Question

An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be
1. 4
2. 2
3. 0.5
4. 0.25

Answer 1

Correct Answer - Option 3 : 0.5

Concept:

According to the Blasius equation, for a laminar flow

Boundary layer thickness (δ) can be calculated by:

\(\delta = \frac{{5x}}{{\sqrt {R{e_x}} }}\)

where Re_x = Reynold's number = \(\frac{{\rho Vx}}{\mu }\) {V = Velocity}

\(\therefore \delta \propto \frac{1}{V}\)

Calculation:

Given:

δ₁ = 1 mm, V₂ = 4V₁

\(As,\,\delta \propto \frac{1}{V}\)

\(\frac{{{\delta _1}}}{{{\delta _2}}} = \sqrt {\frac{{{V_2}}}{{{V_1}}}} \)

\(\frac{1}{{{\delta _2}}} = \sqrt {\frac{4}{1}} = 2\)

 δ₂ = 0.5 mm