Question

In a Rankine cycle the steam enters at 200 bar and 400°C to the turbine, condenser pressure is 10 kPa. Power output of cycle is 100 MW. Cooling water is used to cool the steam in condenser.When pump work is not neglected and cooling water enters at 30° C and leaves at 50°C. The mass flow rate of cooling water required is _____kg/s. Data : at 200 bar, 400°C
$h=3400kJ/kg,s=3.35kJ/kgK$
at 10 kPa
$h_f=191.83kJ/kg,h_g=2584.8kJ/kg$
$s_{\delta }=8.1511kJ/kgK,s_{fg}=7.5018kf/kgK,v_f=0.001m/kg$
Specific heat capacity for cooling water =4.18 kJ/kgk

• A. 1588.27

Answer 1

The correct option is A 1588.27


$s_1=6.35kJ/kgK$
$s_2=s_{f2}+x{s}_{fg2}$
$=(S_{g2}-S_{fg2})+x{s}_{fg2}$
$s_1=s_2$
$6.35=(8.1511-7.5018)+x\times 7.5018$
$x=0.7599\simeq 0.760$
$h_g=h_{f2}+x{h}_{fg2}$
$=191.63+0.760(2584.8-191.83)$
$h_2=2010.48kJ/kg$
Pump work $W_p=v_f\times sp=0.001[20000-10]=19.99kJ/kg$
Net work output $W_N=w_T-w_f$
$w_N=(h_1-h_2)-w_p$
$=(3400-2010.48)-19.99=1369.53kJ/kg$
Power output
$100\times {10}^3={\dot{m}}_s\left(1369.53\right),{\dot{m}}_s=73.01kg/s$
Heat rejected in condenser heat carrid away by circulating water.
$\left({\dot{m}}_s\right)[h_2-h_3]={\dot{m}}_w\times c_p\times \left(\Delta T\right)$
$73.01[2010.48-191.83]={\dot{m}}_w\times 4.18\times (50-30)$
${\dot{m}}_w=1588.27kg/s$