A four-stage centrifugal pump passes liquid through four impeller stages in series. Each stage adds head to the same through-flow. This calculator sums four equal entered stage heads, applies one overall head reduction and estimates water pressure rise and shaft power. It does not select a pump or determine its operating point from a performance curve.
Four Stage Centrifugal Pump Interactive Calculator
Compare four equal stage heads with one overall head-reduction percentage. Flow and efficiency are independent assumptions; the tool does not derive a pump curve.
Equation Used
The calculation is H = 4H_stage(1 − L/100), where L is one reduction applied to the total. It is not compounded between stages. Pressure rise uses water density 1,000 kg/m³; shaft power uses the entered flow and pump efficiency.
- Water density is 1000 kg/m3.
- Pump has exactly 4 equal-head stages.
- Loss percent is applied to the ideal four-stage head.
- Flow is steady and incompressible.
- Pressure rise assumes equal inlet/outlet elevations and velocities. It is not absolute discharge pressure. Suction conditions and NPSH are not calculated.
Successive stages add energy
A rotating impeller transfers shaft work to the liquid. Stationary passages recover part of the velocity head as pressure and guide flow toward the next impeller. Repeating that process allows several stages to contribute to the total head.
Stages in series share the through-flow; their heads add at a given flow. Adding stages is not the same as adding independent outlet flows. A complete pump’s actual flow is determined by its characteristic curve together with the system it supplies.
Casings, seals, bearings and thrust-balancing arrangements depend on the pump. The axial section shows four impellers on a common shaft, with fixed passages returning liquid toward the next inlet eye. Passage shapes and flow markers are simplified; shaft speed and pressure ratings require the specific pump data.
Higher-head liquid duties
Multistage centrifugal pumps are used where the required head makes stages in series useful, including boiler-feed and industrial high-pressure applications. The number of stages is part of selecting a suitable pump, not a guarantee of a fixed pressure range.
Suitability for hot water, dirty fluid, sanitary service or fire protection depends on the exact construction and applicable requirements. This four-stage comparison does not establish certification or recommend a commercial model.
Head, pressure and power
For equal entered stage head H_stage and overall reduction L percent, H_total = 4H_stage(1 − L/100). Head multiple is H_total/H_stage. The reduction is applied once to the sum, not as three successive interstage efficiency factors.
With fixed density ρ = 1,000 kg/m³ and g = 9.80665 m/s², the pressure equivalent is Δp = ρgH_total/100,000 bar. Treating this as static pressure rise assumes no difference in inlet/outlet velocity head or elevation. Add the appropriate inlet pressure separately to obtain outlet pressure.
Convert Q from m³/h to m³/s by dividing by 3,600. Shaft power is P = ρgQH_total/(η × 1,000) kW, with efficiency η entered as a fraction. This is pump shaft input power; motor and drive losses are additional.
Flow, stage head and efficiency are independent inputs. Changing flow does not change head or efficiency automatically. Use a consistent measured or rated duty point, and avoid adding a second loss allowance if the entered stage head already includes those losses.
Example: four 100 m stages
For stage head 100 m, overall head reduction 3%, flow 100 m³/h and pump efficiency 75%, total head is 4 × 100 × 0.97 = 388 m. Head multiple is 3.88.
The water pressure equivalent is 38.05 bar. Hydraulic power is 105.69 kW and estimated shaft power is 140.93 kW. With equal inlet/outlet elevations and velocities and inlet pressure 2 bar gauge, the corresponding outlet pressure would be about 40.05 bar gauge, before downstream pipe losses.
Halving entered flow to 50 m³/h halves the estimated power while the entered head remains unchanged. This is an arithmetic comparison, not a prediction of where a real pump will operate on its curve. The fixed water density also does not represent every hot-water condition.
Complete pump selection needs curves
A pump selection requires the required flow and total system head, along with suitable efficiency, power, allowable operating range and inlet conditions. Manufacturer data supplies the pump curve and NPSH requirement; these do not follow from stage count alone.
More stages introduce additional components and pressure-loading considerations. Alternative impeller sizes, speeds or pump types should be compared at the same duty and fluid conditions rather than using universal life, cost or cavitation claims.
Use the specific pump’s instructions for operation and repair. Removing an impeller or changing a balance arrangement is not justified by simply subtracting one quarter of the head.
Frequently asked questions
Do four stages give four times the outlet pressure?
They ideally add four equal head increments at the same flow. Outlet pressure also depends on inlet pressure, elevation and velocity conditions; it is not generally four times inlet pressure.
Is Overall head reduction applied at every transition?
No. The entered percentage reduces the sum of four stage heads once. It does not compound three transition efficiencies.
Why does flow change power but not head?
The calculator holds stage head and efficiency at their entered values. A real pump curve relates head and efficiency to flow; that curve is not modeled.
Does Shaft Power include motor electrical losses?
No. It is estimated mechanical input at the pump shaft. Electrical input also depends on motor and drive efficiency.
Can this check cavitation or minimum flow?
No. It has no suction-pressure, vapor-pressure, NPSH or manufacturer operating-range model.
Can I use these values for hot water?
The density is fixed at 1,000 kg/m³. Temperature-dependent density, vapor pressure and pump ratings need separate treatment.
Should I subtract a loss percentage from catalog head?
Only if that allowance is not already included in the head data. Applying the same loss twice would understate head.
Can I run the pump with one failed stage removed?
This calculation does not approve mechanical modifications. Rotor support, thrust balance, passages and ratings require the manufacturer’s engineering assessment.
Pump references
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