LE - Plotting pump curves

 Pump curves refer to plots of total head $H^*$, of the power tranferred to the fluid $N^*$ and the efficiency of the pump $\eta$ versus the flow rate $Q^*$.

For reference on definitions of $H^*$, $N^*$, $\eta$ and $Q^*$ please check on the post: Theoretical foundations for pump mesurements and estimations.

You need to measure the pump impeller diameter or at least have a reasonable estimation of it. Another way of doing it is by checking on the pump manufacturer datasheet. The fluid properties will also be required.

Calculation of $H^*$

For this you may refer to the following equation,

$H=\dfrac{p_D-p_A}{\gamma}+\left(z_D-z_A\right)+\dfrac{Q^2}{2g}\left( \dfrac{1}{A_D^2} -\dfrac{1}{A_A^2}\right)$        Eq. (01)

where subscripts $A$ and $D$ stand for admision (or suction) line and discharge line, respectively. $z$ can be measured as the vertical distance between the two points of pressure measurements.

Once, $H$ has been calculated its dimensionless form can be also found from,

$H^*=\dfrac{Hg}{n^2D^2}$        Eq. (02)

Calulation of the flow rate $Q^*$

The dimensionless flow rate can be estimated from,

$Q^*=\dfrac{Q}{n^2D^3}$        Eq. (03)

Calculation of the power transferred to the fluid $N^*$

This parameter can be estimated from,

$N_H=\gamma Q H_P$        Eq. (04)

where $\gamma$ is a property of the fluid. The dimensionless form of $N_H$ is,

$N_H^*=\dfrac{N}{n^3D^5}$        Eq. (05)

Calculation of the motor real power $N$

The power consumed by the electric motor is estimated from,

$N_M=\dfrac{\pi}{30}FRn$        Eq. (06)

where $r$ is the shaft length.

Calculation of the pump efficiency $\eta$

In this case, the formula is simply,

$\eta=\dfrac{N_H}{N_M}$        Eq. (07)

Curves construction

For simplicity, the data is better collected in a sheet so that all calculations can be automated. For data measurement proceed as follows,

• Start the pump
• Set the pump to the lowest possible speed so that flow rate can be measured
• Increase slowly the pump velocity so that several sets of flow rate and pressures can be recorded
• Register the data in a sheet so that calculations can be easily done and plot
• Once, your data are calculated, make plots of it
• Check for smooth of your plots.

As a final comment, you are advised to measure more than 4 data sets.

Any question? Write in the comments and I shall try to help.

Other stuff of interest

• Theoretical foundations for pump mesurements and estimations
• The pros and cons of bulb thermometers
• Some examples of temperature instruments
• Minor losses  - Formulas
• What is a process variable?
• What are the most important process variables?
• Time dependence of process variables
• A list of process variables

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Ildebrando.