301 HW_6_Solution

# 301 HW_6_Solution - MAE 301 Engineering Thermodynamics...

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1 MAE 301: Engineering Thermodynamics Spring 2010 HOMEWORK #6 ( Solutions ) Problem 1. Problem 5.41 from the book. Solution: This is a steady-flow process since there is no change with time. Nitrogen is an ideal gas with variable specific heats. Potential energy changes are negligible. The device is adiabatic and thus heat transfer is negligible. There are no work interactions. The molar mass of nitrogen is M = 28 kg/kmol (Table A-1). The enthalpies are (Table A- 18) kJ/kmol 8580 K 295 = C 22 kJ/kmol 8141 K 280 = C 7 2 2 1 1 = ° = = ° = h T h T (a ) There is only one inlet and one exit, and thus &&& mmm 12 = = . We take diffuser as the system, which is a control volume since mass crosses the boundary. The energy balance for this steady-flow system can be expressed in the rate form as 2 2 0 0) pe W (since /2) + ( ) 2 / ( 2 1 2 2 1 2 2 1 2 2 1 2 2 2 2 2 1 1 V V M h h V V h h Q V h m V h m + = + = Δ = + & & & & , Substituting, () ( ) + = 2 2 2 2 2 /s m 1000 kJ/kg 1 2 m/s 200 kg/kmol 28 kJ/kmol 8141 8580 0 V It yields V 2 = 93.0 m/s ( b ) The ratio of the inlet to exit area is determined from the conservation of mass relation, or, ( ) ( ) 0.625 = = = = = ⎯→ = m/s 200 kPa K/85 295 m/s 93.0 kPa K/60 280 / / / / 1 1 1 2 2 2 1 1 2 1 1 2 2 2 1 1 1 2 2 1 2 1 1 1 1 2 2 2 V V P T P T A A V V P RT P RT V V A A V A V A v

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2 Problem 2. Problem 5.49 from the book. Solution: Air is an ideal gas. The flow is steady. The gas constant of air is R = 0.287 kPa m 3 /kg K (Table A-1). The specific volumes of air at the inlet and outlet are /kg m 2506 . 0 kPa 1000 K) 273 K)(600 /kg m kPa 287 . 0 ( 3 3 1 1 1 = + = = P RT v /kg m 3575 . 1 kPa 100 K) 273 K)(200 /kg m kPa 287 . 0 ( 3 3 2 2 2 = + = = P RT The mass flow rate is kg/s 11.97 = = = /kg m 0.2506 m/s) )(30 m 1 . 0 ( 3 2 1 1 1 V A m & The outlet area is 2 m 1.605 = = = m/s 10 /kg) m 75 kg/s)(1.35 97 . 11 ( 3 2 2 2 V m A & Problem 3. Problem 5.51 from the book.
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301 HW_6_Solution - MAE 301 Engineering Thermodynamics...

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