$5-57$E Air is flowing through a venturi meter whose diameter is $2\mathrm{.}6$ in at the entrance part $($location $1)$ and $1\mathrm{.}8$ in at the throat

$($location $2).$ The gage pressure is measured to be $12\mathrm{.}2$ psia at the entrance and $11\mathrm{.}8$ psia at the throat. Neglecting frictional effects, show

that the volume flow rate can be expressed as

$V^{}=A_2\sqrt[\phantom{2}]{\frac{2(P_1-P_2)}{(1-\frac{A_2^2}{A_1^2})}}$

and determine the flow rate of air. Take the air density to be $0\mathrm{.}075lb\frac{m}{f}{t}^3.$