Non-Linear Doser SU 2009

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. (How was it designed? What were important components?)

Methods

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: (can you show how this is accomplished? Animation?)

where

• Unknown macro: {latex}

  $$
  \Delta H
  $$

  is the difference in head loss between the rapid mix and flocculation tank
• Unknown macro: {latex}

  $$
  K _orifice is the required minor loss coefficient through the orifice

  • V _jet is the velocity in the dosing tube

  This head loss was then used to determine the velocity of the water through the orifice and the residence time. (Why?) Using the following equations:

  Velocity of Jets:

  $$
  V_
  Unknown macro: {jet}

  = {Q \over {C_d *A_

  Unknown macro: {orifice}

  }}
  $$

  Unknown macro: {latex}

  where

  • V~jet~ is the velocity of the jet
  • Q is the flow rate through the system
  • C _d is the vena contracta coefficient for exit condition in orifice
  • A _orifice is the area of the orifice

  Residence time :

  $$
  \theta = {{d_

  } \over {V_

  }}
  $$
  Unknown macro: {latex}

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

  $$
  \varepsilon = {{g*\Delta H} \over \theta }
  $$
  Unknown macro: {latex}

  We sought to keep the energy dissipation rate between .5 and 1 W/kg so that molecular scale diffusion works and in order for small scale turbulent mixing to be effective.

  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.

  $$
  m_
  Unknown macro: {doserful}
  = [({{.375in} \over 2})^2 *\pi *25cm + ({{D_
  Unknown macro: {actual}
  } \over 2})^2 *\pi *1m]\rho _
  Unknown macro: {water}
  + m_
  Unknown macro: {doser}
  $$
  Unknown macro: {latex}
  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. (You made a jump here in logic that I don't see)

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.

(Include a section about how you can make these equations scalable for larger and smaller plant sizes.)