Very Hard Problems are as easy as 1, 2, 3.
That's the mnemonic for remembering the centrifugal pump laws.
Volumetric flow rate (V) is directly proportional to pump speed (1).
Head of the pump (H) is proportional to pump speed squared (2).
Power of the pump (P) is proportional to pump speed cubed (3).
In the below video on the centrifugal pump affinity laws, we mention that the above relationships doesn't work for positive displacement pumps.
To many, that makes it seem like the positive displacement pump laws are even more complicated and difficult. But, they're not. They're actually super easy.
For positive displacement pumps, the volumetric flow rate varies directly with pump speed. The faster the rpms, the higher the volumetric flow rate.
For any given volumetric flow rate, pump discharge head is independent of pump speed. Downstream flow losses and throttling/isolation components such as valves determine the discharge head (pressure). Basically, the pump curve for a positive displacement pump is a vertical line that only depends on pump speed.
But, back to the centrifugal pump laws.
The basic solve for these is determining by what factor the pump speed has changed.
In the below video, we use a simple "speed doubled" problem to give you a straight forward example. However, if you need to solve a more complicated one, the method is the same...
Find the "factor" of change.
Divide the final pump speed by the initial pump speed.
That gives you the number that you then apply the exponent to for the applicable term you want to solve. x^1 for volumetric flow rate, x^2 for pump head, x^3 for power.
Take your factor to the applicable exponent.
Multiply that by the initial value for the term you are solving.
Example:
Initial pump speed = 320 rpm, Final pump speed = 100 rpm
Therefore, 100 rpm / 320 rpm = 0.3125
Initial pump head = 98 feet, and 0.3125^2 = 0.0977
Then, 98 feet * 0.0977 = a final pump head of 9.575 feet
Initial pump power = 200 kW, and 0.3125^3 = 0.0305
Then, 200 kW * 0.0305 = a final pump power of 6.1 kW
Here's the video that shows you how to solve these, with our guest lecturer, Zac Robinson: