660 1400294565
 
\change_unchanged
that satisfy the equation).
 
\begin_inset Formula $h_{f.tubing.min}$
\end_inset

 was equated to the requisite head loss, 
\begin_inset Formula $h_{f.tubing}$
\end_inset

, through the tubing at each house.
\change_deleted 194268660 1400175222

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
but did we? Is that the var below? ermagerd, the en uses 
\begin_inset Quotes eld
\end_inset

avg
\begin_inset Quotes erd
\end_inset

 in physics and 
\begin_inset Quotes eld
\end_inset

min
\begin_inset Quotes erd
\end_inset

 in dist fxns.
 
\end_layout

\end_inset

.
\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
F_{h.f.tubing}(h_{f.tubing.min})=\left(\sqrt{h_{LEMax}-h_{LEMin}+h_{f.tubing.min}}-\sqrt{h_{f.tubing.min}}-\Pi_{Q}*\Pi_{RatioAvgMin}\sqrt{h_{f.tubing.min}}\right)\label{eq:root function}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We also derived an equation 
\change_deleted 194268660 1400294609
for determining 
\change_inserted 194268660 1400294611
to determine 
\change_unchanged
the length of tubing necessary to dissipate the average head for each house
 in the system, illustrated in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Tubing length"

\end_inset

.
 This equation is found by rearranging the equation for turbulent head loss.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
L_{Tubing}=\frac{g*h_{f.tubing}^{2}\left(\frac{\pi D_{Tubing}^{2}}{4}\right)^{2}*D_{Tubing}}{f*Q_{Tubing}^{2}}\label{eq:Tubing length}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Once the base length of tubing
\change_deleted 194268660 1400294630
,
\change_unchanged
 was found for each iteration of code, the elevation of each house was used
 to determine
\change_deleted 1750459017 1400271883
 the
\change_inserted 1750459017 1400253427
 the
\change_unchanged
 length of tubing required to normalize the head losses across the houses,
 given the fact that they each have different elevations.
 The following equation
\change_inserted 194268660 1400294678
, 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:L.Additional"

\end_inset

,
\change_unchanged
 was used to determine how much tubing needed to be added or subtracted
 for each house.
 For houses at a lower elevation than that of the transmission pipe when
 it enters the village (
\begin_inset Formula $E_{In}$
\end_inset

), this additional length will be added to the average length of tubing
 required, as these houses have more potential energy due to the elevation
 drop and consequently need more head loss
\change_deleted 194268660 1400294755
es
\change_unchanged
 through the tubing to equalize flow.

\change_inserted 1750459017 1400271915
 
\change_deleted 194268660 1400294707
The e
\change_inserted 194268660 1400294707
E
\change_inserted 1750459017 1400271915
quation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:L.Additional"

\end_inset

 shown below takes the absolute value of the difference in elevation, so
 the value of 
\change_deleted 194268660 1400294721
L.Additional
\change_inserted 194268660 1400294723

\begin_inset Formula $L_{Additional}$
\end_inset


\change_inserted 1750459017 1400271915
 is always positive.
 For houses at a higher elevation than that of the transmission pipe when
 it enters the village, this additional length will be subtracted from the
 average length of tubing required, as these houses have less potential
 energy due to the elevation drop and consequently need more head los
\change_deleted 194268660 1400294749
se
\change_inserted 1750459017 1400271915
s through the tubing to equalize flow.
 
\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
L_{Additional}=\frac{g*\left|Elevation_{House}-Elevation_{In}\right|^{2}*\left(\frac{\pi D_{Tubing}^{2}}{4}\right)^{2}*D_{Tubing}}{f*Q_{Tier3}^{2}}\label{eq:L.Additional}
\end{equation}

\end_inset


\change_deleted 1750459017 1400253582

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399996720
Is this additional length always a postive number? COuldn't it also be negative.
 In that case the equation needs an additional term to get the sign right.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
In previous iterations of the code, a check was conducted using the set
 length of tubing to ensure that each of the household flow rates remained
 within the equity limits, even with the adjustments to the system (i.e.
 addition of tubing length).
 This check was removed in this iteration in the interest of finishing our
 code; however 
\change_deleted 194268660 1400294798
we may reinstate it
\change_inserted 194268660 1400294801
it should be reinstated
\change_unchanged
 in the future.
\end_layout

