$($Single pipe $-$ determine pressure drop$)$ A fire protection association code requires a minimum pressure of $54$ psi at the outlet end of a $250-$ft$-$long, $4\mathrm{.}5-$in$.-$diameter hose when the flowrate is $500ga\frac{l}{m}in.$ What is the minimum pressure allowed at the pumper truck that supplies water to the hose? Assume a roughness of $=0\mathrm{.}03in.$

$p_1=$ psi.