A graphical picture of the the pump pressure gain against volumetric flowrate aginst (Fig. 1).In most practical cases the pump model can be on the difference between intake and discharge pressure
| LaTeX Math Inline |
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| body | --uriencoded--p_%7B\rm out%7D - p_%7B\rm in%7D |
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and called pump characteristic curve (see Fig. 1):| LaTeX Math Block |
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q = q(p_{\rm out} - p_{\rm in}) |
 Image Modified
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as function of delta pressure | LaTeX Math Inline |
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| body | --uriencoded--p = p_%7B\rm out%7D-p_%7B\rm in%7D |
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The most general Pump model is given as a function of volumetric flowrate of the intake
| LaTeX Math Inline |
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| body | --uriencoded--p_%7B\rm in%7D |
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and discharge pressure | LaTeX Math Inline |
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| body | --uriencoded--p_%7B\rm out%7D |
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:| LaTeX Math Block |
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q = q(p_{\rm out}, p_{\rm in}) |
The electrical power consumption
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle W = \frac%7BdE%7D%7Bdt%7D |
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is given by:| LaTeX Math Block |
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| anchor | eta_pump |
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| alignment | left |
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W = \eta(q) \cdot q \cdot (p_{\rm out}-p_{\rm in}) |
where
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A popular pump proxy model is given by the quadratic equation:
| LaTeX Math Block |
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| anchor | q_pump |
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| alignment | left |
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q = \frac{q_{\rm max}}{2 \cdot k_f} \cdot \left[ -1 + k_f + \sqrt{ (1 + k_f)^2 - 4 \cdot k_f \cdot (p_{\rm out}- p_{\rm in})/\delta p_{\rm max}) \ } \, \right] |
| LaTeX Math Block |
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| anchor | q_pump |
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| alignment | left |
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p_{\rm out} = p_{\rm in} + \delta p_{\rm max} \cdot \left[ 1+
(k_f -1 ) \cdot \frac{q}{q_{\rm max}} - k_f \cdot \left( \frac{q}{q_{\rm max}} \right)^2
\right ] |
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\eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 - q/q_{\rm max}) |
where
| LaTeX Math Inline |
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| body | --uriencoded--\delta p_%7B\rm max%7D |
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| maximum pressure gain that pump can exert over the input pressure |
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| maximum flowrate that pump can produce |
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| total hydraulic pump friction (dimensionless) | pump efficiency |
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| maximum pump efficiency |
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The plunger pump and centrifugal pumps are normally adjusted by working frequency
See also
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Natural Science / Engineering / Device / Pump
[ Pump @model ]
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS)
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