\begin_layout Subsection*
Solar
\end_layout

\begin_layout Standard
Since our system relies on solar pumps to deliver water to each house, we
 developed an algorithm to calculate the amount of solar power generated
 at a given location each year.
 The algorithm requires the following site-specific inputs: latitude, longitude,
 clearness index values, monthly average temperatures, and monthly average
 solar insolation values.
 In an effort to find accurate weather data for Jharkhand, we used procedures
 for estimating various parameters for major cities in India outlined in
 
\shape italic
Estimation of global radiation using clearness index model for sizing photovolta
ic system
\shape default
 
\begin_inset CommandInset citation
LatexCommand cite
key "RefWorks:290"

\end_inset

, a paper by Umanand Ravinder Kumar at the Indian Institute of Science,
 Bangalore.
 In the report, the monthly average daily solar insolation values (
\begin_inset Formula $\overline{H}$
\end_inset

) and the monthly average clearness index values (
\begin_inset Formula $K{}_{T}$
\end_inset

) for Kolkata were calculated for a year.
 We used these values in our calculations, given Kolkata's close proximity
 to Gufu.
 
\end_layout

\begin_layout Standard
Our algorithm includes several steps summarized below.
 These equations were found in the textbook 
\shape italic
Energy Systems Engineering: Evaluation and Implementation
\shape default
 by Vanek, Albright, and Angenent.
 
\end_layout

\begin_layout Standard
The declination angle, calculated in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Declination Angle"

\end_inset

, is the angle at which sunlight hits the surface of the earth, and depends
 on the Julian day and latitude.

\change_deleted 2090522031 1399986142
 
\change_unchanged
 This is used to find out how many hours of sunlight a given location receives
 each day, which determines how much energy is received.
 
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
D_{\delta}=23.45\sin\left[360\frac{\left(284+N_{JD}\right)}{365}\frac{\pi}{180}\right]\label{eq: Declination Angle}
\end{equation}

\end_inset


\change_deleted 194268660 1400175323

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
Did you mean 
\begin_inset Formula $\Pi$
\end_inset

or 
\begin_inset Formula $\pi$
\end_inset

in the previous equation?
\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
The daily solar insolation, from Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Daily Solar Insolation"

\end_inset

, is the the amount of solar power that hits the earth each day and is found
 using the clearness index and the monthly daily average global insolation.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
H_{d}=\overrightarrow{\left[\overline{H}\left(1.39-4.03K_{T}+5.53K_{T}^{2}-3.11K_{T}^{3}\right)\right]}\label{eq: Daily Solar Insolation}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
The solar insolation ratio, in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Solar Insolation Ratio"

\end_inset

, relates the amount of sun power that hits a horizontal surface to the
 amount that hits a tilted surface.
 This ratio is later used in Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Monthly Average Solar Insolation on a Tilted Surface"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Formula $S_{M}$
\end_inset

 is the optimum panel tilt angle that will yield the most energy.
 Each month has an average optimum tilt.
 We decided to tilt the panels at the optimum angle for August, as this
 month receives the least amount of sunlight on average
\change_inserted 1750459017 1400272429
 and we want to optimize the 
\change_deleted 194268660 1400294907
amount of sunlight when there is the least sun.
 
\change_inserted 194268660 1400294920
system for the month that receives the least sunlight.
\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
R_{r}=\overrightarrow{\left[\left(1-\frac{H_{d}}{\overline{H}}\right)R_{Bbeta}\right]}+\overrightarrow{\left[\frac{H_{d}}{2\overline{H}}\right]\left(1+\cos\left(S_{M}\right)\right)}+\overrightarrow{\frac{\left[\rho_{Ref}\left(1-\cos\left(S_{M}\right)\right)\right]}{2}}\label{eq: Solar Insolation Ratio}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
H_{t}=\overrightarrow{\left(\overline{H}*R_{r}\right)}\label{eq: Monthly Average Solar Insolation on a Tilted Surface}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Next, using characteristics of the solar panels such as the temperature
 coefficient and the heat loss coefficient, we were able to find the total
 solar panel efficiency using Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Efficiency Equation"

\end_inset

.
 We then calculated the monthly average power generated per square meter
 of solar panel, using Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Total Power Output"

\end_inset

.
 
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\eta=\eta_{r}\left[\left(1-\beta(T_{C}-T_{A}\right)-\beta(T_{A}-T_{M})-\beta(T_{M}-T_{F})\right]\label{eq: Efficiency Equation}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
ActualOutput=\overrightarrow{\mbox{\ensuremath{\left(H_{t}*\eta*deratingfactor\right)}}}\label{eq: Total Power Output}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We used the lowest monthly actual power output as
\change_deleted 194268660 1400294966
 our
\change_inserted 194268660 1400294968
 the
\change_unchanged
 design power
\change_inserted 1750459017 1400272054
 for our algorithm
\change_unchanged
.
 This ensures the system will successfully pump water as often as possible.
 
