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A steam turbine is supplied with dry saturated steam at 20 bar. The exhaust takes place at 0.3 bar. For a flow rate of 10kg/s. Calculate

i) Quality of steam at the end of expansion

ii) Power required to drive the pump

iii) Turbine power

iv) The Rankine efficiency

v) The heat flow in the condenser

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Given:

P1 = 20 bar; X1= 1;

P2=0.3 bar

Solution:

## i) Finding quality

S1 = S2 (isentropic expansion)

.sg1 = sf2 + X2 × sfg

6.337 = 0.944 + X2 × 6.825

X2 = 0.79

## ii) Pump power

Wp = ∆P/10 = (20 -0.3)/10 = 1.97 kJ/kg

Pp = mWp = 10 × 1.97 = 19.7 kW

Also, Wp = h4-h3 and h3 = hf2

.h4 = Wp + hf2 = 1.97 + 289 = 290.97 kJ/kg

## iii) Turbine power

Wt = h1-h2 = hg1 – (hf2 + X2 × hfg2)

= 2797 – (289 + 0.79 × 2336) = 662 kJ/kg

Pt = mWt = 10 × 662 = 6620kW

Ws = Wt - Wp = 662-1.97 = 660.03 kJ/kg

## iv) Finding efficiency

Q= h1 - h4 = 2797 – 290.97 = 2506.3 kJ/kg

.η = W/Q = 660.03/2506.3 = 0.26

## v) Heat flow in condenser

Qc = h3 - h2 = 289 + 0.79 × 2336 -289 = 1845.4 kJ/kg