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

δ₂ = 15.07 mm

Step-by-step 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 = (\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,

`(\delta _(1))/(x_(1)^(1/2))= (\delta _(2))/(x_(2)^(1/2))`

`(10)/(2.2^(1/2))= (\delta _(2))/(5^(1/2))`

δ₂ = 15.07 mm

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