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Pump & Fan Selection Calculator — H-Q Curve, NPSH & Affinity Laws (ISO 9906)

Governing standard: ISO 9906· ISO 9906:2012 — Rotodynamic pumps: hydraulic performance acceptance tests · Darcy-Weisbach pipe friction (Swamee-Jain) · Affinity laws

How ISO 9906 works — the method explained

The MechanixCalc pump and fan selection calculator sizes and verifies centrifugal, axial and multistage pumps to ISO 9906 — the international standard for rotodynamic pump hydraulic performance acceptance tests. Enter the pump curve (shutoff head, BEP flow and head, efficiency) and the system (static head, pipe geometry, fluid properties), and the tool locates the operating point on the H-Q curve via bisection, checks cavitation using the ISO 9906 NPSHa formula, and returns shaft power, motor size and the affinity-law part-speed savings in a single pass.

It is built for process, HVAC and water-supply engineers who need a defensible pump selection backed by a standards-cited calculation — not a manual graphical intersection. The series/parallel multi-pump module lets you compare single, series and parallel configurations against the same system curve, and the affinity-law panel quantifies the energy saving from a variable-speed drive at any operating fraction.

What this calculator does

  • ISO 9906 H-Q pump curve with bisection-solved operating point on the system curve
  • NPSH cavitation check to ISO 9906 §3.8.4 with safety factor and suction-head sensitivity chart
  • Affinity-law speed and impeller-trim scaling (Q ∝ N, H ∝ N², P ∝ N³) with VSD energy-saving estimate
  • Series and parallel multi-pump configuration analysis with combined H-Q curve and operating point
  • Darcy-Weisbach pipe friction (Swamee-Jain explicit factor) for commercial steel, cast iron and smooth pipe
  • Specific-speed (nq) classification — centrifugal, mixed-flow, axial — with BEP efficiency estimate
  • Branded PDF engineering report with the full method, H-Q canvas and cavitation chart

Method & formulas

Operating point — H-Q curve intersection (ISO 9906)

The pump H-Q curve is modelled as a shape-parametric quadratic anchored at shutoff head H₀ and best-efficiency-point (BEP) flow Q_BEP and head H_BEP. The system curve is H_sys = H_static + R·Q², where R is the Darcy-Weisbach resistance coefficient computed from pipe geometry, roughness and the Swamee-Jain explicit friction factor. The tool finds the intersection by bisection (200 iterations, convergence < 0.001 m), so the operating point is correct even when the system has significant static head — unlike the pure affinity-law shortcut that is only valid for friction-only systems.

At the operating point the tool also reads the pump efficiency from the parabolic efficiency curve (peaked at η_BEP), computes hydraulic power and shaft power, and identifies whether the duty point lies in the acceptable BEP zone (±20% of Q_BEP).

Hydraulic and shaft power
P_hyd = ρ · g · Q · H and P_shaft = P_hyd / η_p

where P_hyd = hydraulic power (W); ρ = fluid density (kg/m³); g = 9.81 m/s²; Q = flow at operating point (m³/s); H = total head at operating point (m); P_shaft = shaft power (W); η_p = pump efficiency at operating point (–)

System resistance coefficient
H_sys = H_static + R · Q² where R = f · (L/D) / (2g · (3600 · A)²)

where H_sys = system head (m); H_static = static head (m); R = resistance coefficient (m·h²/m⁶); f = Darcy-Weisbach friction factor; L = pipe length including equivalent fitting length (m); D = internal pipe diameter (m); A = pipe cross-sectional area (m²); Q = flow (m³/h)

Cavitation check — NPSHa to ISO 9906 §3.8.4

Cavitation occurs when the local static pressure at the pump suction falls below the fluid vapour pressure, collapsing vapour bubbles and causing impeller erosion and noise. ISO 9906 §3.8.4 defines the available net positive suction head as the difference between the absolute pressure at the suction flange and the vapour pressure, expressed as a head — without a separate velocity head correction, since that term is embedded in the pump's own NPSH_r measurement convention. The tool flags a cavitation risk when NPSHa < 1.1 × NPSH_r (less than 10% safety margin over the required NPSH).

ISO 9906 NPSHa
NPSHa = (P_atm − P_v) / (ρ · g) − H_s − h_f

where NPSHa = available net positive suction head (m); P_atm = absolute pressure at pump suction / atmospheric pressure (Pa); P_v = fluid vapour pressure at operating temperature (Pa); ρ = fluid density (kg/m³); g = 9.81 m/s²; H_s = suction lift (positive if pump is above the source, m); h_f = friction loss in the suction line (m)

Affinity laws and specific speed (ISO 9906)

The pump affinity laws describe how flow, head and power scale with impeller speed and diameter. They are exact for dynamically similar operating points (same efficiency contour), and provide a close approximation across the normal speed range of a variable-speed drive. The specific speed nq classifies the pump hydraulic type and predicts the achievable BEP efficiency.

