$5\mathrm{.}20$ Wake$-$survey method: An experimental method of measuring the force exerted on a solid

body consists of placing it in a uniform stream of fluid and studying the velocity pattern

downstream. Using the CV shown, obtain the following dimensionless equation for the

drag force on a cylinder of diameter $D$ :

$C_D=\frac{x-\text{f}\text{o}\text{r}\text{c}\text{e}on\text{c}\text{y}\text{l}\text{i}\text{n}\text{d}\text{e}\text{r}}{\frac{1}{2}{V}_0^2(WD)}=4{\displaystyle \underset{0}{\overset{K}{}}}{V}_{+-}^{*}(1-V_x^{*})d{y}^{*}$

where $W=$ width of the cylinder, $V_{+-}^{*}=\frac{V}{V_0}$ and $y^{*}=\frac{y}{D}.($Hint: The fluid bleeds through

the sides of the $CV$ and the pressures far upstream and downstream can be taken as

eaual.