Pump Curve Theory

Introduction

Centrifugal pumps are the most common type of pump in process industries. Understanding pump and system curves is essential for proper pump selection, sizing, and ensuring reliable operation. The operating point is where the pump curve intersects the system curve.

Pump Curve (H-Q Curve)

The pump curve shows head (H) as a function of flow rate (Q) for a given impeller and speed:

Shutoff Head (H₀)

Maximum head at zero flow. Pump impeller spins but no fluid moves.

Best Efficiency Point (BEP)

Flow rate where pump operates at maximum efficiency. Target operating range: 80-110% of BEP.

Runout

Maximum flow at minimum head. Operating here risks motor overload and cavitation.

System Curve

The system curve represents the head required to move fluid through the piping system:

H_system = H_static + H_friction

Static Head

H_static = (z_discharge - z_suction) + (P_d - P_s)/(ρg)

Elevation difference + pressure difference

Friction Head

H_friction = (fL/D + ΣK) × V²/(2g)

Pipe friction + fitting losses. Proportional to Q²

Operating Point

The operating point is the intersection of pump and system curves:

H_pump(Q) = H_system(Q)

At this point, the pump delivers exactly the head required by the system at a specific flow rate. The operating point should be near BEP for optimal efficiency and pump life.

Pump Power and Efficiency

Hydraulic Power

P_hyd = ρgQH

Power transferred to the fluid (kW)

Shaft Power (Brake Power)

P_shaft = P_hyd / η

Power required from motor (kW)

Pump Efficiency

η = P_hyd / P_shaft

Typical range: 60-85% for centrifugal pumps

NPSH - Net Positive Suction Head

NPSH is critical to prevent cavitation (formation of vapor bubbles that damage the impeller):

NPSHa (Available)

NPSHa = (P_atm - P_vapor)/(ρg) + h_s - h_fs

Head available at pump suction from system design

NPSHr (Required)

Minimum NPSH needed by pump (from manufacturer data). Increases with flow rate.

Design Criterion

NPSHa > NPSHr + Safety margin (typically 1-2 m)

Affinity Laws

When pump speed (N) or impeller diameter (D) changes:

Parameter	Speed Change	Diameter Change
Flow (Q)	Q₂/Q₁ = N₂/N₁	Q₂/Q₁ = D₂/D₁
Head (H)	H₂/H₁ = (N₂/N₁)²	H₂/H₁ = (D₂/D₁)²
Power (P)	P₂/P₁ = (N₂/N₁)³	P₂/P₁ = (D₂/D₁)³

Note: Affinity laws are approximate. Efficiency may change with significant modifications.

Pump Selection Guidelines

1.Select pump with BEP close to required operating point

2.Ensure NPSHa exceeds NPSHr with adequate margin

3.Size motor for maximum expected power (consider runout)

4.Consider future capacity needs (control valve range)

5.Avoid operation below 70% or above 120% of BEP

References

Karassik, I.J. "Pump Handbook"
Hydraulic Institute Standards
McCabe, Smith, Harriott "Unit Operations of Chemical Engineering"
API 610 - Centrifugal Pumps for Petroleum Industries