$[5]$ A train is $100$ m long, $2\mathrm{.}8$ m wide and $2\mathrm{.}75$ m high. The train travels at $180k\frac{m}{h}r$ through air of density $1\mathrm{.}2k\frac{g}{m^3}$ and kinematic viscosity $1\mathrm{.}5{10}^{-5}\frac{m^2}{s}.$ You may assume that the frictional drag of the train is equivalent to the drag of a turbulent boundary layer on one side of a flat plate of length $l=100m$ and breadth $b=8\mathrm{.}3m.$ Taking $\frac{}{x}=0\mathrm{.}37(R_x{)}^{-\frac{1}{5}},$ calculate

$($a$)$ the boundary layer thickness at the rear of the train

$($b$)$ the frictional drag acting on the train,

$($c$)$ the power required to overcome the frictional drag.

$[6]$ Air of density $1\mathrm{.}21k\frac{g}{m^3}$ and kinematic viscosity $15{10}^{-5}\frac{m^2}{s}$ passes over a thin flat