1. Size to the System
A centrifugal pump does not have a single "head" — it has a head-flow curve. Where it actually operates is set by the system it pumps into: the elevation it lifts against, the pressure it discharges into, and the friction of the pipe and fittings. Sizing a pump means building the system head at the design flow (the total dynamic head, TDH), then choosing a pump whose curve passes through that point at good efficiency.
Two halves of the job
(1) System head — from pipe length, fittings, and elevation (this is the "lengths of pipe, elbows, verticals" part). (2) Pump power — head and flow become water, brake, and motor horsepower. This calculator does both in one pass and draws the system curve.
2. Total Dynamic Head
TDH is the sum of four heads, all in feet of the pumped fluid:
TDH = hstatic + hpressure + hfriction + hminor
- hstatic — the elevation difference (discharge level − suction level). The "verticals."
- hpressure — any vessel pressure difference: h = Δp(psi) × 2.31 / SG.
- hfriction — straight-pipe friction (Section 3).
- hminor — fitting losses (Section 3).
Only the static + pressure part is constant; the friction + minor part grows with flow — which is what makes the system curve.
3. Friction & Minor Losses
Straight-pipe friction — Darcy-Weisbach
hfriction = f · (L / D) · V² / 2g
f = Darcy friction factor (Colebrook-White, from Reynolds number and relative roughness); L = length; D = inside diameter; V = velocity; g = 32.174 ft/s²
Fittings — Crane TP-410 K-factor method
Each fitting adds a head of K × velocity head, with K from the fully-turbulent friction factor times an L/D ratio:
hminor = ΣK · V² / 2g, K = fT · (L/D)
| Fitting | L/D (Crane TP-410) |
|---|---|
| 90° standard elbow | 30 |
| 45° elbow | 16 |
| Tee (through / branch) | 20 / 60 |
| Gate valve (open) | 8 |
| Globe valve (open) | 340 |
| Ball valve (open) | 3 |
| Swing check valve | 100 |
| Butterfly valve | 45 |
| Pipe entrance / exit | K = 0.5 / 1.0 (fixed) |
The calculator uses the same Crane TP-410 K-factor map as the site's Pressure Drop calculator; the two agree to the digit on the friction and minor losses.
4. System Curve & Duty Point
Because friction and minor losses scale with V² (and V ∝ Q), the system head is:
Hsys(Q) = (hstatic + hpressure) + (hfriction + hminor)design · (Q / Qdesign)²
This is a parabola that starts at the static head (at zero flow) and rises with the square of flow. The pump runs where its head-flow curve crosses this system curve — the duty point. A flat system (mostly static) gives a stable duty point; a friction-dominated system is more sensitive to throttling and pipe fouling. To combine pumps or match against a real pump curve, use the Series & Parallel calculator.
5. Pump & Motor Power
WHP = Q · TDH · SG / 3960 (Q in gpm, TDH in ft)
BHP = WHP / ηpump
Motor HP ≥ BHP · SF → next standard NEMA size
Electrical input = BHP / ηmotor × 0.746 kW
Water horsepower is the useful hydraulic power; brake horsepower divides by pump efficiency (typically 60–80% for process pumps near BEP). The motor nameplate is a shaft-output rating, so the frame is sized on the design brake power (BHP × service factor) rounded up to a NEMA size — motor efficiency does not enter frame selection; it sets the electrical input power instead. Specific speed Ns = N√Q / TDH0.75 suggests the impeller type (radial, mixed, or axial).
6. NPSH Available
NPSHa = (Pabs − Pvapor) · 2.31 / SG + hs,suction − hf,suction
NPSH available must exceed the pump's NPSH required by a margin (typically ≥ 2–3 ft) to avoid cavitation. The suction static head is positive for a flooded suction and negative for a lift. For a detailed treatment, including margin and recirculation, use the dedicated NPSH Available and Suction Specific Speed calculators.
7. Worked Example
Water (SG 1.0, 1 cP), 8″ Sch 40 pipe (ID 7.981″), 500 ft developed length, 1,000 gpm, 50 ft static lift, fittings: 4 × 90° elbows, 2 gate valves, 1 entrance, 1 exit. Pump efficiency 75%, motor 94%, SF 1.10, 1,800 rpm.
Step 1 — Velocity & friction factor
V = (1,000/448.8) / [(π/4)(7.981/12)²] = 2.228 / 0.347 = 6.41 ft/s
Re ≈ 3.96 × 10⁵ → Colebrook f ≈ 0.0160; velocity head V²/2g = 0.639 ft
Step 2 — Friction & minor heads
hfriction = 0.0160 · (500 / 0.665) · 0.639 = 7.7 ft
ΣK = 4(fT·30) + 2(fT·8) + 0.5 + 1.0 ≈ 3.4 → hminor = 3.4 · 0.639 = 2.2 ft
Step 3 — TDH & power
TDH = 50 + 0 + 7.7 + 2.2 = 59.9 ft
WHP = 1,000 · 59.9 · 1.0 / 3960 = 15.1 hp; BHP = 15.1 / 0.75 = 20.2 hp
Motor ≥ 20.2 · 1.10 = 22.2 → 25 hp NEMA (shaft-rated; electrical input ≈ 20.2/0.94 × 0.746 = 16.0 kW); Ns = 1800√1000 / 59.90.75 ≈ 2,645 (Francis/radial-mixed)
Result
The pump must deliver ~60 ft at 1,000 gpm; select a ~25 hp motor. The static lift (50 ft) dominates here, so the duty point is stable — friction and fittings add only ~10 ft. (Matches the calculator and the site's Pressure Drop engine to the digit.)
8. Where to Go Next
Once you have TDH and the duty point, branch to the specialized pump tools: Pump Sizing (full datasheet), NPSH Available, Pump Type Selector, Series & Parallel, Minimum Flow, Affinity Laws, Viscosity Correction, Power & Energy Cost, and the mechanical tools (nozzle loads, bearing life, seal flush plan). The calculator page carries the full roadmap.
Preliminary design. Confirm the duty point against the actual manufacturer pump curve, run a detailed NPSH check, and verify with a licensed engineer before procurement.
Frequently Asked Questions
How do you size a pump from the piping system?
Build the total dynamic head (TDH) from the system: static head from elevation, pressure head from any vessel pressure difference, friction head in the straight pipe (Darcy-Weisbach), and minor losses from fittings (Crane TP-410 K-factors for elbows, tees, valves, entrances and exits). TDH at the design flow is the head the pump must deliver. Brake horsepower is then Q×TDH×SG/3960 divided by pump efficiency, and the motor is the next NEMA size above BHP×service factor (the nameplate is a shaft-output rating; motor efficiency sets the electrical input, not the frame).
What is the system curve and the duty point?
The system curve plots required head versus flow: a constant static part (elevation plus pressure head) plus a dynamic part (friction plus minor losses) that grows with the square of flow. The pump operates where its own head-flow curve crosses the system curve — the duty point. This calculator reports the system curve at 0 to 125 percent of the design flow.
What pump head do I need for elbows and valves?
Each fitting adds a minor-loss head of K times the velocity head V² over 2g, where K = fT × (L/D) from Crane TP-410 (for example L/D ≈ 30 for a 90° standard elbow, 8 for a gate valve, 340 for a globe valve). The calculator sums all fittings into the minor-loss head.
How is NPSH available calculated?
NPSH available equals the absolute pressure at the suction source minus vapor pressure (converted to feet), plus the static suction head (positive if the source is above the pump, negative if it is a lift), minus suction-line friction. Keep NPSHa at least 2 to 3 feet above the pump NPSHr.