Pump Sizing
Engineering fundamentals for centrifugal pump selection
1. Pump Fundamentals
Centrifugal pumps convert mechanical energy to fluid pressure through impeller rotation. Sizing requires matching pump performance to system requirements.
Key Parameters
| Parameter |
Symbol |
Units |
| Flow rate |
Q |
GPM, BPD, m³/hr |
| Total Dynamic Head |
TDH |
ft, m |
| Differential pressure |
ΔP |
psi, kPa |
| NPSH Available |
NPSHa |
ft, m |
| NPSH Required |
NPSHr |
ft, m |
| Brake horsepower |
BHP |
HP, kW |
| Efficiency |
η |
% |
📊 Centrifugal Pump Cross-Section
Cutaway diagram of single-stage centrifugal pump showing: Suction inlet (eye), impeller with vanes, volute casing, discharge nozzle, shaft, mechanical seal, bearing housing. Show flow path from suction through impeller to discharge. Label key dimensions: impeller diameter, suction/discharge sizes. Indicate rotation direction.
Head vs. Pressure
Converting pressure to head:
H (ft) = P (psi) × 2.31 / SG
H (m) = P (kPa) / (SG × 9.81)
Where SG = specific gravity of liquid
Why use head? Head is independent of fluid density—
a pump develops the same head regardless of fluid pumped.
2. Head Calculations
Total Dynamic Head (TDH) is the total head the pump must develop to move fluid through the system.
TDH = H_static + H_friction + H_velocity + H_pressure
Where:
H_static = Elevation difference (discharge - suction)
H_friction = Friction losses in piping
H_velocity = Velocity head change (usually negligible)
H_pressure = Pressure difference (P_discharge - P_suction) × 2.31/SG
Static Head
H_static = Z_discharge - Z_suction
Positive if pumping uphill, negative if downhill.
Friction Head
H_friction = H_pipe + H_fittings
Darcy-Weisbach:
H_pipe = f × (L/D) × (V²/2g)
Hazen-Williams (water):
H_pipe = 10.44 × L × Q^1.85 / (C^1.85 × D^4.87)
Where:
f = Friction factor
L = Pipe length (ft)
D = Inside diameter (ft or inches)
V = Velocity (ft/s)
C = Hazen-Williams coefficient (100–150)
Q = Flow rate (GPM)
Fitting Losses (K-Method)
| Fitting |
K Factor |
| 90° elbow (standard) |
0.75 |
| 90° elbow (long radius) |
0.45 |
| 45° elbow |
0.35 |
| Tee (through) |
0.40 |
| Tee (branch) |
1.50 |
| Gate valve (full open) |
0.17 |
| Check valve (swing) |
2.00 |
| Strainer |
2.00 |
H_fittings = Σ(K × V²/2g)
Where g = 32.2 ft/s²
📈 System Curve vs. Pump Curve
Graph with Flow (GPM) on X-axis, Head (ft) on Y-axis. Show: (1) System curve starting at static head, curving upward parabolically due to friction; (2) Pump curve starting high at shutoff, curving downward to runout. Mark intersection as "Operating Point." Show BEP (Best Efficiency Point) on pump curve. Indicate stable vs. unstable operating regions.
3. NPSH Requirements
Net Positive Suction Head ensures the pump doesn't cavitate. Available NPSH (system) must exceed required NPSH (pump) with margin.
NPSH Available:
NPSHa = H_atm + H_static,suction - H_friction,suction - H_vapor
NPSHa = (P_suction - P_vapor) × 2.31/SG + Z_liquid - H_f,suction
Where:
H_atm = Atmospheric pressure head (33.9 ft at sea level)
P_suction = Absolute pressure at liquid surface
P_vapor = Vapor pressure of liquid
Z_liquid = Height of liquid above pump centerline
H_f,suction = Friction loss in suction piping
NPSH Margin
Required margin:
NPSHa ≥ NPSHr + Margin
Typical margins:
- General service: 3 ft or 10% of NPSHr
- Hot water: 5 ft minimum
- Boiler feed: 10 ft minimum
- Hydrocarbon: 3–5 ft or per API 610
Vapor Pressure (Selected Fluids)
| Fluid |
Temperature |
Vapor Pressure (psia) |
| Water |
60°F |
0.26 |
| Water |
100°F |
0.95 |
| Water |
200°F |
11.5 |
| Propane |
60°F |
92 |
| Butane |
60°F |
23 |
| Gasoline |
100°F |
8–12 |
⚠ Cavitation: If NPSHa < NPSHr, the pump will cavitate—vapor bubbles form and collapse violently, causing noise, vibration, reduced performance, and impeller damage. Always verify NPSH margin.
4. Power and Efficiency
Hydraulic Power
Hydraulic (water) horsepower:
WHP = Q × H × SG / 3960
Where:
WHP = Water horsepower (HP)
Q = Flow rate (GPM)
H = Total head (ft)
SG = Specific gravity
Alternate (with pressure):
WHP = Q × ΔP / 1714
Where ΔP in psi, Q in GPM
Brake Horsepower
BHP = WHP / η = Q × H × SG / (3960 × η)
Where:
BHP = Brake horsepower (shaft power)
η = Pump efficiency (decimal, e.g., 0.75)
Motor sizing:
Add 10–25% margin to BHP for motor selection
Typical Pump Efficiencies
| Flow Range (GPM) |
Typical Efficiency |
| < 50 |
40–55% |
| 50–200 |
55–70% |
| 200–1000 |
70–80% |
| 1000–5000 |
75–85% |
| > 5000 |
80–90% |
Example Calculation
Given: Q = 500 GPM, TDH = 250 ft, SG = 0.85, η = 72%
WHP = 500 × 250 × 0.85 / 3960 = 26.8 HP
BHP = 26.8 / 0.72 = 37.2 HP
Motor: 37.2 × 1.15 = 42.8 → Select 50 HP motor
5. Pump Selection
Selection Criteria
- Operating point: Should fall on pump curve at 80–110% of BEP flow
- NPSH margin: NPSHa > NPSHr + margin
- Speed: 1750 or 3500 RPM typical (lower speed = longer life)
- Materials: Compatible with fluid (corrosion, erosion)
- Seal type: Packed, mechanical seal, or sealless
Pump Types by Application
| Application |
Pump Type |
Notes |
| Pipeline transfer |
Multistage centrifugal |
High head, API 610 |
| Process circulation |
ANSI centrifugal |
Interchangeable, economical |
| High viscosity |
Positive displacement |
Gear, screw, or progressive cavity |
| Metering/injection |
Reciprocating |
Precise flow control |
| Low NPSH |
Vertical can pump |
Impeller submerged |
Affinity Laws
For speed changes or impeller trim:
Q₂/Q₁ = N₂/N₁ = D₂/D₁
H₂/H₁ = (N₂/N₁)² = (D₂/D₁)²
BHP₂/BHP₁ = (N₂/N₁)³ = (D₂/D₁)³
Where:
N = Speed (RPM)
D = Impeller diameter
VFD savings: Reducing speed by 20% cuts power by ~50% (cube law). Variable frequency drives offer significant energy savings for variable-flow systems.
References
- API 610 – Centrifugal Pumps for Petroleum, Heavy Duty
- Hydraulic Institute Standards
- Crane Technical Paper 410
- Cameron Hydraulic Data Book