BIZOMAT MAKEOS · Hydraulics
Pump and Fan Affinity Laws
What flow, head and power will this centrifugal pump or fan give at a new speed or impeller size?
Flow, head (pressure) and power of a centrifugal pump or fan at a new speed or trimmed impeller diameter by the affinity laws, with the power saving.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Present flow | m³/h | Flow at the present operating point, from the pump curve or a flow meter. |
| Present head | m | Head (or fan pressure) at that point. |
| Present shaft power | kW | Shaft power at that point, from the curve or measured input × motor efficiency. |
| Present speed | rpm | Present speed. |
| New speed | rpm | New speed (e.g. with a VSD or new pulleys). |
| Present impeller diameter | mm | Present impeller diameter. |
| New impeller diameter | mm | New (trimmed) impeller diameter; equal to the present one for speed changes only. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Present flow
- What it is
- The flow the pump or fan delivers now at the present speed and impeller size, from its curve at the operating point or a flow meter.
- Units and format
- Enter a number in m³/h: cubic metres per hour. The form accepts 0.000001 m³/h to 10000000 m³/h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 m³/h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- New flow scales in direct proportion.
- Get it right
- Use a real operating point, not the pump’s best-efficiency rating unless it runs there.
What this means: Present head
- What it is
- The head the pump develops now at the present operating point, or the pressure for a fan, from the pump curve or measured pressures.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 100000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- New head scales in direct proportion.
- Get it right
- The affinity laws assume no static head; with a large static lift the real new point differs.
What this means: Present shaft power
- What it is
- The power going into the pump or fan shaft now at the present operating point, from the pump curve or measured motor input times motor efficiency.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 1000000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- New power scales in direct proportion.
- Get it right
- Use shaft power, not electrical input, unless you accept that motor losses are ignored.
What this means: Present speed
- What it is
- The speed the pump or fan shaft runs at now, from the motor nameplate, drive display or a tachometer.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2900 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher present speed for the same new speed means a larger reduction.
- Get it right
- Use the actual running speed under load, not the synchronous speed of the motor.
What this means: New speed
- What it is
- The speed you plan to run at, for example with a variable speed drive or different pulleys.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2400 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow scales with speed, head with its square and power with its cube.
- Get it right
- Set it equal to the present speed when only trimming the impeller.
What this means: Present impeller diameter
- What it is
- The diameter of the impeller fitted now, from the pump data sheet or by measuring.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For speed changes only, enter the same value as the new diameter.
What this means: New impeller diameter
- What it is
- The diameter of the impeller after trimming, or the same as the present diameter if only the speed changes.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow scales with diameter, head with its square and power with its cube.
- Get it right
- Large trims make the affinity laws inaccurate; the tool warns when that happens.
Method and formulas
- Q₂ = Q₁ (n₂/n₁)(D₂/D₁).
- H₂ = H₁ (n₂/n₁)²(D₂/D₁)².
- P₂ = P₁ (n₂/n₁)³(D₂/D₁)³.
- Example: slowing from 2900 to 2400 rpm cuts power from 7 to 3.9677 kW.
Limitations
- Applies along a system curve with no static head; with static head, the operating point and savings are smaller.
- Impeller trimming beyond about 10–20% departs from the laws and lowers efficiency.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate savings from a variable speed drive
- Predict the effect of trimming an impeller
- Re-rate a fan at a new pulley ratio
Who it is for
- Hydraulic and process engineers
- Maintenance engineers
- Design engineers
What you get
- New flow, head and power
- Power saving
Interpreting the result
- Plot the new pump curve against the system curve to find the real operating point.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Pumps, fans and similarity: affinity laws and specific speed
In Scale Models by the Numbers
What it covers: Derive the affinity laws from dimensionless groups, apply them to a variable-speed pump and a ventilation fan, classify machines by specific speed, and see why model pump efficiency is stepped up.
Method explained here · BIZOMAT original book
Fans, pumps and energy savings
In Variable-Speed Drives by the Numbers
What it covers: How the fan and affinity laws predict the power saved by slowing a fan or pump, why static head cuts the saving, how to measure the before and after, and how to appraise a drive as an investment.
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