| 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
- Determine Q_design and H_design (from system curve at design flow)
- Calculate NPSH_A
- Calculate specific speed N_s → select impeller type
- 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
- Check viscosity correction (Hydraulic Institute correction for μ > 5 cSt)
- 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.
