2. [30 points] Consider a flat plate at zero angle of attack in an airflow at standard sea level conditions. The chord length of the plate (c, distance from the leading edge to the trailing edge) is 2 m. The planform area of the plate is 40 m². Assume the viscosity coefficient, $\mu_{\infty}$, remains a constant. One can obtain the velocity gradient from the laminar boundary layer theory: $\left(\frac{\partial u}{\partial y}\right)_{wall} = 0.332 V_{\infty} \sqrt{\frac{\rho_{\infty} V_{\infty}}{\mu_{\infty} x}}$, where x is the distance from the leading edge.
a) Obtain the skin friction coefficient as a function of x:
$C_f = 2\tau_w/(\rho_{\infty} V_{\infty}^2)$
b) Calculate the drag coefficient for the entire surface.
c) Discuss the variation of skin friction coefficient and the boundary layer thickness as the chord length increases.
