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Fluid Mechanics - Engineering

Q1:

Power required by a centrifugal pump is proportional to (where, D = diameter, N = r.p.m)

A N2D3

B ND2

C N2D

D N3D5

ANS:D - N3D5

N3D5 ChatGPT The power required by a centrifugal pump is proportional to N3D5N^3D^5N3D5, where NNN is the rotational speed (in revolutions per minute, r.p.m) and DDD is the diameter of the impeller. Here's why: The power PPP required by a centrifugal pump can be derived from the affinity laws (also known as the pump laws), which relate the various parameters of pump operation. According to these laws:

  1. The flow rate QQQ is proportional to the rotational speed NNN and the cube of the diameter DDD: Q∝ND3Q \propto ND^3Q∝ND3
  2. The head HHH developed by the pump is proportional to the square of the rotational speed NNN and the square of the diameter DDD: H∝N2D2H \propto N^2D^2H∝N2D2
  3. The power PPP required is proportional to the product of the flow rate QQQ and the head HHH: P∝QHP \propto QHP∝QH
Substituting the proportional relationships for QQQ and HHH: P∝(ND3)(N2D2)=N3D5P \propto (ND^3)(N^2D^2) = N^3D^5P∝(ND3)(N2D2)=N3D5 Therefore, the power required by a centrifugal pump is proportional to N3D5N^3D^5N3D5.