GATE CE 2025 Set 2 — Question 48
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Water Resources Engineering → Dimensional Analysis & Similitude → Buckingham Pi Theorem
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Question
The drag force, on a sphere due to a fluid flowing past the sphere is a function of viscosity, , the mass density, , the velocity of flow, , and the diameter of the sphere, .Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.
Correct answer
(A) (F_D)/(ρ V² D²); (C) (ρ V D)/(μ)
Solution
Using dimensional analysis or standard fluid mechanics definitions:
1.The drag coefficient is defined as . Since area , the term is a non-dimensional parameter representing the force coefficient. Thus, (A) is correct.
2.The Reynolds number is the standard non-dimensional parameter for viscous flow past a body. Thus, (C) is correct.
3.Checking (B): , which is not dimensionless.
4.Checking (D): , which is not dimensionless.
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