pump-curve-analysis

name	pump-curve-analysis
description	Pump curve analysis — H-Q, P-Q, η-Q curves, system curve, operating point, parallel/series pumps, NPSH, affinity laws, specific speed, variable speed drive, pump selection.
metadata	{"priority":7,"promptSignals":{"phrases":["pump curve","pump operating point","system curve","pump selection","pump affinity laws","NPSH pump","pump specific speed"],"minScore":3}}

Pump Curve Analysis — Complete Skill

H-Q (Head-Flow) Curve

Pump head vs. flow rate; characteristic of pump at given speed N Shut-off head H_0: head at Q = 0; no flow Best Efficiency Point (BEP): maximum η; design operating target

Typical curve equation (approximation): H = H_0 - A × Q² [parabolic; for most centrifugal] Or: H = H_0 - B × Q^n (n ≈ 1.5–2.0)

Steep vs. flat curve: Steep: H changes a lot with Q → better for variable flow Flat: H nearly constant → better for stable pressure requirement

System Curve

Represents resistance that system imposes on pump: H_sys = H_static + H_friction H_static = elevation difference + pressure difference [m] H_friction = R × Q² (friction dominated) R = system resistance coefficient [m/(m³/s)²]

Operating point: intersection of pump H-Q and system H-Q curves Stable operation: system curve slope > pump curve slope at intersection (Positive pump curve slope at low Q can cause instability)

Affinity Laws (Speed Change N₁ → N₂)

Q₂/Q₁ = N₂/N₁ H₂/H₁ = (N₂/N₁)² P₂/P₁ = (N₂/N₁)³

Impeller diameter change D₁ → D₂ (trim): Q₂/Q₁ = D₂/D₁ H₂/H₁ = (D₂/D₁)² P₂/P₁ = (D₂/D₁)³

Effect on efficiency: η ≈ constant for similar operating point on affinity curve BEP shifts along Q∝N, H∝N² parabola through origin

Specific Speed

Dimensionless: N_s,dim = N × Q^(1/2) / (g × H)^(3/4) [N in rpm → need unit conversion; more useful: below]

US customary: N_s = N [rpm] × Q^0.5 [gpm]^0.5 / H [ft]^0.75

Metric: N_q = N × Q^0.5 / H^0.75 [N in rpm, Q in m³/s, H in m]

Impeller type vs. N_s: N_s < 500 (US): radial; 500–3500: mixed flow; 3500–15000: axial

Efficiency Curves

η = P_hydraulic / P_shaft = (ρ g Q H) / P_shaft

Typical peak η: Small pumps (<10 kW): 55–70% Medium (10–100 kW): 70–82% Large (>100 kW): 80–90%

Efficiency at off-BEP: η falls both left and right of BEP Operating below 70% BEP flow → recirculation, vibration, bearing loads Operating above 130% BEP → cavitation, overloading

NPSH (Net Positive Suction Head)

NPSH_A (available): NPSH_A = (P_suction,abs - P_v) / (ρ g) + V_suction²/(2g) = H_atm - H_vapor - H_suction_friction - H_elevation_suction

NPSH_R (required): from pump curve (minimum pressure at impeller eye to avoid cavitation) Typically 1–8 m for most pumps; increases with Q

Design requirement: NPSH_A > NPSH_R + 0.5 m (NPSH margin) Or NPSH_A / NPSH_R > 1.1–1.3 (margin ratio)

3% head drop definition: NPSH_R at which H drops 3% from non-cavitating value (standard manufacturer test)

Sigma (Thoma cavitation number): σ = NPSH_A / H_pump → compare to σ_c (critical from Pfleiderer)

Parallel and Series Pump Operation

Parallel (common discharge header)

Same head H; total flow Q_total = Q₁ + Q₂ Operating point: combined curve vs. single system curve Useful when: single pump can't provide required flow; redundancy needed Caution: flat system curve → one pump may shut off (its H < system H)

Parallel H-Q combined: At each H value: Q_combined = Q₁(H) + Q₂(H)

Series (one feeds next)

Same flow Q; total head H_total = H₁ + H₂ Useful when: single pump can't achieve required pressure Application: boiler feed pumps (multi-stage = series)

Series combined H-Q: At each Q value: H_combined = H₁(Q) + H₂(Q)

Variable Speed Drive (VSD) Operation

Energy saving at reduced flow: Without VSD: throttle valve → dissipate excess head; motor runs at full power With VSD: reduce speed → reduce H and Q following affinity laws; P ∝ N³ → cubic savings

Annual energy savings: At 60% of design flow: P_ratio = (0.6)³ = 0.216 → 78% power reduction (theoretical) With system curve effects: typical 40–65% energy saving depending on duty cycle

Minimum speed: typically 20–25% of rated; below → cooling fan issues, lubrication VSD penalty: ~2–5% drive efficiency loss

Pump Selection Procedure

1. Determine Q_design and H_design (from system curve at design flow)
2. Calculate NPSH_A
3. Calculate specific speed N_s → select impeller type
4. Select pump from manufacturer curves:
   • Operating point at or near BEP (70–110% BEP flow)
   • NPSH_A > NPSH_R + margin
   • Motor power rating at maximum possible flow (end of curve) + service factor
5. Check viscosity correction (Hydraulic Institute correction for μ > 5 cSt)
6. Check minimum flow requirement (manufacturer specified)

Viscosity Correction (Hydraulic Institute)

For viscous liquids (μ > 5 mPa·s = 5 cP): Apply corrections: Q_actual = C_Q × Q_water; H_actual = C_H × H_water; η_actual = C_η × η_water Correction factors < 1; obtain from HI Std. 9.6.7 nomograph vs. viscosity and N_s

Output

Provide: H-Q curve equation, BEP operating point (Q_BEP, H_BEP, η_BEP), operating point (Q_op, H_op) on system curve, NPSH_A vs. NPSH_R [m], specific speed N_s, power absorbed P [kW], affinity law scaled curves at N₂, parallel/series combined curve data, VSD savings estimate [%], motor size recommendation.