Air flows steadily in a pipe at $300$kPa,$27C,$ and $30\frac{m}{s}$ at a rate of $20k\frac{g}{m}in.$

Figure $1$: Air flows steadily in a pipe.

Answer the followings:

$($a$)$ Explain "flow work" or "flow energy".

$[2$ marks$]$

$($b$)$ Using the symbols provided in Figure $1,$ derive the expression for flow work $($in kJ$).$

$[3$ marks$]$

$($c$)$ Calculate the rate of flow work of air in the pipe $($in kW $).$

$[3$ marks$]$

$($d$)$ Determine the pipe cross$-$sectional area $($in $m^2).$

$[3$ marks$]$

$($e$)$ Determine the rate of energy transport in the pipe, $E_{\text{m}\text{a}\text{s}\text{s}}^{}($in kW $).$

$[4$ marks$]$