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[!Non Linear Doser Diagram.JPG|width=320px!|Illustration of Non- Linear Doser]
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h3. Introduction

The non-linear dose controller was redesigned in order to reduce the amount of aeration caused as water traveled through the plant.  For more information about the theory of the non-linear dose controller see the page for the [original non-linear CDC design|Nonlinear Chemical Dose Controller].

h3. Methods


h4. Sizing the Orifice

The orifice between the rapid mix and floculation tanks is designed to produce a difference in water level high that can then be sensed by a float which would then change the flow rate of aluminum sulfate :
{latex}$$
h_l  = K_{DoseOrifice} {{V_{DoseTube}^2 } \over {2g}}
$${latex}
where
* h ~l~ the difference in head loss between the maximum CDC head loss and the actual head loss in the flexible dosing tube
* K ~DoseOrifice~ is the required minor loss coefficient through the orifice
* V ~DoseTube~ is the velocity in the dosing tube

This head was then used to determine the velocity of the water through the orifice and the residence time.  Using the following equations:
•	{latex}
\large
•	% MathType!Translator!2!1!Plain TeX.tdl!TeX -- Plain TeX!
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•	% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
•	% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
•	% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
•	% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2
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•	% caWGMbGaamyAaiaadogacaWGLbaabeaakiaadgeaaaaaaa!3FF6!
•	$$
•	V = {Q \over {K_{Orfice} A}}
•	$$
•	% MathType!End!2!1!
{latex}


Residence time :

•	{latex}
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•	% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
•	% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
•	% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9
•	% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x
•	% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdeNaey
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•	% dMgacaWGJbGaamyzaaqabaaakeaacaWGwbaaaaaa!4029!
•	\[
•	\theta  = \frac{{d_{Orfice} }}{V}
•	\]
•	% MathType!End!2!1!
{latex}


Once these values were determined, we were able to calculate the energy dissipation rate using the following equation.

We sought  to keep the energy dissipation between .5 and 1 W/kg.

h4. Lever Arm and Float

We first must determine the size of the counterweight on the doser arm in order to ensure that the dosage will only be a function of the difference in water height in the flocculation and rapid mix tanks. The mass of the weight is calculated by determining the mass of the doser when full.

\]

where D.actual is the difference between the given diameter of the dosing tube and the measured diameter of the dosing tube

The size of the float can be determined using a moment balance around the pivot of the lever arm. This is to ensure that a change in head in the entrance tank will cause a similar change in the relative height of the float. The float was sized using the same float sizing algorithm used by the linear CDC.  Based on this we found that a float of 13.3 inches would theoretically be able to measure a .25cm height difference.

h3. Conclusion

Based on our calculations, we found that an orifice of 8cm would give us an acceptable energy dissipation rate of .927 W/kg and would require a 13.3in float.  This float would have a .25cm sensitivity over a 20.3cm height difference.