Pump head calculator
Enter each pipe segment's size, flow, length and fittings, add static head, equipment losses and a margin, and get the pump total head and shaft power. Straight-pipe loss uses the same Darcy-Weisbach solver as the pipe sizing calculator.
Basis
Each segment adds straight, fitting and equivalent-length losses; static head and equipment losses are added and the margin is applied to give total head. The pump flow is taken as the largest segment flow.
| Item | Equation | Notes · basis |
|---|---|---|
| Straight pipe | Δp_L = R · L, R = (f / D) · ρV²/2 | f from Colebrook (64/Re if laminar). Roughness is the pipe type's default (steel 0.046 mm, copper 0.0015 mm). Same function as the pipe sizing calculator |
| Fittings and valves | Δp_K = K · ρV²/2, K = f_T · Σ n·(L/D) | Crane TP-410 method. n is the count, L/D from the table below |
| Fully turbulent friction factor | f_T = [−2 log₁₀(ε_T / (3.7 D))]⁻², ε_T = 0.046 mm | Crane defines f_T as the fully turbulent value for clean commercial steel; copper and stainless use it too (50A SGP: 0.0190). Values from this formula can differ from the f_T in Crane's table by up to about 4 % depending on size (e.g. 4 in: table 0.017, formula 0.0163) |
| Equivalent length | Δp_E = R · L_e | For strainers and special valves not in the table, enter the maker's equivalent length in m |
| Total head | H = (H_s + Σ Δp / (ρ g) + H_e) × (1 + m) | H_s static head (negative if the discharge level is lower), H_e equipment head (kPa divided by ρ g), m the margin. This calculator applies the margin to the whole sum; some practice applies it to friction losses only. If H is 0 or less, the result says no pump is needed |
| Water and shaft power | P_w = ρ g Q H, P_s = P_w / η | Q in m³/s, H in m, η the pump efficiency at the duty point |
Fitting L/D values
Only values checked in the Crane TP-410 appendix are listed. K is shown for 50A SGP pipe (f_T 0.0190). Enter other fittings in the equivalent-length field.
| Fitting | L/D | K (50A SGP) |
|---|---|---|
| 90° elbow | 30 | 0.57 |
| Tee, run | 20 | 0.38 |
| Tee, branch | 60 | 1.14 |
| Gate valve | 8 | 0.15 |
| Swing check valve | 100 | 1.90 |
Worked example
Water at 20 °C (ρ = 998.21 kg/m³), SGP steel. Segment 1: 80A (bore 80.7 mm), 600 L/min, 50 m straight, 6 elbows, 2 tees on the run, 2 gate valves, 1 swing check. V = 1.955 m/s, f = 0.01960, R = 463.3 Pa/m, so the straight loss is 23.16 kPa. Σ L/D = 6×30 + 2×20 + 2×8 + 100 = 336, f_T = 0.01720, K = 5.780 and ρV²/2 = 1,907.7 Pa give 11.03 kPa for fittings. Total 34.19 kPa = 3.493 m.
Segment 2: 65A (bore 67.9 mm), 300 L/min, 30 m straight, 4 elbows, 1 tee branch, 1 gate valve and a strainer of 3 m equivalent length. V = 1.381 m/s, R = 297.0 Pa/m: straight 8.91 kPa, Σ L/D = 188, f_T = 0.01790, K = 3.365 give 3.20 kPa for fittings, and 0.89 kPa for the strainer. Total 13.00 kPa = 1.328 m.
Static head 15 m, chiller evaporator 50 kPa = 5.108 m. Subtotal 15 + 4.821 + 5.108 = 24.93 m; with a 10 % margin the total head is 27.42 m (268.4 kPa). Water power = 998.21 × 9.80665 × 0.01 × 27.42 = 2.68 kW; at 60 % efficiency the shaft power is 4.47 kW.
Limits
Check pump selection and the performance curve (duty point, efficiency, NPSH) against the maker's data. This calculator sums one path in series; it does not balance flows between parallel branches or include control-valve drops.
L/D values are representative; actual fittings and valves vary with maker and size. If you have maker's data, use the equivalent-length field.
Sources
- Crane Co., Technical Paper No. 410, Flow of Fluids Through Valves, Fittings, and Pipe: K = f_T·(L/D), L/D table, definition of f_T
- ASHRAE Handbook, Fundamentals (SI), Pipe Sizing: Darcy-Weisbach and Colebrook
- IAPWS R6-95 (water density), IAPWS R12-08 (water viscosity)
- JIS G 3452 carbon steel pipes, JIS G 3459 stainless steel pipes, ASTM B88 copper tube
Last updated 2026-10-07.