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\begin_body

\begin_layout Title
Turbidimeter
\end_layout

\begin_layout Abstract
AguaClara needs a reliable and simple method for candidate communities to
 monitor the turbidity of their water supply.
 Portable turbidimeters cost $400 or more and thus are too expensive to
 provide to a large number of candidate communities.
 The goals of providing candidate communities with turbidimeters is to determine
 the source water turbidity range and hence the type of water treatment
 that will be required.
 For example, if the source water turbidity never exceeds 10 NTU, then it
 may not be necessary to provide flocculation and sedimentation.
 The turbidimeter should be very inexpensive (less than $20).
 It should have an error of less than 50%.
 One possible approach is to use a Jackson style turbidimeter (a long tube
 that you fill with water until you can't see the candle below the end of
 the tube).
 Instead of a candle you could use a waterproof LED in the bottom of a PVC
 pipe.
 Preliminary tests with a submersible LED display during the spring of 2011
 were very promising.
 
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
students 3 FT
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\begin_layout Labeling
\labelwidthstring 00.00.0000
skills some fabrication and experimentation
\end_layout

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
Additional experiments can be done using the same test apparatus as was
 used during the spring of 2011 (Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Test-apparatus-schematic"

\end_inset

).
\end_layout

\begin_layout Itemize
Determine the effect of particle aggregation on turbidity measurements.
 Reduce particle aggregation by adding 2 mg of humic acid per 100 mg of
 clay.
 Prepare a stock solution that contains both humic acid and clay and add
 it incrementally to the suspension in the test apparatus to obtain turbidity
 as a function of optical resolution depth (Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Test-apparatus-schematic"

\end_inset

).
 Compare with the results for clay (Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Turbidity graph"

\end_inset

).
 Determine if the addition of humic acid causes a significant change in
 response of the AguaClara turbidimeter.
 If the AguaClara turbidimeter is very sensitive to 
\end_layout

\begin_layout Itemize
Test fine rectangular grid patterns rather than words on the LED display
\end_layout

\begin_layout Itemize
Determine the influence of line thickness and line spacing on the LED display
\end_layout

\begin_layout Itemize
Determine which pattern (line thickness and line spacing) would be best
 for measuring low turbidities.
\end_layout

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

\begin_layout Plain Layout
\begin_inset Graphics
	filename turbidity test apparatus schematic.png

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Test-apparatus-schematic"

\end_inset

Test apparatus used to simultaneously measure the turbidity using an online
 meter and using the AguaClara turbidimeter.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\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 turbiditygraph.emf
	width 10cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

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

\end_inset

Turbidity as a function of the depth at which fine text can be resolved.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Resolution Depth Analysis
\end_layout

\begin_layout Standard
The equations describing the resolution depth as a function of turbidity
 are given below.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
Turbidity\left(Depth\left(m\right)\right)=\frac{b\cdot NTU}{\left(\frac{Depth}{m}\right)^{\frac{7}{4}}}\label{eq:NTU(depth)}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
where 
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\begin_inset Formula $b$
\end_inset

 is a coefficient from the curve fit equal to 2.14.
 
\end_layout

\begin_layout Standard
Equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:NTU(depth)"

\end_inset

 can be solved for the depth as a function of turbidity to create a turbidity
 scale.
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
Depth(Turbidity)=\left(\frac{b*NTU}{Turbidity}\right)^{\frac{4}{7}}m\label{eq:Turbidity model}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
The simplest model for loss of resolution is that the photons originating
 from the display are blocked by clay.
 It is possible to estimate the blocking effect of the clay particles.
 The density of clay is
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\rho_{Clay}=2650\frac{kg}{m^{3}}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
The number of clay particles in an optical path is
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
N_{Clay}=\frac{C_{Clay}}{\rho_{Clay}}\frac{A_{Clay}}{V_{Clay}}L_{Path}\label{eq:N.Clay(A/V)}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
For a sphere the ratio of area to volume is 
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\frac{A_{Clay}}{V_{Clay}}=\frac{2}{3}d
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Substituting into equation 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:N.Clay(A/V)"

\end_inset

 we obtain
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
N_{Clay}=\frac{2}{3}d\frac{C_{Clay}}{\rho_{Clay}}L_{Path}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
The number of clay particles in the optical path between the observer and
 the display pattern is calculated based on the turbidity model (equation
 
\begin_inset CommandInset ref
LatexCommand ref
reference "eq:Turbidity model"

\end_inset

).
 The number of clay particles is a function of the diameter of the particles.
 For an assumed diameter of 2 
\begin_inset Formula $\mu m$
\end_inset

 the number of clay particles in the optical path approaches 1 for low turbidity
 samples.
 It seems logical that the display pattern would be obscured when there
 is on average one clay particle in the optical path.
 It is less clear why it is necessary to have multiple particles in the
 optical path when the turbidity is higher.
 One possibility is that the clay particles aggregate at higher turbidities
 and thus the number of aggregates in the optical path may be approaching
 1 at the measured optical resolution depth.
 If particle aggregation is influencing the results, then further study
 is warranted to assess the influence of particle size and particle aggregation
 on the turbidity measurements made with the AguaClara turbidimeter.
\end_layout

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

\begin_layout Plain Layout
\begin_inset Graphics
	filename Nclay in optical path.emf
	width 10cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Clay in path"

\end_inset

Number of clay particles in the optical path given a path length equal to
 the resolution depth.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Fabrication
\end_layout

\begin_layout Standard
We would like to send 10 turbidimeter prototypes to Honduras for field testing
 on July 28.
 Development of these prototypes should be done simultaneously with other
 laboratory testing of the turbidimeter to ensure that the 10 turbidimeters
 are ready for deliver on July 28.
 Prior to use in Honduras, a waterproof scale will be need to be calibrated
 and labeled at regular intervals with turbidity measurements rather than
 depth measurements.
 This eliminates the need for the operator to perform a conversion from
 depth to turbidity each measurement, reducing this potential source of
 error.
\end_layout

\begin_layout Standard
The PVC pipe columns can be assembled in Honduras.
 The specifications for those tubes should be provided by the Turbidimeter
 team.
\end_layout

\end_body
\end_document
