Answer
$\dot{W}_e=308\ kW$
Work Step by Step
With
$\dot{Q}_L=(\rho\dot{V})c_p(T_e-T_i)$
Given: $\rho=64.0\ lbm/ft³,\ \dot{V}=13300\ gal/min=29.63\ ft³/s,\ c_p=1.0\ Btu/lbm.°F,\ (T_e-T_i)=6°F$:
$\dot{Q}_L=11380\ Btu/s$
$\eta = \dot{W}_e/(\dot{W}_e+\dot{Q}_L)=0.025$
$\dot{W}_e=292\ Btu/s=308\ kW$
