Question

3. The Rankine cycle is the ideal cycle for vapor-driven power plants. A Rankine cycle with water as the working fluid operates between the pressure limits of 4 MPa in the boiler and 20 kPa in the condenser. The turbine inlet temperature is 700°C and the flow rate is 30 kg/s. State the assumptions and show the complete reduction of the governing equations. (Total: 20 pts.) (a) Show the cycle on a T-s diagram. (b) Determine the power produced by the turbine and consumed by the pump. (c) If the turbine inlet conditions are fixed, what is the effect of lowering condenser pressure on the turbine power output, the heat rejected, and the liquid content at the turbine exit? Show this on the T-s diagram.

Answer 1

solution [a] P2 = 13 = 4 mia + Tz = Food P1 = lu= 20414 1 . Process 132 Process 23 Process 34 : Process 4+1 : S+ Pump Boiler (constant Pressure heat addition) Turbine (reversible adiabatic expansion) Conden sor constant Pressure heat rejection) Assumption ② No heal loss in loss in Boiler. ® isentropic efficiency of the turbine is Leo X © efficiency of the pump is loo 7. enthalphy at point 1 hu 20 kPa hy Thi @ ho РА 251.4 KJ / kg & specific volume at point 1 is : VE ef @ P1 = 20 kPa Tu 9.0172 x 103 mstky] CSscanned with Carlscanner

0.8320 + x (7.9085-0.8320) = 7.6198 2 : 0:9592 where, X steam at Dryness fraction of the turbine exit. enthalpy at point 4 is hy - hu hp + X (heg) @ Py = 20 kPa 251.40 + 0,9592 12358,3) hu 2513.468 KI/kg [6] mass flow date (m) 30 kg / see Given Power produce by the turbine für J = m (hz-hu) 30 kg / seed ( 3905: 9 - 2513.488) Kg/kg WI WT RW 41772.34 (OT) 41.77 mW we Powey consumed by the pump / Wp) = mx Wp Wp = (30 kg) See) * (4.048 kJ) Kg Twp 121.44 KW csscarmed-wittrarscanner

ICI T A 1/1 47 & When Condenser pressure is elecrease : ha same hy decrease • Turbine Power output (WT) = m(hz - hut increase 3 heat rejee teel e scanned with CamScanner I dout) ml hy-hy)

it depends Condision given, ((or) increase o decrease ) dryness fraction at steam turbine exit decrease mean liquid content is increase. CScanned with CamScanner