Question

The boundary layer thickness at a given distance from the leading edge of a flat plate is.
1. More for lighter fluid
2. More for denser fluid
3. same for both lighter and denser fluid
4. Less for lighter fluid

Answer 1

Correct Answer - Option 1 : More for lighter fluid

Boundary layer thickness is inversely proportional to the square root of Reynold’s number for laminar flow

\(\delta \propto \frac{1}{{\sqrt R e}}\)

Reynold’s number, Re = \(\frac{{\rho vD}}{\mu }\)

D = hydraulic diameter

V = velocity

ρ = density

μ = coefficient of viscosity

Therefore,

\(\delta \propto \frac{1}{{\sqrt \rho }}\)

Hence, Lighter fluid will have more boundary layer thickness at a particular point as compared to a denser fluid.

Note: For turbulent flow \(\delta = \frac{{0.379x}}{{R{e^{\frac{1}{5}}}}}\)

 \(\delta \propto \frac{1}{{R{e^{\frac{4}{5}}}}}\)

∴ the boundary layer thickness in laminar flow will also have the same variation with the density, i.e. if the fluid is lighter boundary layer thickness will be more.