$[25$ MARKAH$]$

Question $2$

A boundary layer for laminar flow of a fluid over the plate, as shown in Figure $2,$ is to be

approximated by the equation $\frac{u}{U}=C_1(\frac{y}{})+C_2(\frac{y}{}{)}^2+C_3(\frac{y}{}{)}^3.$ Determine the

constants $C_1,C_2$ and $C_3$ using the boundary conditions when $u=U,y=$; when

$d\frac{u}{d}y=0,y=$ and when $d^2\frac{u}{d}{y}^2=0,y=0.$ Then, obtain the thickness of the

boundary layer as a function of $x$ and $R{e}_x$ using the momentum integral technique.

$[25$ MARKS$]$

Gambarajah $2/$Figure $2$