Mechanical Engineering - Hydraulic Machines - Discussion

I think C is the right answer.

The relationship can be explained by the Affinity laws as described below:

Law 1. With impeller diameter (D) held constant:

Law 1a. Flow is proportional to shaft speed:
(Q1/Q2) = (N1/N2).

Law 1b. Pressure or Head is proportional to the square of shaft speed:
(H1/H2) = (N1/N2)^2.

Law 1c. Power is proportional to the cube of shaft speed:
(P1/P2) = (N1/N2)^3.

Law 2. With shaft speed (N) held constant:

Law 2a. Flow is proportional to impeller diameter:
(Q1/Q2) = (D1/D2).

Law 2b. Pressure or Head is proportional to square of impeller diameter:
(H1/H2) = (D1/D2)^2.

Law 2c. Power is proportional to the cube of impeller diameter:
(P1/P2) = (D1/D2)^3.

where
Q is the volumetric flow rate (e.g. CFM, GPM or L/s),
D is the impeller diameter (e.g. in or mm),
N is the shaft rotational speed (e.g. rpm),
H is the pressure or head developed by the fan/pump (e.g. psi or Pascal), and
P is the shaft power (e.g. W).

According to affinity law, discharge is proportional to rpm, head is proportional to the square of the head, &power is proportional to the cube of rpm. On the other hand, discharge is proportional to shaft diameter, head is proportional to the square of diameter & power is proportional to the cube of shaft diameter.

Not right.

The correct answer Will be d^5.

As per affinity law break horse power is directly proportional to cube of diameter or cube of rpm.