Pump head from system losses and boundaries
A pump must supply the difference in total energy between system boundaries plus dissipative losses. Separate static lift from friction: static requirements can remain when flow is zero, while velocity-dependent losses change with flow.
Worked numbers are illustrative. Use your own operating conditions and documented material/process data.
Required inputs
- Boundary elevations and pressures on a consistent gauge or absolute basis.
- Flow, pipe segments and fitting/equipment losses.
- Fluid density and pump efficiency at the intended duty; a user-supplied pump curve if seeking an operating point.
Governing equations
Hrequired = Δz + Δp/(ρg) + Δ(v²)/(2g) + Σhloss
Phydraulic = ρgQH
Pshaft = Phydraulic/ηpump
Variables and units
- H, z and losses: m; p: Pa; Q: m³/s; P: W.
- ηpump is a decimal between 0 and 1; motor electrical input requires a separate motor efficiency.
Assumptions
- Steady liquid-flow energy balance between stated boundaries.
- For two large open tanks, equal boundary pressure and negligible tank velocity remove the pressure and velocity terms.
Calculation workflow
- Define start and end boundaries before counting losses.
- Sum static, pressure, velocity and dissipative contributions without counting a component twice.
- Compare required head with a supplied pump curve only over its supported flow range.
Worked example
- Two open tanks differ by 10 m elevation; flow is 25 m³/h. Entered pipe/equipment losses sum to 4 m.
- Hrequired = 10 + 4 = 14 m. With ρ = 1000 kg/m³ and g = 9.81 m/s², Phydraulic = 0.953750 kW.
- At entered pump efficiency 0.75, Pshaft = 1.271667 kW.
Limitations
- NPSHA requires pressure, vapor pressure, elevations and suction losses on the correct absolute basis; NPSHr requires pump data.
- Parallel-network balancing, cavitation approval and water-hammer analysis are not provided by this energy balance.
Common mistakes
- Adding static lift to a pressure-head term that already includes it.
- Using gauge pressure as absolute pressure in NPSH work.
- Extrapolating a pump curve or treating hydraulic power as electrical input.
Practical interpretation
At a specified flow, this is the required duty, not proof that a pump will achieve it. The operating point is the intersection with a real supplied pump curve. An illustrative system curve cannot create a manufacturer pump curve or establish NPSHr.
Related formulas
The governing equations, units and calculation steps above provide the formula basis for this guide. The related workspace also shows its calculation trace.
Head, pressure and flow unit bases →Related workspace
Open Fluid Systems →Sources and reference basis
Equations and worked examples are independently explained here. References reviewed 2026-10-17; no copyrighted standard tables are reproduced.