$\frac{u}{U}=2(\frac{y}{δ})-2(\frac{y}{δ})^2+(\frac{y}{δ})^3$ where u is the velocity at distance y from the surface of the flat plate and U be the free stream velocity at the boundary layer thickness $δ$ Obtain an expression for boundary layer thickness, shear stress and force on one side of the plate in terms of Reynolds number.

Consider the Laminar boundary layer velocity distribution over a flat plate,

$\frac{u}{U} =2(\frac{Y}{δ})-2(\frac{Y}{δ})^2+(\frac{y}{δ})^3$

For the Boundary layer thickness, we know the Von Karman’s Momentum Integral equation,

$\frac{\tau_0}{ρU^2}= \frac{∂θ}{∂x}$

Where,

$\tau_0$→Shear stress in the fluid

ρ→Density of the fluid

U→Free stream velocity of the fluid

θ→Momentum thickness

We know that the …