Affinity laws (speed change)
Q₂/Q₁ = (N₂/N₁) · (D₂/D₁) H₂/H₁ = (N₂/N₁)² · (D₂/D₁)² P₂/P₁ = (N₂/N₁)³ · (D₂/D₁)³

where Q = volumetric flow (m³/h); H = total head (m); P = shaft power (kW); N₁, N₂ = rotational speeds (rpm); D₁, D₂ = impeller diameters (m or mm, ratio only)

Specific speed
nq = N · √Q / H^0.75

where nq = specific speed (dimensionless metric form); N = speed (rpm); Q = BEP flow (m³/s); H = BEP head (m). nq < 25: radial/centrifugal; 25–70: mixed-flow; > 70: axial

Worked example

Select the motor size for a centrifugal pump delivering 50 m³/h at 30 m total head with a pump efficiency of 75 %, pumping water (ρ = 1000 kg/m³).

Given

  • Flow Q50 m³/h (= 0.01389 m³/s)
  • Total head H30 m
  • Pump efficiency η_p0.75 (75 %)
  • Fluid density ρ1000 kg/m³

Result

  • Hydraulic power P_hyd4.08 kW
  • Shaft power P_shaft5.44 kW
  • Recommended motor7.5 kW (IEC standard)
  1. Convert flow to SI: Q = 50 / 3600 = 0.013 89 m³/s.
  2. Compute hydraulic power: P_hyd = ρ · g · Q · H = 1000 × 9.81 × 0.013 89 × 30 = 4 083 W = 4.08 kW.
  3. Compute shaft power: P_shaft = P_hyd / η_p = 4 083 / 0.75 = 5 444 W = 5.44 kW.
  4. Apply a 15 % service margin and motor efficiency of 92 %: P_motor = 5.44 / 0.92 = 5.91 kW; with 15 % margin, select next standard motor above 5.91 × 1.15 = 6.80 kW.
  5. Standard IEC motor sizes: 4, 5.5, 7.5, 11 kW — select 7.5 kW motor.

Illustrative — verify against your actual pump curve, system curve and fluid properties. Always confirm with pump manufacturer data and account for suction-side NPSH margin before final selection.

Frequently asked questions

Which standard does this pump calculator use?

The operating-point and NPSH calculations follow ISO 9906:2012 — the international standard for rotodynamic pump hydraulic performance acceptance tests. The NPSH available formula uses the ISO 9906 §3.8.4 convention (no separate velocity-head term at the suction flange). Pipe friction follows the Darcy-Weisbach equation with the Swamee-Jain explicit approximation for the friction factor. The affinity laws (Q ∝ N, H ∝ N², P ∝ N³) are standard dimensional-analysis results valid for dynamically similar pump operation. The governing method is shown in the generated PDF report.

What is cavitation and how does the NPSH check work?

Cavitation happens when local pressure at the pump inlet drops below the fluid's vapour pressure, causing vapour bubbles to form and then violently collapse on the impeller — eroding metal and causing noise and vibration. The calculator computes NPSHa = (P_atm − P_v)/(ρg) − H_s − h_f (ISO 9906 §3.8.4) and flags a cavitation risk whenever NPSHa < 1.1 × NPSH_r (less than 10 % safety margin). To fix a marginal result, raise suction pressure, lower suction lift, reduce suction-line losses, or select a pump with lower NPSH_r.

How do series and parallel pump configurations work?

Pumps in series add heads at the same flow, so the combined H-Q curve is shifted upwards — useful for high static-head systems. Pumps in parallel add flows at the same head, shifting the combined curve to the right — useful for high-flow, low-head systems. The calculator finds the operating point of the combined curve against the system curve via bisection, so the result is correct even when the two pumps have different characteristic curves or the system has significant static head.

How do affinity laws help with variable-speed drives (VSDs)?

The affinity laws state that flow scales linearly with speed, head scales with speed squared, and power scales with speed cubed. Halving the speed therefore reduces shaft power to one eighth — an 87.5 % saving in ideal frictionless conditions. The calculator computes the real part-speed operating point by intersecting the speed-scaled H-Q curve with the actual system curve (not the purely affinity-scaled duty point), giving an honest power saving that accounts for static head.

Is the pump calculator free?

You can use the full calculator during a free 30-minute preview with no sign-up required, and a free 14-day account trial unlocks every tool with no credit card. The branded PDF engineering report and saved calculations are part of a paid plan.

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