\change_inserted 1750459017 1400272257
This assumption does not incorporate any variability 
\change_deleted 194268660 1400294988
within 
\change_inserted 194268660 1400294990
from the 
\change_inserted 1750459017 1400272257
weather data; this is 
\change_deleted 194268660 1400285275
incoporated
\change_inserted 194268660 1400285275
incorporated
\change_inserted 1750459017 1400272257
 after the algorithm below has determined system parameters.
 We used the hourly actual power output data to determine the 
\begin_inset Formula $\Pi_{SunHours}$
\end_inset

 term used above to calculate the house target flow rate.
 This was done by taking a conservative estimate of the number of hours
 per day during which there is 
\change_inserted 194268660 1400295029
sufficient 
\change_inserted 1750459017 1400272257
sunlight to power the pump.
\change_inserted 2090522031 1399996842

\end_layout

\begin_layout Standard
We
\change_deleted 2090522031 1399986142
 
\change_unchanged
 accounted for inefficiencies in the pump by fitting several curves to data
 points from
\change_inserted 194268660 1400285281
 
\change_unchanged
Grundfos pump specifications
\change_deleted 194268660 1400295047
,
\change_unchanged
 
\begin_inset CommandInset citation
LatexCommand cite
key "RefWorks:312"

\end_inset

.
 This allowed us to create a function that defines efficiency based on incoming
 solar power.
 These curves can be seen in
\change_inserted 194268660 1400295066
 Figure
\change_unchanged
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Fitting-Efficiency-Curves"

\end_inset

.

\change_deleted 2090522031 1399986142
 
\change_unchanged
 We then used the design power, the efficiency function, and the desired
 pump head from the previous section to select
\change_deleted 2090522031 1399986142
 
\change_unchanged
 an optimum pump and number of solar panels.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/Efficiency Curves.png
	lyxscale 50
	scale 70

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset

 
\begin_inset Caption

\begin_layout Plain Layout
Fitting Efficiency Curves
\begin_inset CommandInset label
LatexCommand label
name "fig:Fitting-Efficiency-Curves"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
These efficiency curves were fit to data points from Grundfos pump specification
s.
 They were used to find the pump efficiency based on incoming panel wattage.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Figure
\change_deleted 194268660 1400284592
 
\change_unchanged
 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:Grundfos-Pump-Costs-"

\end_inset


\change_inserted 194268660 1400295105
 
\change_unchanged
shows the pump curves we input into our code.
 The optimal pump is then selected to ensure equity and minimize cost.
 
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="9" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
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<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pump Model
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pump Power (hp)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pump Head Range (m)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pump Cost (USD)
\end_layout

\end_inset
</cell>
</row>
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<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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3.96 - 7.01
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\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Grundfos Pump Costs
\begin_inset CommandInset label
LatexCommand label
name "tab:Grundfos-Pump-Costs-"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection*
Overall Algorithm
\change_inserted 2090522031 1399997515

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399997526
Consider putting the flow chart that you created here.
\change_unchanged

\end_layout

\end_inset


\change_inserted 194268660 1400182522

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400182525
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400183166
\begin_inset Graphics
	filename images/Algorithm Map Part 1.PNG
	scale 70

\end_inset


\change_unchanged

\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400182525
\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 194268660 1400182845
Algorithm Map Part 1
\begin_inset CommandInset label
LatexCommand label
name "fig:Algorithm-Map-Part1"

\end_inset


\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400295491
A diagram of the basic design algorithm steps.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400295143
A diagram of our algorithm can be seen in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Algorithm-Map-Part1"

\end_inset

.
 
\change_inserted 1750459017 1400270895
This algorithm is designed to optimize two factors, cost and equity.
 Equity is forced during the first stages of the code (head loss through
 tubing required to ensure equity is found based on our equity constraint).
 Throughout the rest of the code, design parameters are chosen to maintain
 this equity and minimize cost.
 This primarily involves 
\change_deleted 194268660 1400295182
pitting
\change_inserted 194268660 1400295185
weighing
\change_inserted 1750459017 1400270895
 solar cost against cost of PVC piping.
 Larger PVC pipes cost more, however they also have significantly less head
 loss and consequently require less initial pumping head (equating to fewer
 solar PV panels and a smaller pump).
 These two factors are 
\change_deleted 194268660 1400295234
iterated against each other 
\change_inserted 194268660 1400295240
varied in each iteration of code 
\change_inserted 1750459017 1400270895
until a system with the lowest cost is found.
 This trade
\change_deleted 194268660 1400295243
 
