1
Minimum Power from Pressure (Head)
Affinity Law — Head Scaling
P₂ = ((H₂ / H₁)^1.5) × P₁
—
W
Since H ∝ n², head ratio relates to speed as n₂/n₁ = (H₂/H₁)^0.5,
and since P ∝ n³, it follows that P₂ = (H₂/H₁)^1.5 × P₁
2
Minimum Power from Flow Rate
Affinity Law — Flow Scaling
P₂ = (Q₂ / Q₁)³ × P₁
—
W
Since Q ∝ n (flow proportional to speed), P ∝ n³ gives P₂ = (Q₂/Q₁)³ × P₁
3
Minimum Power from RPM
Affinity Law — Speed Scaling
P₂ = (n₂ / n₁)³ × P₁
—
W
Direct application of the affinity cube law: power varies with the cube of rotational speed.
1
Minimum Power from Flow Rate
Flow Scaling
P₂ = (Q₂ / Q₁)³ × P₁
—
W
P₂ = (Q₂ / Q₁)³ × P₁
2
Minimum Power from RPM
Speed Scaling
P₂ = (n₂ / n₁)³ × P₁
—
W
P₂ = (n₂ / n₁)³ × P₁