Problem $1$

$15+5+5+5=30$

Derive $V_{\text{a}\text{v}\text{g}}=\frac{1}{2}{U}_{\text{m}\text{a}\text{x}}$ where $U_{\text{m}\text{a}\text{x}}$ is the maximum velocity and show

$($i$),P_L=f(\frac{(L)V^2}{(D)2})$

$($ii$)h_L=\frac{(L)V^2}{(D)2g}$

$($iii$)V^{}=\frac{P{D}^4}{128L}$