\change_inserted 1750459017 1400270895
off between pump/PV and PVC is seen in both the overarching code, and the
 transmission section of the code nested within the main code.
\end_layout

\begin_layout Standard
The basic structure of our code is as follows: 
\end_layout

\begin_layout Enumerate
Head loss per length values are found for all possible diameters for each
 tier, given the estimated
\change_inserted 1750459017 1400253650
 average
\change_unchanged
 
\change_inserted 1750459017 1400253782
maximum 
\change_unchanged
flow that each tier will carry.
 Tier 3, which carries water to each house, will carry an average 
\change_inserted 1750459017 1400253788
maximum 
\change_unchanged
flow of 
\begin_inset Formula $Q_{TargetHouse}$
\end_inset

.
 The estimated flows for the other tiers are found by summing the number
 of Tier 3 pipes that each tier services and
\change_deleted 194268660 1400295322
 then
\change_unchanged
 multiplying that number by 
\begin_inset Formula $Q_{TargetHouse}$
\end_inset

.
 
\change_inserted 1750459017 1400253658

\end_layout

\begin_deeper
\begin_layout Enumerate

\change_inserted 1750459017 1400254128
This average maximum flow rate is then used to determine the maximum major
 losses (
\change_deleted 194268660 1400295336
HL.Max
\change_inserted 194268660 1400295338

\begin_inset Formula $H_{LMax}$
\end_inset


\change_inserted 1750459017 1400254128
) for this flow for all possible diameter sizes.
 An average 
\change_deleted 194268660 1400295357
HL
\change_inserted 194268660 1400295357

\begin_inset Formula $H_{L}$
\end_inset


\change_inserted 1750459017 1400254128
 is then estimated for each possible pipe diameter to be 1/3 of this 
\change_deleted 194268660 1400295361
HL.Max
\change_inserted 194268660 1400295361

\begin_inset Formula $H_{LMax}$
\end_inset


\change_inserted 1750459017 1400254128
 for each tier.
 This rough estimate is used in this case because each tier
\change_inserted 194268660 1400295421
 loses energy
\change_deleted 194268660 1400295417
,
\change_inserted 1750459017 1400254128
 as it carries water through the distribution system
\change_deleted 194268660 1400295440
, loses energy, which should be accounted for in this calculation.
\change_inserted 194268660 1400295440
.
\change_inserted 1750459017 1400254128

\end_layout

\end_deeper
\begin_layout Enumerate
A threshold for maximum diameter is set based on the point where head loss
 values become negligible (i.e.
 
\change_inserted 1750459017 1400254047
the diameter of the Tier 1 pipe for which 
\change_deleted 1750459017 1400254039
when 
\change_unchanged
values for head loss per length are below 0.001)
\change_inserted 1750459017 1400254110
.
 The Tier 1 pipe is used to set this limit because the Tier 1 pipe will
 always be carrying the most flow of all the tiers (and consequently will
 have the largest head loss).
\change_unchanged

\end_layout

\begin_layout Enumerate
Possible combinations of pipe size and tubing are determined by eliminating
 pipe combinations for which no connector exists and eliminating pipes that
 are above the aforementioned maximum diameter threshold.
 Tees are used to connect pipes to each other and adapters are used to connect
 pipes to tubing.
 
\change_deleted 1750459017 1400254177
The maximum diameter threshold determined from the above calculation is
 used to set an additional limit on the combinations
\change_deleted 194268660 1400295535
.
 
\change_unchanged
Possible connections are compiled into a matrix that serves as an input
 to the main code.
\end_layout

\begin_layout Enumerate
Major losses throughout the distribution system are found for each house
 for each possible combination of pipes and tubing, using the head loss
 per length values found in step 1.
 Each house has a given length of pipe leading up to it; when the estimated
 head loss per length values 
\change_deleted 1750459017 1400254213
described in step 1 
\change_inserted 1750459017 1400254207
for the given diameter chosen in the iteration 
\change_unchanged
are multiplied by the length of pipe leading up to each house, an estimate
 of the head loss for each house can be found.
\end_layout

\begin_layout Enumerate
The calculated head losses are used in conjunction with the head loss through
 tubing equation shown above to determine the average head loss required
 through the tubing to maintain equity.

