Question

A fluid whose viscosity is unknown flow past a flare plate at a free stream velocity such that the the boundary layer thickness is 10mm at a distance of 2.2m from the leading edge. Assuming laminar flow throughout. Determine the boundary layer thickness at a distance 5m from the leading edge.

Answer 1

Answer:

δ₂ = 15.07 mm

Explanation:

Given :

When the leading edge, $x_{1}$ is 2.2 m, then boundary layer thickness,δ₁ = 10 mm = 0.01 m

$x_{2}$ = 5 m

Now we know that for a laminar flow, the boundary layer thickness is

δ = $\frac{5.x}{\sqrt{Re_{x}}}$ -------(1)

and Reyonlds number, Re is

               $Re = \frac{\rho .v.x}{\mu }$------(2)

where ρ is density

           v is velocity

           x is distance from the leading edge

           μ is dynamic viscosity

from (1) and (2), we get

δ∝$x^{1/2}$

Therefore,

$\frac{\delta _{1}}{x_{1}^{1/2}}= \frac{\delta _{2}}{x_{2}^{1/2}}$

$\frac{10}{2.2^{1/2}}= \frac{\delta _{2}}{5^{1/2}}$

δ₂ = 15.07 mm

Therefore, boundary layer thickness is 15.07 mm when the leading edge is 5 m.