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Publication Title | AME 50531 Homework Solutions1 Fall 2011

Organic Rankine Cycle

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Homework 1

AME 50531 Homework Solutions1 Fall 2011

1. CPIG air enters an isentropic nozzle at 1.30 atm and 24 ◦C with a velocity of 2.5 m/s. The nozzle entrance diameter is 120 mm. The air exits the nozzle at 1.24 atm with a velocity of 90 m/s. Determine the temperature of the exiting air and the nozzle exit diameter. Given:CPIGair, 1 T1 =24◦C,P1 =1.30atm,v1 =2.5m/s,d1 =120mm 2 P2 =1.24 atm, v2 = 90 m/s

Assumptions:

Find: T2, d2

For T2, use energy conservation:

1004.5 J kg K

For d2, use mass conservation:

v12 v22 h1+ 2 =h2+ 2

v12 v22 (h1−h2)+ 2 = 2

v12 v22 cp(T1 −T2)+ 2 = 2

cp(T1 − T2) = 1/2(v22 − v12)

(T1 − T2) = 1/2((90 m/s)2 − (2.5 m/s)2)

T→−T =4.029◦C 12

m ̇ 1 = m ̇ 2

ρ1A1v1 = ρ2A2v2

P =ρRT →ρ=P/RT P1A1v1 = P2A2v2

T1 T2 A2 = T2P1v1A1

T1P2v2

πd2 = T2P1v1 πd21

T2 = 19.97 ◦C.

4 T1P2v2 4

d2 = (293.12 K)(1.30 atm)(2.5 m/s)(120 mm)2

(297.15 K)(1.24 atm)(90 m/s) →

2. 9.47 Consider a steam turbine power plant operating near critical pressure. As a first approximation, it may be assumed that the turbine and the pump processes are reversible and adiabatic. Neglect any changes in kinetic and potential energies.

1Solutions adapted from Borgnakke, Sonntag (2008) “Solutions Manual,” Fundamentals of Thermodynamics, 7th Edition and previous AME 50531 Homework Solutions documents.

d2 = 20.34 mm.

1

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