\change_inserted 1750459017 1400254312
 The entire explanation of this process can be found above.
\change_unchanged

\end_layout

\begin_layout Enumerate
This average head loss required through the tubing is then used to determine
 the average length of tubing required to dissipate this requisite head.
\end_layout

\begin_layout Enumerate
The additional length required for each house given the elevation variations
 within the village, 
\begin_inset Formula $L_{additional}$
\end_inset

, is then determined and added to or subtracted
\change_deleted 1750459017 1400254263

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399997483
equation is written is always positive.
\change_unchanged

\end_layout

\end_inset

 
\change_unchanged
from the initial length of tubing to find the tubing length required for
 each house.
\end_layout

\begin_layout Enumerate
The head required to push water through the system and maintain equity is
 then found by adding the requisite head loss through the tubing to the
 maximum head loss throughout the distribution system.
 This 
\begin_inset Quotes eld
\end_inset

equity head
\begin_inset Quotes erd
\end_inset

 is essentially the amount of additional input head required to ensure that
 each house throughout the system receives equitable flow.
\end_layout

\begin_layout Enumerate
The following steps occur as their own mini
\change_inserted 1750459017 1400254352
 
\change_deleted 1750459017 1400254352
-
\change_unchanged
iteration within the code.
 These steps determine the transmission line diameter and the corresponding
 pump and number of solar panels required for the 
\change_deleted 194268660 1400295657
given 
\change_unchanged
diameter chosen.
 The code starts by setting the diameter of the transmission pipe equal
 to the diameter of the Tier 3 pipe from the current iteration.
 It then 
\change_deleted 194268660 1400295685
follows
\change_inserted 194268660 1400295682
proceeds through 
\change_deleted 194268660 1400295678
 
\change_unchanged
the following steps for each increasing size of pipe diameter.
 Once these iterations are complete, the code picks the lowest cost option.

\change_inserted 1750459017 1400255625
 One change to implement in the system would be to allow for a "sliding
 centrifugal pump
\change_inserted 194268660 1400295704
.
\change_inserted 1750459017 1400255625
"
\change_deleted 194268660 1400295703
.

\change_inserted 1750459017 1400255625
 This means that the centrifugal pump could be located at any point along
 the length of the transmission line.
 The centrifugal pump would be required to pump water through the length
 of transmission pipe located after it
\change_inserted 194268660 1400295727
,
\change_inserted 1750459017 1400255625
 and a submerged pump located at the well would be required to pump water
 up from the well and through the length of transmission pipe leading to
 the centrifugal pump.
\change_unchanged

\end_layout

\begin_deeper
\begin_layout Enumerate
A pump and number of solar panels are chosen based on the pump head required
 to ensure equity and the total flow rate for the system.
 A series of pumps, with their pumping head capacities and costs, are sorted
 through to find an adequate pump, given input values.
 An associated cost is then found for the PVC pipe chosen.
\change_deleted 2090522031 1399997551
.
\change_unchanged

\end_layout

\begin_layout Enumerate
The solar wattage required to power the chosen pump is then found by using
 a series of pump efficiency curves that are shown above
\change_deleted 2090522031 1399986142
 
\change_unchanged
 in Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Fitting-Efficiency-Curves"

\end_inset


\change_deleted 194268660 1400295776
 
\change_unchanged
.
 Given this requisite solar power input, the number of PV panels required
 for the system is then chosen.
\change_inserted 2090522031 1399999696

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399999741
There isn't any step where you check the performance given variability of
 sunshine.
 Yet your design seems to have taken that into account.
 Add that step and explain how it was accomplished.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Enumerate
The cost of PVC, cost of the pump, and cost of PV panels are summed to find
 the total cost for
\change_inserted 2090522031 1399997570
 
\change_unchanged
this iteration of the code.
\change_inserted 1750459017 1400254416

\end_layout

\end_deeper
\begin_layout Enumerate
The cost of the distribution system can be found with equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Village System Cost"

\end_inset

, which uses the length and cost of each tier of pipe and the tees or adapters
 selected by the code.
\end_layout

\begin_layout Enumerate
The code outputs the optimal (minimum cost) solution, given the possible
 pipe, pump, and panel requirements
\begin_inset Formula 
\begin{equation}
Cost_{tiers}=\begin{cases}
L_{Tier1*}Cost_{Pipes\left(ind_{Ex_{0}}\right)}\\
L_{Tier2}*Cost_{Pipes\left(ind_{Ex_{1}}\right)}+\sum Nodes_{Tier1}*Tees_{ind_{Ex_{1}},ind_{Ex_{2}}}\\
\sum\overrightarrow{L_{Tiers}^{<2>}}*Cost_{Pipes\left(ind_{Ex_{2}}\right)}+\sum Nodes_{Tier2}*Tees_{ind_{Ex_{1}},ind_{Ex_{2}}}\\
L_{Tubing}*Cost_{Tubing\left(ind_{Ex_{2}}\right)}+\sum Nodes_{Tier2}Adapters_{ind_{Ex_{2}},ind_{Ex_{3}}}
\end{cases}\label{eq:Village System Cost}
\end{equation}

