# Varying flow through Centrifugal pump

A centrifugal pump is used to pump fluid from one reservoir to another with varying pump speeds (Using a variable frequency drive).

The system looks something like this

The pump performance curve (QH) is given as illustrated: (The black dot is the duty point):

The maximum height of the two reservoirs is $$0.5$$ meters.

Based on this information how can I calculate the pump flow dynamically?

I tried using the Affinity law: $$Q' = Q \cdot \frac{\omega'}{\omega}$$. using the duty point from the pump specification (black dot) which is (38,2.2). I'm not sure if this is the correct approach as the maximal head of the system is below the duty point head.

I don't know how I should calculate this in another way, can anyone help me with this?

• So convert the head to a pressure term that the pump has to overcome. Nov 21, 2022 at 13:22
• How should the pressure be implementet in the flow equation then ?
– Nil
Nov 21, 2022 at 15:24

Firstly, redraw that pump curve to have dimensionless flow coefficient on one axis and dimensionless head coefficient on the other. That is to say, for each $$\left(Q,H\right)$$ point on the original pump curve, compute the value of the flow coefficient $$K_Q := \frac{Q}{D^3\omega_{\textrm{test}}}$$ and the value of the head coefficient $$K_H := \frac{gH}{D^2\omega_{\textrm{test}}^2}\mathrm{,}$$ where $$D$$ is the diameter of the pump impeller and $$\omega_{\textrm{test}}$$ is the rotation rate at which the pump was running when the pump curve data were measured

Then plot a new graph of $$K_Q$$ against $$K_H$$. That new graph is a universal version of the pump curve, which (under a not-very-restrictive assumption about the Reynolds number of the flow) will still be correct even if you change the rotation rate at which you run the pump, and indeed even if you swap in a larger or smaller pump, as long as its impeller has the same blade angles.

Then calculate the value of the head coefficient $$K_H = \frac{gH_{\textrm{planned}}}{D^2\omega_{\textrm{planned}}^2}$$ at the values of head $$H_{\textrm{planned}}$$ and rotation rate $$\omega_{\textrm{planned}}$$ for which you want to predict the flow rate. On your universal pump curve, look up the value of $$K_Q$$ for that value of $$K_H$$, then find the flow rate in those conditions through $$Q = D^3\omega_{\textrm{planned}}K_Q\textrm{.}$$

See Douglas et al., Fluid mechanics, Pearson Prentice Hall, pages 809-812 and 814-815 of the 5th (2005) edition or equivalent passages of other editions.

• Sorry, what do you mean?
– Nil
Nov 21, 2022 at 13:38
• @Nil I've expanded my answer to give (much) more detail. Hope that helps. Nov 21, 2022 at 21:43

You have one pump curve. What you need is all the pump curves for different speeds. Only then will you have the data set you need.

• Can I just use the function from that curve to construct the others? The pump manufacturer only gave this
– Nil
Nov 21, 2022 at 19:58
• well curves tend to look the same, I don't know how they are derived. Nov 21, 2022 at 20:05
• But how should I do if i have the all pump curves ?
– Nil
Nov 21, 2022 at 20:53
• I'm not sure what you're after really. The old method is throttling the output, no one tried calculating how much throttling was required. Nov 21, 2022 at 20:59
• I am just looking for a way to describe the flow through the pump as a function of the pump velocity
– Nil
Nov 22, 2022 at 10:36