From Robert Balmer\'s Modern Engineering Thermodynamics, problem 51 of chapter 6
ID: 1939935 • Letter: F
Question
From Robert Balmer's Modern Engineering Thermodynamics, problem 51 of chapter 6.In a steady flow process, a 1300 hp adiabatic steam turbine is supplied with 10.0 x 10^3 lbm of steam per hour. At the inlet to the turbine, the pressure of the steam is 500 psia and its velocity is 100 ft/s. The temperature of the steam leaving the turbine is 60.0°F, its quality 0.870, and its velocity is 700 ft/s. On leaving the turbine, the steam is condensed at constant pressure and exits the condenser as a saturate liquid at 60.0°F with negligible velocity. Find the temperature of the steam supplied to the turbine and the heat transfer rate in the condenser.
I would appreciate as detailed a reply as possible, with units and descriptions of the process for solving. There is no lecture associated with the class that is utilizing this text, and we are expected to teach ourselves. This book is not a good resource for that endeavor. I would like to be able to solve similar problems on my own in the future. Thanks.
Explanation / Answer
Powerturbine = m_dot x wturbine
(1hp=2544.4 Btu/hr)
1300 x 2544.4 = 10 x 103 x wturbine , wturbine = 330.77 Btu/lb
State 1 (Turbine inlet) : P1=500 psia V1=100 ft/s T1=?
State 2 (Turbine outlet) : T2=60 F x2=0.87 V2=700 ft/s ---> h2 = 949.60 Btu/lb (from steam table)
Apply first law at turbine, (1Btu/lb = 25037 ft2/s2)
h1+(v12/2)(1/25037) = h2+(v22/2)(1/25037) + wturbine (adiabatic Q=0)
h1 = 949.60 +(7002-1002)/2/25037 + 330.77 = 1289.96 Btu/lb
From steam table P1=500 psia , h1 = 1289.96 Btu/lb --> T1 = 587 F
State 3 (Condenser exit) : T3=60 F x3=0 h3 = 28.05 Btu/lb
Apply first law at condenser,
Q23 = h2-h3 = 949.6 - 28.05 = 921.55 Btu/lb
Heat transfer rate = m_dot * Q23 = 10000*921.55 = 9.2155x106 Btu/ hr
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