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For similar operation of the same pump, flow, head and power approximately scale with powers of rotational speed.
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Formula
Q in m3/s; H in m; P in W; n in s−1
| Symbol | Meaning | Unit |
|---|---|---|
| Volumetric flow | m3/s | |
| Pump head | m | |
| Power under a consistent definition | W | |
| Rotational speed | s−1 |
Q\propto n,\quad H\propto n^2,\quad P\propto n^3The laws approximate geometrically similar operating states for the same centrifugal pump, constant fluid density and similar efficiency. System curve, cavitation, Reynolds effects and minimum flow shift the operating point. Compare power using the same hydraulic or shaft-power definition.
The laws approximate geometrically similar operating states for the same centrifugal pump, constant fluid density and similar efficiency. System curve, cavitation, Reynolds effects and minimum flow shift the operating point. Compare power using the same hydraulic or shaft-power definition.
For similar operation of the same pump, flow, head and power approximately scale with powers of rotational speed.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Centrifugal-pump affinity laws under speed change” and check its unit and magnitude.
At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Q in m3/s; H in m; P in W; n in s−1.
Formula cluster
For similar operation of the same pump, flow, head and power approximately scale with powers of rotational speed.
At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original.
Estimate effects of centrifugal-pump speed control.
Here is how to work through a typical Centrifugal-pump affinity laws under speed change (Q∝n; H∝n²; P∝n³) task step by step:
Task
Work through the numerical example for “Centrifugal-pump affinity laws under speed change” and check its unit and magnitude.
Solution path
At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original.
Hydraulic power scales with flow times head. Under similarity, Q is roughly proportional to n and H to n2, so power is approximately proportional to n3. Efficiency changes, system curve and cavitation alter actual input. These are approximate similarity laws for the same pump near corresponding operating points. Application: Estimate effects of centrifugal-pump speed control. The numerical example At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original anchors the idea in a concrete measurement case.
No. Minimum flow, motor and drive limits, cooling, bearings, cavitation and process requirements constrain speed range. Affinity laws estimate scaling, not operating-point stability or safe continuous operation. These are approximate similarity laws for the same pump near corresponding operating points. The corresponding units are Q in m3/s; H in m; P in W; n in s−1. At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original. This checks that the reference quantities are compatible.
State whether P means hydraulic fluid power or shaft power. They scale similarly at similar efficiency but not exactly if efficiency changes with speed. Name the system boundary when comparing. These are approximate similarity laws for the same pump near corresponding operating points. Scope: The laws approximate geometrically similar operating states for the same centrifugal pump, constant fluid density and similar efficiency. System curve, cavitation, Reynolds effects and minimum flow shift the operating point. Compare power using the same hydraulic or shaft-power definition. A practical application is Estimate effects of centrifugal-pump speed control.
Write the quantity and unit from the variable list next to every value: Q in m3/s; H in m; P in W; n in s−1. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example At 80% speed, ideal Q is 80%, H is 64% and P about 51.2% of the original. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. These are approximate similarity laws for the same pump near corresponding operating points.
The background states this starting condition: The laws approximate geometrically similar operating states for the same centrifugal pump, constant fluid density and similar efficiency.. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. These are approximate similarity laws for the same pump near corresponding operating points.
Quanta exam set
Curated exam set for "Centrifugal-pump affinity laws under speed change":
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Which formula describes Centrifugal-pump affinity laws under speed change?
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How do you rearrange Centrifugal-pump affinity laws under speed change for Base equation for the target quantity?
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Which common mistake happens with Centrifugal-pump affinity laws under speed change?
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