Cold feedwater enters a 200-kPa open feedwater heater of a regenerative Rankine cycle at 70°C with a flow rate of 20 kg/s. Bleed steam is available from the turbine at 200 kPa and 160°C. At what rate must the bleed steam be supplied to the open feedwater heater so that the feedwater leaves this unit as a saturated liquid?
The mass flow rate of bleed steam to be supplied to the open feedwater heater so that the feedwater leaves this unit as a saturated liquid is kg/s.

The mass flow rate of bleed steam to be supplied is; m'_s = 1.85 Kg/s

Explanation:

From the first table i attached, at temperature of 70°C, the enthalpy of the cold water feed is;

h_c = 293 KJ/Kg

Also from the same table, at a temperature of 160°C and by interpolation, the enthalpy of the steam is;

h_s = 2790 KJ/Kg

Now, the exiting water is leaving the water heater at a combined rate of m'_c + m'_s and we know that it is a saturated liquid at Pressure of 200 KPa.

Where m'_c is mass flow rate of cold water feed while m'_s is mass flow rate of bleed steam.

Thus, from the second table attached and at 200KPa,the enthalpy of the saturated liquid is;

h_e = 504.71 KJ/kg

Now, from energy balance equation, we have;

E'_e = E'_c + E'_s

(m'_c + m'_s)h_e = (m'_c)h_c + (m'_s)h_s

Plugging in the relevant values, we have;

(20 + m'_s)504.71 = (20)293 + (m'_s)2790

10094.2 + 504.71m'_s = 5860 + 2790m'_s

2790m'_s - 504.71m'_s = 10094.2 - 5860

2285.29m'_s = 4234.2

m'_s = 4234.2/2285.29

m'_s = 1.85 Kg/s

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