6-125 6-150 Air is accelerated in a nozzle. The density of air at the nozzle exit is to be determined. Assumptions Flow through the nozzle is steady. Properties The density of air is given to be 4.18 kg/m3 at the inlet. 1 Analysis There is only one inlet and one exit, and thus m m 1 U 1 A1V1 2 m . Then, m m 2 1 U 2 A2V 2 A1 V1 U1 A2 V 2 U2 2 120 m/s (4.18 kg/m 3 ) 380 m/s AIR 2 2.64 kg/m 3 Discussion Note that the density of air decreases considerably despite a decrease in the cross-sectional area of the nozzle. 6-151 An air compressor consumes 4.5 kW of power to compress a specified rate of air. The flow work required by the compressor is to be compared to the power used to increase the pressure of the air. Assumptions 1 Flow through the compressor is steady. 2 Air is an ideal gas. Properties The gas constant of air is 0.287 kPa·m3/kg·K (Table A-1). 1 MPa 300°C Analysis The specific volume of the air at the inlet is RT1 P1 v1 (0.287 kPa m 3 /kg K )(20 273 K ) 120 kPa 0.7008 m 3 /kg Compressor The mass flow rate of the air is V1 m v1 0.010 m 3 /s 0.7008 m 3 /kg 120 kPa 20°C 0.01427 kg/s Combining the flow work expression with the ideal gas equation of state gives the flow work as wflow P2v 2 P1v 1 R(T2 T1 ) (0.287 kJ/kg K)(300 20)K 80.36 kJ/kg The flow power is W flow m wflow (0.01427 kg/s)(80.36 kJ/kg) 1.147 kW The remainder of compressor power input is used to increase the pressure of the air: W W total,in W flow 4.5 1.147 3.353 kW PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.