\end_inset


\change_inserted 1750459017 1400254508

\end_layout

\begin_layout Enumerate

\change_inserted 1750459017 1400270946
A separate step f
\change_inserted 194268660 1400295821
rom
\change_deleted 194268660 1400295819
orm
\change_inserted 1750459017 1400270946
 this code, discussed in detail in the 
\begin_inset Quotes eld
\end_inset

Variability Check
\begin_inset Quotes erd
\end_inset

 section of this document, takes this system design and weather data from
 India and determines how often our system provides adequate water to villagers.
\change_unchanged

\end_layout

\begin_layout Section*
Results and Analysis 
\end_layout

\begin_layout Standard
This system is designed to ensure equitable flow, where all houses receive
 a flow within 10% of the average, which places stringent constraints on
 our system design.
 Maintaining this level of equity requires a costly system, mainly due to
 the 
\change_inserted 1750459017 1400273067
relatively 
\change_unchanged
long length of tubing required at each house to ensure significant head
 is dissipated.

\change_inserted 194268660 1400285297
 The tubing size is limited by the availability of tubing adapters.
 
\change_deleted 194268660 1400175643

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399997642
Why can't you use smaller diameter tubing? I'd propose that no tubing should
 be longer than a few meters.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
After 
\change_deleted 194268660 1400175445
modifying
\change_inserted 194268660 1400175447
running
\change_unchanged
 the distribution code, we determined 
\change_deleted 194268660 1400295871
the total flow
\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399997809
Under what conditions? What does 
\begin_inset Quotes eld
\end_inset

total
\begin_inset Quotes erd
\end_inset

 mean? The flow rate varies widely.
 
\change_unchanged

\end_layout

\end_inset

 to all houses and 
\change_unchanged
the
\change_inserted 194268660 1400295876
 total
\change_unchanged
 cost of the village distribution system.
 The 
\change_deleted 194268660 1400175472
total flow is
\change_deleted 2090522031 1399986142
 
\change_deleted 194268660 1400295995
 
\begin_inset Formula $\unitfrac[0.84]{L}{s}$
\end_inset

 and the 
\change_unchanged
cost is shown in 
\change_deleted 194268660 1400295900
t
\change_inserted 194268660 1400295900
T
\change_unchanged
able 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:Cost-Summary"

\end_inset

.
 The total cost of the village distribution system with our current input
 parameters is 
\begin_inset Formula $\$27,220$
\end_inset

 and the full system design can be seen in
\change_inserted 194268660 1400295916
 Table
\change_unchanged
 
\begin_inset CommandInset ref
LatexCommand ref
reference "tab:Optimal-System-Values"

\end_inset

.
\change_deleted 194268660 1400175485
.
\change_inserted 194268660 1400295934

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400295934
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
Component
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
Cost (USD)
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
PVC Pipe
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
$6,953.00
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
PV Panels
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
$18,800.00
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
Pump
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
$1,384.00
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
Total
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
$27,140.00
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400295934


\backslash
centering
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 194268660 1400295934
Cost Summary
\begin_inset CommandInset label
LatexCommand label
name "tab:Cost-Summary"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard

\change_deleted 194268660 1400284684
 
\change_unchanged

\begin_inset Float table
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Tabular
<lyxtabular version="3" rows="10" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0">
<column alignment="center" valignment="top" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Tubing Diameter (in)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.25
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Tier 3 Diameter (in)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.5
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Tier 2 Diameter (in)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
0.75
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Tier 1 Diameter (in)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.0
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Transmission Pipe Diameter (in)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
2.0
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Total Tubing Length (m)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
540
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Optimal Number of Solar Panels
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
11
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Optimal Pump Power (hp)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.5
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pump Head (m)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
16.2
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Equity Head (m)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
1.9
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
centering
\end_layout

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Optimal System Values
\begin_inset CommandInset label
LatexCommand label
name "tab:Optimal-System-Values"

\end_inset


\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard

\change_inserted 2090522031 1399998776
\begin_inset Note Note
status open

\begin_layout Plain Layout

\change_inserted 2090522031 1399999930
Can you show using a graph or some other method the tradeoff that you are
 making between PVC and PV? Where is the majority of the head loss in the
 system? What happens if you increase that pipe size.
\end_layout

\begin_layout Plain Layout

\change_inserted 2090522031 1399999959
Also isn't there a separate decision making process to choose the diameter
 of the transmission line from the well to the village?
\end_layout

\begin_layout Plain Layout

\change_inserted 2090522031 1399998971
Your report needs an image of overall system design.
 I didn't see any mention of the fact that you sre using two pumps, one
 in the well and one to lift water from the treatment plant to the village.
 
