If the velocity distribution in a laminar boundary layer on a flat plate is

$\frac{\upsilon}{U}=a+b(\frac{y}{\delta})+c(\frac{y}{\delta})^2+d(\frac{y}{\delta})^3$

Determine the coefficient a,b,c and d. Here u is the velocity at the distance y from the surface of the flat plate and U be the free stream velocity at the boundary layer thickness $\delta$

Consider the velocity distribution in a laminar boundary layer over a flat plate,

We know that at the surface of the plate y=0 ⇒ u=0 due to no slip condition.

Substituting in the above equation,

$\frac{0}{U}=a+b(\frac{0}{δ})+c(\frac{0}{δ})^2+d(\frac{0}{δ})^3$

$0=a+b(0)+c(0)^2+d(0)^3$

∴a=0

∴$\frac{u}{U}=b(\frac{y}{δ})+c(\frac{y}{δ})^2+d(\frac{y}{δ}^3$

Now, At the boundary layer thickness, we know that $y=δ⇒u=U,\frac{du}{dy}$=0 and …