The affinity laws of pumps are fundamental principles used to predict how changes in pump speed (N) or impeller diameter (D) affect pump performance. These laws are derived from dimensionless analysis of three critical parameters: flow (Q), total head (H), and power (P).
While actual pump performance curves must be determined by experimental testing, affinity laws provide a reliable way to estimate performance under different operating conditions, assuming the pump impeller is geometrically similar and operates at equal specific speed.
🔹 Why Affinity Laws Matter
Help engineers predict pump performance without full-scale testing.
Useful for pump resizing, retrofitting, and system optimization.
Allow comparison of flow, head, and power requirements when speed or impeller diameter changes.
Support energy conservation strategies by optimizing pump operation.
🔹 Variables Affecting Pump Performance
Pump Speed (N) – measured in revolutions per minute (RPM).
Impeller Diameter (D) – measured in millimeters or inches.
If, Pump speed-N(rpm) is constant,
If pump with a constant speed(N), the capacity will be directly proportional to the impeller diameter, the head will be directly proportional to the square of the impeller diameter, and the required power will be directly proportional to the cube of the impeller diameter.
Q2 = Q1 (D2/D1),
H2 = H1 Sqr of (D2/D1)
P2 = P1 Cubic of (D2/D1)
where,
Q2 = New capacity (Flow rate)
Q1 = Initial capacity (Flow rate)
H2 = New Head in mtr
H1 = Initial Head in mtr
D2 = New Diameter of impeller
D1 = Initial Diameter of impeller
P2 = New Power in KW
P1 = Initial Power in KW
If, Pump Impeller Diameter-D is constant,
If pump with a fixed diameter impeller(D), the capacity will be directly proportional to the speed, the head will be directly proportional to the square of the speed, and the required power will be directly proportional to the cube of the speed.
Q2 = Q1 (N2/N1),
H2 = H1 Sqr of (N2/N1)
P2 = P1 Cubic of (N2/N1)
where,
Q2 = New capacity (Flow rate)
Q1 = Initial capacity (Flow rate)
H2 = New Head in mtr
H1 = Initial Head in mtr
N2 = New speed of pump in rpm
N1 = Initial speed of pump in rpm
P2 = New Power in KW
P1 = Initial Power in KW
If Diameter-D and Pump speed-N(rpm) change,
Q2 = Q1 (D2/D1 x N2/N1)
H2 = H1 Sqr of (D2/D1 x N2/N1)
P2 = P1 Cubic of (D2/D1 x N2/N1)
where,
Q2 = New capacity (Flow rate)
Q1 = Initial capacity (Flow rate)
H2 = New Head in mtr
H1 = Initial Head in mtr
N2 = New speed of pump in rpm
N1 = Initial speed of pump in rpm
P2 = New Power in KW
P1 = Initial Power in KW
D2 = New Diameter of impeller
D1 = Initial Diameter of impeller
Practical Applications of Affinity Laws
Pump resizing: Estimate performance after trimming impeller diameter.
Variable speed drives (VFDs): Predict flow and head changes when speed varies.
Energy optimization: Reduce power consumption by adjusting speed instead of throttling.
System design: Match pump curves to system requirements without trial‑and‑error.
🔹 Key Takeaways
Affinity laws link flow, head, and power to pump speed and impeller diameter.
They are valid only when pumps are geometrically similar and operate at equal specific speed.
Engineers use these laws for performance prediction, energy savings, and pump selection.
Always verify results with actual pump curves for accuracy.
