LOGOS Learning · 17
How to size a pump step by step: TDH, NPSH and motor power
The total dynamic head is TDH = dz + hf + hm + dP/(rho*g): static lift plus friction and fitting losses (the pressure term is zero here, with both ends open to atmosphere). In the worked example the pump runs at 60.1 m3/h and 26.77 m, not at the 50 m3/h desired, so NPSHa and power are checked there.
A pump will move water at 25 °C through a short DN 150 suction and a 280 m DN 100 discharge up to a point 15 m above the suction level. We want 50 m³/h, but the real flow is set by where the pump curve crosses the system curve. So the order is: plot the system curve, plot the pump curve, find the operating point, and only then compute velocity, Reynolds, friction, losses, NPSH and power at that flow.
- Step 1 of 14
Water properties
Density and viscosity at 25 °C enter the Reynolds number and the conversion to pressure and power.
ρ = 997 kg/m³ · μ = 0.00089 Pa·s · g = 9.80665 m/s²
Formulas in plain text
- Total dynamic head (system curve)
TDH = Hst + sum[ (f * L / D + sumK) * v^2 / (2 * g) ]- TDH = total dynamic head (m) · Hst = static head, suction level to highest point of the discharge (m) · f = Darcy friction factor (-) · L = section length (m) · D = internal diameter (m) · sumK = sum of fitting loss coefficients (-) · v = velocity Q / (pi * D^2 / 4) (m/s) · g = 9.81 m/s2
- Swamee-Jain friction factor
f = 0.25 / [ log10( eps / (3.7 * D) + 5.74 / Re^0.9 ) ]^2, Re = rho * v * D / mu- eps = absolute roughness (m) · Re = Reynolds number (-) · rho = density (kg/m3) · mu = dynamic viscosity (Pa*s)
- NPSH available
NPSHa = patm / (rho * g) - pv / (rho * g) - z_axis - hf_suc- NPSHa = net positive suction head available (m) · patm = atmospheric pressure (Pa) · pv = vapor pressure (Pa) · z_axis = pump centerline above the suction level (m) · hf_suc = suction losses at the operating flow (m)
- Pump power
Ph = rho * g * Q * H ; P_shaft = Ph / eta ; P_motor >= 1.15 * P_shaft- Ph = hydraulic power (W) · Q = operating flow (m3/s) · H = operating head (m) · eta = pump efficiency (-) · P_motor = next commercial motor size (kW)
Frequently asked questions
What is the difference between TDH and static head?
Static head is only the elevation the pump has to lift, and it does not change with flow. TDH adds the friction and fitting losses, which grow roughly with Q^2, so TDH is what the pump must deliver at a given flow.
Why is the pump not sized at the desired flow?
The pump runs where its curve crosses the system curve, not at the flow you wish for. In the example the desired flow is 50 m3/h but the operating point is 60.1 m3/h; sizing the motor at 50 m3/h would give 5.5 kW instead of the 7.5 kW needed.
Why is Colebrook solved by iteration?
The Colebrook equation has the friction factor on both sides, inside a logarithm, so it cannot be isolated. Explicit approximations such as Swamee-Jain give f directly, within about 1 % of Colebrook in turbulent flow.
Why must NPSH available exceed NPSH required?
If the pressure at the impeller eye falls below the vapor pressure, the water flashes into bubbles that collapse and erode the impeller (cavitation). NPSHa must stay above the catalog NPSHr at the operating flow, with a safety margin.