\[\]
\[
\textbf{Difficult MCQs on Fluid Dynamics with Answers}
\]
\[
\textbf{Q1: The Navier-Stokes equations are derived from which fundamental principle?}
\]
\[
\text{(A) } Conservation of Mass \quad \text{(B) } Conservation of Momentum \quad \text{(C) } Conservation of Energy \quad \text{(D) } Bernoulli’s Principle
\]
\[
\textbf{Answer: (B) Conservation of Momentum}
\]
\[
\textbf{Q2: In fluid dynamics, the Reynolds number is used to predict:}
\]
\[
\text{(A) } Laminar or turbulent flow \quad \text{(B) } Compressibility effects \quad \text{(C) } Viscosity variation \quad \text{(D) } Stability of flow
\]
\[
\textbf{Answer: (A) Laminar or turbulent flow}
\]
\[
\textbf{Q3: The condition of incompressible flow in fluid dynamics is represented mathematically by which equation?}
\]
\[
\text{(A) } \nabla \cdot \vec{v} = 0 \quad \text{(B) } \nabla \times \vec{v} = 0 \quad \text{(C) } \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0 \quad \text{(D) } \nabla^2 \phi = 0
\]
\[
\textbf{Answer: (A) } \nabla \cdot \vec{v} = 0
\]
\[
\textbf{Q4: Bernoulli’s equation is applicable under which of the following conditions?}
\]
\[
\text{(A) } Compressible and turbulent flow \quad \text{(B) } Steady and inviscid flow \quad \text{(C) } Rotational flow \quad \text{(D) } Unsteady and viscous flow
\]
\[
\textbf{Answer: (B) Steady and inviscid flow}
\]
\[
\textbf{Q5: The vorticity vector is mathematically defined as:}
\]
\[
\text{(A) } \nabla \cdot \vec{v} \quad \text{(B) } \nabla \times \vec{v} \quad \text{(C) } \frac{\partial \vec{v}}{\partial t} \quad \text{(D) } \vec{v} \cdot \nabla \vec{v}
\]
\[
\textbf{Answer: (B) } \nabla \times \vec{v}
\]
\[
\textbf{Q6: The dimensionless number that compares inertial forces to surface tension forces in fluid dynamics is:}
\]
\[
\text{(A) } Reynolds number \quad \text{(B) } Weber number \quad \text{(C) } Froude number \quad \text{(D) } Mach number
\]
\[
\textbf{Answer: (B) Weber number}
\]
\[
\textbf{Q7: Which type of flow is characterized by a linear velocity profile across the cross-section of a pipe?}
\]
\[
\text{(A) } Turbulent flow \quad \text{(B) } Laminar flow \quad \text{(C) } Compressible flow \quad \text{(D) } Rotational flow
\]
\[
\textbf{Answer: (B) Laminar flow}
\]
\[
\textbf{Q8: The Kármán vortex street is observed in fluid flow when:}
\]
\[
\text{(A) } Reynolds number is very low \quad \text{(B) } Reynolds number is moderate \quad \text{(C) } Flow is supersonic \quad \text{(D) } Flow is incompressible
\]
\[
\textbf{Answer: (B) Reynolds number is moderate}
\]
\[
\textbf{Q9: The Stokes flow regime is valid when the Reynolds number is:}
\]
\[
\text{(A) } Much greater than 1 \quad \text{(B) } Much less than 1 \quad \text{(C) } Equal to 1 \quad \text{(D) } Infinite
\]
\[
\textbf{Answer: (B) Much less than 1}
\]
\[
\textbf{Q10: In potential flow theory, the velocity potential, \(\phi\), satisfies which equation?}
\]
\[
\text{(A) } \nabla \cdot \vec{v} = 0 \quad \text{(B) } \nabla \times \vec{v} = 0 \quad \text{(C) } \nabla^2 \phi = 0 \quad \text{(D) } \nabla \phi \cdot \vec{v} = 0
\]
\[
\textbf{Answer: (C) } \nabla^2 \phi = 0
\]