BIZOMAT MAKEOS · Hydraulics
Pump Operating Point on the System Curve
Where will this centrifugal pump actually run on my system, how efficiently, and what speed gives the flow I want?
Operating point of a centrifugal pump on a pipe system: a quadratic pump curve through shut-off head and the best-efficiency point, a system curve from static head and one known duty point, their intersection (flow, head), efficiency there from a parabolic efficiency curve, absorbed power, the position relative to the best-efficiency flow, and the speed (by the affinity laws) that gives a target flow.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pump at rated speed | ||
| Shut-off head | m | Head at zero flow from the pump curve. |
| Best-efficiency flow | L/min | Flow at the best-efficiency point (BEP). |
| Head at best efficiency | m | Head at the BEP. |
| Best efficiency | % | Efficiency at the BEP. |
| Rated speed | rpm | Speed the curve applies to. |
| System | ||
| Static head (lift plus pressure difference) | m | Static head of the system: level difference plus pressure difference as head. |
| Known system flow | L/min | A flow at which the system head is known (from a pipe loss calculation). |
| System head at that flow | m | Total system head at that flow. |
| Liquid density | kg/m³ | Liquid density. |
| Target flow (for the speed change) | L/min | Flow you want; the tool finds the pump speed that gives it. |
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.
Pump at rated speed
What this means: Shut-off head
- What it is
- Head the pump develops at zero flow (discharge valve closed), read from the maker’s curve at rated speed.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be above both the best-efficiency head and the static head of the system.
What this means: Best-efficiency flow
- What it is
- Flow at the pump’s best efficiency point (BEP), read from the maker’s curve at rated speed.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Head at best efficiency
- What it is
- Head the pump develops at its best-efficiency flow, from the same curve. With the shut-off head it fixes the shape of the fitted pump curve.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be below the shut-off head.
What this means: Best efficiency
- What it is
- Pump efficiency at the best efficiency point, from the maker’s curve; the tool scales it down for flows away from the BEP.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 5% to 95%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Absorbed power is inversely proportional to the efficiency at the operating point.
What this means: Rated speed
- What it is
- Speed the pump curve applies to. It is used only to turn the speed ratio for the target flow into rpm.
- 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 1450 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
System
What this means: Static head (lift plus pressure difference)
- What it is
- Head the system needs at zero flow: the difference in liquid level plus any pressure difference between suction and delivery vessels, expressed as head.
- Units and format
- Enter a number in m: metres. The form accepts 0 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Convert pressure to head of the actual liquid: head = pressure ÷ (ρ g).
What this means: Known system flow
- What it is
- A flow at which you know the total system head, from a pipe friction calculation or a test. It fixes the steepness of the system curve.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: System head at that flow
- What it is
- Total system head at that known flow: static head plus pipe, fitting and valve losses.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 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.
- Get it right
- It must be greater than the static head.
What this means: Liquid density
- What it is
- Density of the liquid being pumped at its working temperature, used for the absorbed power.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Absorbed power is proportional to density; the operating flow and head do not change.
What this means: Target flow (for the speed change)
- What it is
- The flow you want from the same system; the tool finds the pump speed that gives it using the affinity laws.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- 0 = no speed calculation.
Method and formulas
- Pump: H = H₀ − a Q², with a = (H₀ − H_BEP) ÷ Q_BEP²; system: H = H_s + k Q², with k = (H_d − H_s) ÷ Q_d².
- Operating flow Q = √[(H₀ − H_s) ÷ (a + k)].
- Efficiency η = η_BEP (2x − x²), x = Q ÷ Q_BEP; power = ρ g Q H ÷ η.
- Speed ratio s for a target flow (affinity laws): s² H₀ − a Q_t² = H_s + k Q_t².
- Example: the pump runs at 390.8 L/min and 40.455 m, 97.701% of its BEP flow.
Limitations
- Quadratic fits to the pump and system curves; use the maker’s curve near the ends of the range.
- Affinity laws hold for speed changes on the same impeller; static head limits how far speed can drop.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Predict the flow a pump will deliver on a new pipe system
- Check that a pump runs near its best efficiency point
- Set a variable-speed drive for a target flow
Who it is for
- Plant engineers
- Maintenance engineers
- Process engineers
What you get
- Operating flow and head
- Efficiency, power and position against BEP
- Speed for the target flow
Interpreting the result
- Run between about 70% and 120% of BEP flow for long seal and bearing life.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3021–3026. 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 · Library collection
Pipe flow, pressure drop and pump selection: getting fluid where it needs to go efficiently
In Fluids, HVAC and Building Services
What it covers: How head, velocity, friction and fittings set pressure drop, how system and pump curves fix the operating point, why efficiency and NPSH matter, and how pipe size affects energy cost.
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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