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GATE 2025 CE (CE2) – Question 48

Hydraulics · Dimensional analysis and hydraulic similitude · 2 marks · Multiple select

The drag force, $F_D$ on a sphere due to a fluid flowing past the sphere is a function of viscosity, $\mu$, the mass density, $\rho$, the velocity of flow, $V$, and the diameter of the sphere, $D$.
Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.

  1. $\frac{F_D}{\rho V^2D^2}$
  2. $\frac{\rho F_D}{V^2D^2}$
  3. $\frac{\rho VD}{\mu}$
  4. $\frac{\mu\rho}{VD}$

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Correct answer: (A) $\frac{F_D}{\rho V^2D^2}$; (C) $\frac{\rho VD}{\mu}$

Explanation

The variables are $F_D, \mu, \rho, V, D$, which is 5 variables with 3 basic dimensions (M, L, T), so there are 2 dimensionless groups (Buckingham $\Pi$ theorem). They are the drag coefficient form $\frac{F_D}{\rho V^2D^2}$ (A) and the Reynolds number $\frac{\rho VD}{\mu}$ (C). The expressions in B and D are not dimensionless.