According to the affinity laws for geometrically similar centrifugal pumps, how do performance variables scale with rotational speed $N$ for a fixed impeller diameter?
Options:
(A) Discharge varies directly with speed ($Q \propto N$)
(B) Head varies directly with the square of speed ($H \propto N^2$)
(C) Power consumption varies directly with the cube of speed ($P \propto N^3$)
(D) Efficiency varies directly with the fourth power of speed ($\eta \propto N^4$)
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
1. Flow velocity $v \propto u \propto N \implies Q \propto N$ (A is true).
2. Head $H \propto v^2/2g \propto N^2$ (B is true).
3. Power $P = \gamma Q H \propto N \cdot N^2 = N^3$ (C is true).
4. Efficiency is dimensionless and remains approximately constant across modest speed shifts (D is false).