Mechanical Engineering - Hydraulic Machines - Discussion

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).

I think C is the right answer.

There are so much of answers if we look into this from different laws and formulas. What answer should we choose in the exams?

Is someone there to give the most appropriate answer?

Power = density * acceleration due to gravity * discharge * head loss.

Where Q = A * V = area * velocity.

Area= (pi/4) *d^2.

Velocity= (pi * d * N/60).

Head loss= (friction * length * velocity^2)/(2 * g * d).

= (f * length * (pi * d * N/60) ^2)/(2 * g * d).

Assume f, length and N are constant.

Head loss proportional to diameter.

Power = constant * d^4.

I think C is the correct answer.

I think D^5 is right answer.

Because from similarity law come the equation of power coefficient P/(N^3 D^5) that's it.

Answer D is correct, if there is a difference between the velocity triangles and if not then answer C is correct.

@Safy.

I think its d^5.

Because p/(N^3*D^5) = Constant.

Cube of diameter. As per affinity laws option C is correct.

Power is proportional to cube of diameter.