Pump Sizing Guide: Flow Rate, TDH and NPSH Calculations (with Free Calculator)

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Engineering Guide · Fluid Systems

Pump Sizing: Flow Rate, TDH and NPSH Calculations

Step-by-step method aligned with ANSI/HI (American), BS EN ISO (British/European) practice.

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Figure 1: Pump system and TDH components

1. Which standard applies?

Region	Reference	Typical use
American	ANSI/HI 9.6.1 (NPSH margins), ANSI/HI 14.6 (tests), API 610	US units (gpm, ft, psi)
British	BS EN ISO 9906, BS EN 806, CIBSE Guide C	SI (m³/h, m, kPa)
European	EN ISO 9906, EN ISO 5199, EN 733	SI

The physics is identical; the standards differ in units, test grades and recommended margins.

2. Flow rate (Q)

Establish the design flow from demand, then add a margin (typically 5–10%) and keep pipe velocity within 1–3 m/s (3–10 ft/s).

$Q=v·A=v·\frac{\pi D^2}{4}$ Q in m³/s; 1 m³/h = 4.403 US gpm.

3. Total Dynamic Head (TDH)

$\mathrm{TDH}=H_s+h_f+h_m+\frac{P_d-P_s}{\rho g}+\frac{v_d^2-v_s^2}{2g}$ H_s static head, h_f friction loss, h_m minor (fitting) losses.

Friction loss – Darcy–Weisbach (ISO/European/British practice; also accepted in the US):

$h_f=f\frac{L}{D}\frac{v^2}{2g}$ f from Colebrook–White or Moody chart.

Hazen–Williams (common in US water/fire systems, SI form):

$h_f=10.67\frac{L}{C^{1.852}{D}^{4.87}}{Q}^{1.852}$

Minor losses:

$h_m=K\frac{v^2}{2g}$

Figure 2: Pump curve, system curve and duty point

4. NPSH available and required

${\mathrm{NPSH}}_a=\frac{P_a-P_v}{\rho g}\pm Z_s-h_{f,s}$ P_a absolute suction-surface pressure, P_v vapour pressure, Z_s static suction head (+ flooded, − lift), h_f,s suction line losses.

Acceptance criterion:

${\mathrm{NPSH}}_a\ge M·{\mathrm{NPSH}}_r$ M ≈ 1.1–1.3 (or +0.6 m minimum). ANSI/HI 9.6.1 gives higher margins for high-energy or large pumps; NPSH_r is taken at 3% head drop per EN ISO 9906 / ANSI/HI 14.6.

5. Power

$P_h=\rho gQH,P_{\mathrm{shaft}}=\frac{P_h}{{\eta }_p}$ US form: BHP = Q(gpm)·H(ft)·SG / (3960·η).

6. Try it: interactive calculator (SI)

Pick the unit for each value from its drop-down. Values convert automatically when you change a unit.

Show results in:

Optional: manufacturer pump curve
One "flow, head, efficiency" line per point (5-6 points). Efficiency is optional: use % (e.g. 72) or a fraction (0.72). Use the flow unit chosen above and the Head unit chosen in "Show results in".

Darcy–Weisbach with Swamee–Jain friction factor; single pipe size; water properties from temperature. Indicative only.

7. Worked example (SI)

Clean water at 20 °C (ρ = 998 kg/m³, P_v = 2.34 kPa), Q = 50 m³/h, 100 mm pipe, 120 m long, ε = 0.045 mm, ΣK = 6, flooded suction. These are the calculator's default values, so you can reproduce every line below above.

Item	Value
Static head Hs	18.0 m
Friction loss (v = 1.77 m/s, Re ≈ 176,000, f = 0.0189)	3.61 m
Minor losses (ΣK = 6)	0.96 m
TDH (≈ 74 ft)	22.6 m
NPSHa = 10.11 + 2.0 − 0.8	11.3 m
NPSHr (datasheet) ×1.3	3.5 × 1.3 = 4.55 m → OK
Shaft power at η = 70%	≈ 4.4 kW (select next motor size, e.g. 5.5 kW). Flow ≈ 220 gpm.

8. Common mistakes

• Using gauge instead of absolute pressure for NPSH_a.
• Ignoring viscosity, temperature or altitude corrections.
• Selecting far from the best efficiency point (aim for 70–120% of BEP flow).
• Skipping the NPSH margin on hot or hydrocarbon services.

Disclaimer: for educational use. Verify with the applicable standard and manufacturer data before design.

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