Boundary Layer Theory MCQ with answer and solution

Concept

Shear velocity definition and turbulent boundary layer scaling

Formula

u_* = √(τ₀ / ρ)

Step-by-step solution

1. Shear velocity (u_*) is defined as u_* = √(τ₀ / ρ), relating boundary shear stress τ₀ to fluid density ρ. Thus, statement (i) is true. 2. In turbulent flow near boundaries, u_* is the characteristic velocity scale in the universal law of the wall (u+ = f(y+)). Thus, statement (ii) is true. 3. Because both statements accurately describe shear velocity formulation and scaling, option C is correct. Answer: C

Explanation

Shear velocity (friction velocity, u_*) is defined as the square root of boundary shear stress divided by fluid density: u_* = √(τ₀ / ρ). It provides a characteristic velocity scale relating wall friction to inertia and serves as the fundamental dimensionless scaling velocity throughout the turbulent boundary layer and the universal law of the wall.

Why the other options are wrong

A) Statement (ii) is also true as shear velocity is the universal velocity scale in turbulent boundary layers. B) Statement (i) is also true as it defines shear velocity. D) Both statements are fundamental, established facts in fluid mechanics.

Shortcut

Shear velocity u_* = √(τ₀ / ρ) (scales wall shear stress and turbulent near-wall velocity profiles).

Common mistake

Believing shear velocity is an actual physically measurable velocity rather than a scaling velocity parameter.