Homework $5$

For a constant$-$density flow, the continuity equation can be taken as

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}=0$

Then, $v(x,y)$ can be calculated if $u(x,y)$ is known. For that purpose, assume that the velocity

profile is

$\frac{u}{U_e}=3(\frac{y}{}{)}^1-3(\frac{y}{}{)}^2+1(\frac{y}{}{)}^3$

and

$\frac{}{x}=5\mathrm{.}0R{e}_x^{-\frac{1}{2}}$

for laminar flow over a flat plate.

Write out the equation for how $v(x,y)$ is at the boundary layer edge.