A centrifugal pump transfers energy from a rotating impeller to a liquid. Flow enters the impeller eye and travels outward into a casing that collects it for discharge. Use the calculator to estimate hydraulic and shaft power from an entered flow, total head, specific gravity and pump efficiency. These inputs do not establish whether a particular pump can deliver that operating point.
Centrifugal Pump Interactive Calculator
Vary flow, head, fluid specific gravity, and efficiency to see pump power, pressure rise, and animated flow through the impeller and volute.
Equation Used
Hydraulic power is the power delivered to the liquid. Brake horsepower is the required pump shaft power after pump losses. The Motor Power card expresses that same shaft power in kW; motor electrical losses and a motor selection margin are not included. The pressure-rise card is the pressure equivalent of total head, not necessarily the difference between two pressure gauges when velocity or elevation changes matter.
- Steady incompressible liquid flow.
- US customary pump constant 3960 is used.
- Efficiency is overall pump efficiency and eta = efficiency_pct / 100.
From the impeller eye to the discharge
Liquid enters near the shaft axis. The rotating vanes transfer energy to it as it moves toward the impeller perimeter. The volute collects the flow around the impeller and directs it to the outlet. Pressure change occurs within the pump; it is not confined to one sudden conversion after the vanes.
The cutaway identifies the suction eye, rotating impeller, stationary volute and tangential discharge. Moving markers show the flow direction, not calculated fluid trajectories. Rotation is illustrative: no speed or impeller dimensions are entered.
Parts and their roles
- Impeller: transfers shaft work to the liquid.
- Casing: contains and collects the flow.
- Shaft and bearings: transmit torque and locate the rotating assembly.
- Shaft seal: limits leakage where the shaft crosses the casing.
Impellers may be open, semi-open or enclosed. Their suitability depends on the liquid and duty. The illustration does not specify clearances, bearing life or seal service limits for a physical pump.
Checking a proposed pumping duty
The four inputs describe a proposed steady operating point. Flow is the volume delivered per unit time; total head includes the energy needed for elevation, pressure differences and system losses. Specific gravity accounts for liquid density, and pump efficiency relates hydraulic output to shaft input.
Use actual fluid properties and a suitable pump performance curve. The calculation does not select wetted materials, solids clearance, seal arrangement or a commercial model. It also does not calculate the system curve or locate its intersection with a pump curve.
The Formula Behind the Centrifugal Pump
For the calculator, hydraulic horsepower is QHSG/3960 and required shaft horsepower is QHSG/(3960η), with Q in US gallons per minute, H in feet and η as a fraction. Shaft kW is horsepower × 0.7457. The displayed pressure equivalent is HSG/2.31 psi.
The separate Euler equation below describes theoretical impeller energy transfer from inlet and outlet velocity components. Those velocities are not inputs to this power calculator. Neither equation supplies a tested pump curve or establishes the actual operating point.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Hth | Theoretical (Euler) head developed by the impeller | m | ft |
| u2 | Impeller tip tangential velocity at vane exit | m/s | ft/s |
| cu2 | Tangential component of absolute fluid velocity at vane exit | m/s | ft/s |
| u1 | Impeller tangential velocity at vane inlet | m/s | ft/s |
| cu1 | Tangential component of absolute fluid velocity at inlet (≈0 for axial entry) | m/s | ft/s |
| g | Gravitational acceleration | 9.81 m/s² | 32.2 ft/s² |
Worked example: power at an entered duty point
Enter Q = 100 gpm, H = 100 ft, SG = 1 and efficiency = 75%.
- Hydraulic power = 100 × 100 × 1 / 3960 = 2.53 hp.
- Shaft power = 2.53 / 0.75 = 3.37 hp.
- The same shaft power in kW is 3.37 × 0.7457 = 2.51 kW.
- The pressure equivalent of the head is 100 / 2.31 = 43.29 psi.
At the same flow, head and efficiency, changing SG to 1.2 increases all four outputs by 20%. At the same flow, head and density, lowering efficiency increases shaft power but leaves hydraulic power and the pressure equivalent unchanged.
This example does not certify a motor rating or a pump model. The entered duty must be checked against actual pump and system performance, and motor selection requires the full operating range and drive data.
Operating point and suction conditions
Best efficiency point is the peak of a pump’s efficiency curve. Preferred and allowable operating regions depend on pump design and service. Operation outside them can bring recirculation, vibration, heating or excessive loads; there is no universal percentage range that qualifies every pump.
Cavitation can occur when local liquid pressure falls low enough for vapor to form. Compare available suction head with the manufacturer’s requirement and the appropriate margin for the application. A published NPSH3 value corresponds to a 3% head reduction during testing, not a guarantee that cavitation starts only below it.
This calculator contains no suction-pressure, temperature, vapor-pressure or piping inputs. It cannot diagnose cavitation, establish dry-running time, or predict wear. Follow the selected pump’s operating and maintenance instructions rather than inferring a fault from noise or a single change in head.
Questions about the pump calculation
Does entering a flow and head prove a pump can deliver them?
No. They define the duty used for the power calculation. A pump curve and the system requirements are needed to establish the operating point.
Is the Motor Power card electrical input?
No. It is the calculated pump shaft power converted from horsepower to kW. Motor and drive losses are not included.
Why does efficiency affect shaft power but not hydraulic power?
Hydraulic power follows the entered flow, head and liquid density. Dividing by pump efficiency gives the larger shaft input needed to supply that hydraulic output.
Why does specific gravity affect power?
At the same volume flow and head, denser liquid requires more power. The formula scales hydraulic and shaft power directly with specific gravity.
Is the pressure-rise value a gauge differential?
It is the pressure equivalent of entered total head. Gauge measurements require allowance for differences in velocity and elevation between the measurement locations.
Can this calculator check cavitation or choose an impeller?
No. Suction conditions, vapor pressure, speed, impeller geometry and manufacturer performance data are not supplied.
Does the animation predict the liquid flow field?
No. It shows the suction, outward passage through the impeller and discharge direction. The markers are illustrative, not a fluid-dynamics solution.
References
- KSB Centrifugal Pump Lexicon: efficiency — pump output, shaft input and pump-set efficiency.
- Hydraulic Institute: pump principles — impeller configurations and suction-head definitions.
- Hydraulic Institute: NPSH and operating regions — application-dependent operating and suction limits.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