\change_unchanged

\end_layout

\end_inset


\change_inserted 270189200 1400201385

\end_layout

\begin_layout Standard

\change_inserted 270189200 1400201610
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout

\change_inserted 270189200 1400201465
\begin_inset Graphics
	filename images/Cost Graph.PNG
	scale 80

\end_inset


\change_unchanged

\end_layout

\begin_layout Plain Layout

\change_deleted 194268660 1400284905
With each iteration of pipe sizes the cost of the system varies.

\change_inserted 270189200 1400201517
 
\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 270189200 1400201415
Cost Optimization Analysis
\begin_inset CommandInset label
LatexCommand label
name "fig:Cost-Optimization-Analysis"

\end_inset


\change_unchanged

\end_layout

\end_inset


\change_inserted 194268660 1400284910

\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400285304
Illustration of how system cost varies with each iteration of pipe size.
 
\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Standard

\change_inserted 270189200 1400201944
Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Cost-Optimization-Analysis"

\end_inset

 shows how the cost of each component varies with each iteration of pipe
 sizes.
 The pump cost is a step function because there are a set number of pumps
 inputted.
 Because the number of solar panels i
\change_inserted 194268660 1400296071
s
\change_deleted 194268660 1400296071
n
\change_inserted 270189200 1400201944
 determined by the pump chosen, this causes the PV
\change_inserted 1750459017 1400273170
 
\change_inserted 270189200 1400201944
cost to be step function as well.
 The cost functions are ultimately limited by the 
\change_deleted 194268660 1400285489
availibility
\change_inserted 194268660 1400285489
availability
\change_inserted 270189200 1400201944
 of pipe sizes and adapters.

\change_inserted 1750459017 1400273230
 This 
\change_deleted 194268660 1400285492
greaph
\change_inserted 194268660 1400285492
graph
\change_inserted 1750459017 1400273230
 
\change_deleted 194268660 1400285495
demonstates
\change_inserted 194268660 1400285495
demonstrates
\change_inserted 1750459017 1400273230
 the slight tradeoff between PVC and PV/pump costs; as the PVC costs increase,
 the PV/pump costs decrease.

\change_deleted 1750459017 1400273176
 
\change_unchanged

\end_layout

\begin_layout Subsection*
Variability Check 
\change_inserted 194268660 1400183446

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400183448
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400284964
\begin_inset Graphics
	filename images/Algorithm Map Part 2.PNG
	scale 70

\end_inset


\begin_inset ERT
status open

\begin_layout Plain Layout

\change_inserted 194268660 1400284966


\backslash
centering
\change_unchanged

\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400284959
\begin_inset Caption

\begin_layout Plain Layout

\change_inserted 194268660 1400183465
Algorithm Map Part 2 
\begin_inset CommandInset label
LatexCommand label
name "fig:Algorithm-Map-Part2"

\end_inset


\change_unchanged

\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\change_inserted 194268660 1400284959
A diagram of the steps carried out in the variability check.
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
Our design is based off average weather data but we wanted to see how our
 system would perform under realistic conditions.
 
\change_inserted 194268660 1400296108
The steps we carried out to check this performance can be seen in Figure
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Algorithm-Map-Part2"

\end_inset

.
 
\change_unchanged
We used hourly weather data to create a simulation to test our design.
 Using the information and studies provided by the National Renewable Energy
 Laboratory (NREL) of India 
\begin_inset CommandInset citation
LatexCommand cite
key "RefWorks:299"

\end_inset

, we obtained an Excel spreadsheet with daily hourly average horizontal
 global irradiance, temperature, and the day and hour in which the data
 was collected.
 The website claims to use the “The SUNY model [to produce] estimates of
 global and direct irradiance at hourly intervals on the 10-km grid for
 all of India, as shown on the India solar maps.” We extracted the information
 into a matrix in Mathcad and wrote functions to convert the data into a
 more usable format.
 The date values were converted to Julian days, the hourly global insolation
 values were summed to get the total daily global insolation, and the hourly
 temperatures were averaged to get daily temperatures.
 
