Pump Shaft Power Calculator

Hydraulic, shaft, and drive power for a centrifugal pump with the API 610 rated-power margin, plus seal PV, specific speed, and suction specific speed.

When to use this calculator

Use once the duty point is fixed and you need to size the driver, or when screening a pump selection before it is bought. It takes flow, head, specific gravity, and pump efficiency and works down the power chain — hydraulic power, then shaft power at the coupling, then drive output after the API 610 margin and the transmission efficiency — which is the number a motor is actually selected against. Three further tabs screen the selection: the mechanical seal PV product, the specific speed Ns with its impeller classification, and the suction specific speed S against Sa. Head is an input here, taken from the system curve; the suction side is checked separately with the NPSHA calculator.

Required inputs

  • Flow rate Q and head H at the duty point, with specific gravity
  • Pump efficiency at the duty point (%)
  • Transmission type — direct coupling, gearbox, fluid coupling, V-belt or flat belt
  • Rated-power margin α, defaulted from the API 610 bracket
  • Seal tab: face diameter, speed, sealed and spring pressure, balance ratio b and k factor
  • Speed tabs: rotational speed, stages, number of suctions, NPSHR and NPSHA

Expected outputs

  • Hydraulic power, shaft power, and drive output
  • Seal face velocity and PV product
  • Specific speed Ns in SI and US, with the impeller type it implies
  • Suction specific speed S and Sa, the Thoma number, and whether S ≥ Sa

Formula overview

SI: Q in m³/h (m³/min on the specific-speed tabs), H in m, power in kW, seal diameter in mm. US: gpm, ft, hp, inches. Ns in SI converts to the US convention by ×6.68. Efficiency is entered as a percentage, transmission efficiency and margin as fractions.

Shaft and drive power:
  P_hyd   = Q · H · SG / 367        SI, Q in m³/h, H in m
          = Q · H · SG / 3960       US, Q in gpm, H in ft
  P_shaft = P_hyd × 100 / η_pump%
  P_drive = P_shaft × (1 + α) / η_trans

API 610 margin α, bracketed on shaft power:
  ≤ 22 kW → 25%      22–55 kW → 15%      > 55 kW → 10%

Seal PV:   v  = d · rpm / 19099
           PV = (P_sp + P_p · (b − k)) · v

Specific speed:          Ns = rpm · √(Q/suctions) / (H/stages)^0.75
Suction specific speed:  S  = rpm · √(Q_BEP/suctions) / NPSHR^0.75
                         Sa = the same with NPSHA;  σ = NPSHR / H

Worked example

Water transfer pump at its duty point: Q = 100 m³/h, H = 33.4 m,
SG = 1.0, pump efficiency 75%, direct coupling (η_trans = 1.0)

P_hyd   = 100 × 33.4 × 1.0 / 367 = 9.10 kW
P_shaft = 9.10 × 100 / 75        = 12.13 kW
α       = 25%   (shaft power ≤ 22 kW → API 610 bracket)
P_drive = 12.13 × 1.25 / 1.0     = 15.16 kW

→ select the next standard motor up, 18.5 kW.
On a V-belt drive (η_trans = 0.95) the same duty needs 15.96 kW,
which still lands on 18.5 kW but eats most of the margin.

Common mistakes

  • Sizing the motor on shaft power. Shaft power is what the pump absorbs at one point on the curve; the driver is selected on drive output, after the API 610 margin and the transmission efficiency.
  • Using the efficiency at best efficiency point for a duty that sits away from it. Pump efficiency falls off on both sides of BEP, and taking the BEP figure at a run-out or minimum-flow case under-predicts the power the motor has to deliver.
  • Forgetting specific gravity, or taking it at the wrong temperature. Power scales directly with SG, so a pump handling a liquid of SG 1.3 draws 30% more than the same duty on water.

FAQ

pump
shaft power
API 610
specific speed
seal PV
motor sizing

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