GATE ME 2020 Set 1 — Question 25

MCQ+1 / -0.33EasyDimensionless NumbersDimensional Analysis & SimilitudeFluid MechanicsDimensionless ParametersConvectionHeat Transfer

Fluid Mechanics → Convection → Dimensionless Numbers

Last updated 5 September 2026

Question

\frac{\text{Buoyancy force}}{\text{Viscous force}}

Non-dimensional number	Definition
P Reynolds number	1 $\frac{\text{Buoyancy force}}{\text{Viscous force}}$
Q Grashof number	2 $\frac{\text{Momentum diffusivity}}{\text{Thermal diffusivity}}$
R Nusselt number	3 $\frac{\text{Inertia force}}{\text{Viscous force}}$
S Prandtl number	4 $\frac{\text{Convective heat transfer}}{\text{Conduction heat transfer}}$

Correct answer (D) P-3, Q-1, R-4, S-2 Solution The standard definitions for these dimensionless numbers are: Reynolds number (P) : Ratio of inertia force to viscous force. (P-3) Grashof number (Q) : Ratio of buoyancy force to viscous force, typically used in natural convection. (Q-1) Nusselt number (R) : Ratio of convective heat transfer to conductive heat transfer across a boundary. (R-4) Prandtl number (S) : Ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. (S-2) Matching these gives: P-3, Q-1, R-4, S-2, which corresponds to option (D). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (D) P-3, Q-1, R-4, S-2 Solution The standard definitions for these dimensionless numbers are: Reynolds number (P) : Ratio of inertia force to viscous force. (P-3) Grashof number (Q) : Ratio of buoyancy force to viscous force, typically used in natural convection. (Q-1) Nusselt number (R) : Ratio of convective heat transfer to conductive heat transfer across a boundary. (R-4) Prandtl number (S) : Ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. (S-2) Matching these gives: P-3, Q-1, R-4, S-2, which corresponds to option (D).

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