\end_layout

\begin_layout Standard
The daily global insolation values can be seen in
\change_inserted 194268660 1400296209
 Figure
\change_unchanged
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Daily-Global-Insolation"

\end_inset

.
 Although the insolation is higher in the summer, there is also significantly
 more variability.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/Daily Insolation Plot.PNG
	scale 50

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Daily Global Insolation
\begin_inset CommandInset label
LatexCommand label
name "fig:Daily-Global-Insolation"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
The daily global insolation varies significantly on a daily basis and throughout
 the year.
\end_layout

\end_inset

This real hourly data will be used to test the variability of our distribution
 system by determining how much water will be pumped on any given day.
 We converted the hourly global insolation values to insolation on a tilted
 surface values using Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Solar Insolation Ratio"

\end_inset

 and then found the hourly flow rate using
\change_inserted 194268660 1400296245
 Equation
\change_unchanged
 
\change_inserted 194268660 1400184705

\begin_inset CommandInset ref
LatexCommand ref
reference "eq: Flow rate from panel power"

\end_inset

 and 
\change_unchanged
the chosen pump and the efficiency function described above.
\change_inserted 194268660 1400184469

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400184472
\begin_inset Formula 
\begin{equation}
Q=\frac{P\epsilon}{h\rho g}\label{eq: Flow rate from panel power}
\end{equation}

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard

\change_inserted 194268660 1400184136
Using the hourly flow rate, 
\change_deleted 194268660 1400184137
W
\change_inserted 194268660 1400184137
w
\change_unchanged
e calculated the total volume of water pumped each day
\change_deleted 194268660 1400184709

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399998239
explain how you calculated the amount of water pumped.
 I don't understand you your design steps led to such high performance.
 How did your design based on average values end up producing such a high
 water supply ratio?
\change_unchanged

\end_layout

\end_inset


\change_unchanged
 and compared this value to the village's demand to quantify how many days
 sufficient water will be provided.
 The resulting ratio of water supplied to water required is shown in Figure
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Water-Ratio"

\end_inset

.
 For each day the graph falls below a ratio of one, the village does not
 receive enough water.
 We also wrote a function that counts the number of consecutive days this
 occurs.
 With our final design, there are at most three days in a row without sufficient
 water supplied and this only occurred twice during the year.
 We believe this system would be feasible if it incorporated
\change_deleted 194268660 1400296293
 a
\change_unchanged
 large enough 
\change_inserted 194268660 1400184013
household 
\change_unchanged
storage tank
\change_inserted 194268660 1400296357
s that could hold a three-day supply of water for each family.
 These could be filled on days when a surplus of water is pumped and emptied
 when insufficient water is pumped
\change_unchanged
.
\change_deleted 194268660 1400184042

\begin_inset Note Note
status collapsed

\begin_layout Plain Layout

\change_inserted 2090522031 1399998730
Clarify.
 Are you proposing an even larger overhead storage tank than the current
 design or are you proposing larger storage tanks at the household level?
\change_unchanged

\end_layout

\end_inset


\change_unchanged

\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename images/Supply Ratio.PNG

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Water Ratio
\begin_inset CommandInset label
LatexCommand label
name "fig:Water-Ratio"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout
Using this variability simulation, we can adjust our final design to meet
 the needs of the village.
 
\end_layout

\end_inset


\end_layout

\begin_layout Section*
Future Work
\end_layout

\begin_layout Standard
In future semesters, we hope to improve our code by accounting for flow
 type variability.
 We currently assume flow is turbulent, but this may not always be the case.
 We also want to find more accurate pump efficiencies.
 The current efficiency functions are from different pumps than those currently
 used in India.
 Finally, we would like to make our code more user-friendly by minimizing
 and simplifying the inputs.
 
\end_layout

\begin_layout Standard
Furthermore, the simulation could be improved with data from multiple years.
 Future teams should look into other data sources to improve the simulation's
 accuracy.
 
\end_layout

\begin_layout Standard
Other useful research areas include the 
\change_inserted 194268660 1400296405
sizing and 
\change_unchanged
implementation of a storage tank, the design of household infrastructure,
 and options for handling human waste.
 
\end_layout

\begin_layout Standard
\begin_inset CommandInset bibtex
LatexCommand bibtex
bibfiles "Reents,kumar,solar data,VanPelt,sunpumps"
options "plain"

\end_inset


\end_layout

\end_body
\end_document
