Problems #1 & #2 (2x credit)
Consider two-dimensional, steady flow along a flat plate of length $L$ and width $b$ at zero inclination
to incoming flow of constant speed $U$. Assume the velocity profile is given by the 4th order
polynomial:
$u = U \left[ 2\left(\frac{y}{\delta}\right) - 2\left(\frac{y}{\delta}\right)^3 + \left(\frac{y}{\delta}\right)^4 \right]$.
Determine the following:
(a) Boundary layer thickness $\delta$ as a function of $x$ and downstream distance-based Reynolds
number ($Re_x = Ux/\nu$).
(b) Momentum thickness $\theta$ as a function of $x$ and $Re_x$.
(c) Displacement thickness $\delta^*$ as a function of $x$ and $Re_x$.
(d) Skin friction coefficient $c_f$ as a function of $Re_x$.
(e) Drag force acting on both sides of the plate, evaluated using wall shear stress ($\tau_w$):
$D_{1-side} = b \int_0^L \tau_w \, dx$
