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!Non Linear Doser Diagram.jpg|width=300px, align=center!
h5. Illustration of non-linear chemical doser
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h3. Introduction
The |
Introduction
The non-linear
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dose
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controller
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was
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redesigned
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in
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order
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to
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reduce
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the
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amount
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of
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aeration
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caused
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as
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water
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traveled
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through
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the
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plant.
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For
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more
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information
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about
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the
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theory
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of
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the
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non-linear
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dose
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controller
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see
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the
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page
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for
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the
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...
...
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Methods
Sizing the Orifice
The orifice between the rapid mix and flocculation 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:
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|Nonlinear Chemical Dose Controller Fall08-Summer09]. h3. Methods h4. Sizing the Orifice The orifice between the rapid mix and flocculation 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}$$ \Delta H = K_{_{orifice} } {{V_{jet} ^2 } \over {2*g}} $$ {latex} where * |
where
Wiki Markup {latex}$$ \Delta H $${latex}
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is
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- the
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- difference
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- in
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- head
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- loss
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- between
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- the
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- rapid
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- mix
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- and
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- flocculation
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- tank
- 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. Using the following equations:
Velocity of Jets:
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* 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. Using the following equations: Velocity of Jets: {latex} $$V_{jet} = {Q \over {C_d *A_{orifice} }} $${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 :
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* 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 : {latex}$$ \theta = {{d_{orifice} } \over {V_{jet} }} $${latex} where * |
where
Wiki Markup {latex} $$ \theta $$ {latex}
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is
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- the
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- residence
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- time
- d orifice is the diameter of the orifice
- V jet is the velocity of the jet
Once these values were determined, we were able to calculate the energy dissipation rate using the following equation:
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* d ~orifice~ is the diameter of the orifice * V ~jet~ is the velocity of the jet Once these values were determined, we were able to calculate the energy dissipation rate using the following equation: {latex}$$ \varepsilon = {{g*\Delta H} \over \theta } $${latex} where * |
where
Wiki Markup {latex}$$ \varepsilon $${latex}
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is
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- the
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- energy
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- dissipation
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- rate
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- g
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- is
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- gravity
Wiki Markup {latex}$$ \Delta H $${latex}
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is
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- the
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- head
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- loss
Wiki Markup {latex}$$ \theta $${latex}
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is
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- the
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- residence
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- time
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We
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sought
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to
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keep
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the
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energy
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dissipation
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rate
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between
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.5
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and
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1
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W/kg
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so
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that
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molecular
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scale
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diffusion
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works
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and
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in
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order
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for
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small
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scale
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turbulent
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mixing
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to
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be
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effective.
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Lever
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Arm
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and
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Float
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We
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first
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must
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determine
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the
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size
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of
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the
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counterweight
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on
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the
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doser
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arm
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in
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order
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to
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ensure
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that
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the
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dosage
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will
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only
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be
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a
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function
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of
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the
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difference
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in
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water
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height
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in
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the
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flocculation
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and
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rapid
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mix
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tanks.
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The
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mass
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of
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the
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weight
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is
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calculated
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by
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determining
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the
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mass
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of
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the
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doser
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when
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full.
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{latex}$$ m_{doserful} = [({{.375in} \over 2})^2 *\pi *25cm + ({{D_{actual} } \over 2})^2 *\pi *1m]\rho _{water} + m_{doser} $${latex} |
where
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- D actual is the difference between the given diameter of the dosing tube and the measured diameter of the dosing tube
Wiki Markup {latex}$$ \rho _{water} $${latex}
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is
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- the
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- density
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- of
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- water
Wiki Markup {latex}$$ m_{doser} $${latex}
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is
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- the
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- mass
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- of
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- the
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- doser
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- empty
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The
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size
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of
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the
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float
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can
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be
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determined
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using
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a
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moment
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balance
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around
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the
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pivot
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of
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the
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lever
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arm.
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This
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is
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to
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ensure
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that
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a
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change
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in
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head
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in
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the
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entrance
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tank
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will
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cause
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a
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similar
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change
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in
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the
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relative
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height
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of
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the
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float.
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The
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float
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was
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sized
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using
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the
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same
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float
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sizing
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algorithm
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used
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by
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the
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linear
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CDC.
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Based
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on
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this
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we
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found
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that
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a
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float
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of
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13.3
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inches
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would
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theoretically
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be
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able
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to
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measure
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a
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.25cm
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height
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difference.
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 15.2cm height difference.
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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 15.2cm height difference. {float:left|border=2px solid black|width=300px} !head loss vs flow rate.jpg|width=300px, align=center! h5. Graph showing the non-linear relationship between the head loss vs. the flow rate through a 8cm diameter orifice {float} |
Additionally
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we
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found
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2
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solutions
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with
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multiple
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orifices.
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We
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did
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this
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because
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more
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orifices
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at
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a
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smaller
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diameter
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will
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keep
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energy
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dissepation
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constant
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while
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increasing
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overall
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headloss
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across
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the
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system.
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The
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first
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solution
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gave
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us
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8
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orifices
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with
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a
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4.5cm
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diameter
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and
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a
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minimum
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energy
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dissipation
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rate
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of
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.831.
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{float:left|border=2px solid black|width=300px} !8 orifices.jpg|width=300px, align=center! h5. Graph showing the non-linear relationship between the head loss vs. the flow rate through eight 4.5cm diameter orifices {float} |
The
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second
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solution
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gave
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us
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175
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orifices
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with
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a
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2
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cm
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diameter
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and
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a
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minimum
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energy
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dissipation
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rate
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of
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.496.
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{float:left|border=2px solid black|width=300px}
!175 orifices.jpg|width=300px, align=center!
h5. Graph showing the non-linear relationship between the head loss vs. the flow rate through 175 2cm diameter orifices
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