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Pumps

Power demand, system head and cavitation safety (NPSH).

Pump Power

hydraulic power and shaft power

Flow rate Q [m³/h]

Head H [m]

Density ρ [kg/m³]

Pump η [-] (0.6–0.85)

Motor η [-] (IE3 ≈ 0.93)

Hydraulic power P_hyd–

Shaft power P_W–

Electrical input power P_el–

Differential pressure Δp–

Theory

Power transferred to the fluid (hydraulic power):

P_hyd = ρ · g · Q · H

Shaft power and electrical power via the efficiencies:

P_W = P_hydη_P · P_el = P_Wη_M

Q in m³/s, H in m, g = 9.81 m/s²
η_P: centrifugal pumps 0.6–0.85 (depending on size)
Δp = ρ·g·H (1 bar ≈ 10.2 m water column)

System Head

elevation + pressure difference + losses

Elevation difference z [m]

Pressure drop in piping Δp_L [bar]

Pressure in discharge tank p₂ [bar abs]

Pressure in suction tank p₁ [bar abs]

Density ρ [kg/m³]

Elevation component–

Pressure difference component–

Loss component–

System head H_A–

Theory

The system head combines all components the pump has to overcome:

H_A = z + p₂ − p₁ρ · g + Δp_Lρ · g

z: elevation difference between suction and discharge side
(p₂−p₁): pressure difference between the tanks (open tanks: 0)
Δp_L: friction losses (rise with the square of Q)

The operating point lies at the intersection of the system curve and the pump curve.

NPSH: Cavitation Check

net positive suction head available at the pump inlet

Pressure in suction tank p_e [bar abs]

Fluid temperature [°C] (for p_vap of water)

Suction head z_e [m] (negative = suction lift)

Suction line loss h_L [m]

Density ρ [kg/m³]

Pump NPSH_r [m] (data sheet)

Vapor pressure p_vap (water)–

NPSH available (NPSH_a)–

Margin over NPSH_r + 0.5 m–

Assessment–

The vapor pressure of water is approximated from the temperature (Antoine equation). For other fluids, check p_vap manually.

Theory

NPSH (Net Positive Suction Head) = margin between the pressure at the impeller inlet and the vapor pressure:

NPSH_a = p_e − p_vapρ · g + z_e − h_L

Cavitation-free operation requires:

NPSH_a ≥ NPSH_r + 0.5 m

Cavitation = vapor bubble formation → implosion → material erosion, noise, head drop
Remedies: increase suction head, shorten or enlarge the suction line, cool the fluid

Rough estimate for preliminary design. Does not replace pump selection and sizing by the manufacturer.