Thermodynamics

880 | Thermodynamics17–135 Helium expands in a nozzle from 1 MPa, 500 K,and negligible velocity to 0.1 MPa. Calculate the throat andexit areas for a mass flow rate of 0.25 kg/s, assuming thenozzle is isentropic. Why must this nozzle be converging–diverging? Answers: 3.51 cm 2 , 5.84 cm 217–136E Helium expands in a nozzle from 150 psia, 900R, and negligible velocity to 15 psia. Calculate the throat andexit areas for a mass flow rate of 0.2 lbm/s, assuming thenozzle is isentropic. Why must this nozzle be converging–diverging?17–137 Using the EES software and the relations inTable A–32, calculate the one-dimensionalcompressible flow functions for an ideal gas with k 1.667,and present your results by duplicating Table A–32.17–138 Using the EES software and the relations inTable A–33, calculate the one-dimensionalnormal shock functions for an ideal gas with k 1.667, andpresent your results by duplicating Table A–33.17–139 Consider an equimolar mixture of oxygen andnitrogen. Determine the critical temperature, pressure, anddensity for stagnation temperature and pressure of 800 Kand 500 kPa.17–140 Using EES (or other) software, determine theshape of a converging–diverging nozzle for airfor a mass flow rate of 3 kg/s and inlet stagnation conditionsof 1400 kPa and 200°C. Assume the flow is isentropic.Repeat the calculations for 50-kPa increments of pressuredrops to an exit pressure of 100 kPa. Plot the nozzle to scale.Also, calculate and plot the Mach number along the nozzle.17–141 Using EES (or other) software and the relationsgiven in Table A–32, calculate the onedimensionalisentropic compressible-flow functions byvarying the upstream Mach number from 1 to 10 in incrementsof 0.5 for air with k 1.4.17–142 Repeat Prob. 17–141 for methane with k 1.3.17–143 Using EES (or other) software and the relationsgiven in Table A–33, generate the onedimensionalnormal shock functions by varying the upstreamMach number from 1 to 10 in increments of 0.5 for air withk 1.4.17–144 Repeat Prob. 17–143 for methane with k 1.3.17–145 Air is cooled as it flows through a 20-cm-diameterduct. The inlet conditions are Ma 1 1.2, T 01 350 K, and P 01 240 kPa and the exit Mach number is Ma 2 2.0. Disregardingfrictional effects, determine the rate of cooling of air.17–146 Air is heated as it flows subsonically through a10 cm 10 cm square duct. The properties of air at the inletare maintained at Ma 1 0.4, P 1 400 kPa, and T 1 360 Kat all times. Disregarding frictional losses, determine thehighest rate of heat transfer to the air in the duct withoutaffecting the inlet conditions. Answer: 1958 kWQ maxP 1 400 kPaT 1 360 KMa 1 0.4FIGURE P17–14617–147 Repeat Prob. 17–146 for helium.17–148 Air is accelerated as it is heated in a duct with negligiblefriction. Air enters at V 1 100 m/s, T 1 400 K, andP 1 35 kPa and then exits at a Mach number of Ma 2 0.8.Determine the heat transfer to the air, in kJ/kg. Also determinethe maximum amount of heat transfer without reducingthe mass flow rate of air.17–149 Air at sonic conditions and static temperature andpressure of 500 K and 420 kPa, respectively, is to be acceleratedto a Mach number of 1.6 by cooling it as it flows througha channel with constant cross-sectional area. Disregardingfrictional effects, determine the required heat transfer from theair, in kJ/kg. Answer: 69.8 kJ/kg17–150 Saturated steam enters a converging–diverging nozzleat 3.0 MPa, 5 percent moisture, and negligible velocity,and it exits at 1.2 MPa. For a nozzle exit area of 16 cm 2 ,determine the throat area, exit velocity, mass flow rate, andexit Mach number if the nozzle (a) is isentropic and (b) hasan efficiency of 90 percent.Fundamentals of Engineering (FE) Exam Problems17–151 An aircraft is cruising in still air at 5°C at a velocityof 400 m/s. The air temperature at the nose of the aircraftwhere stagnation occurs is(a) 5°C (b) 25°C (c) 55°C (d) 80°C (e) 85°C17–152 Air is flowing in a wind tunnel at 15°C, 80 kPa,and 200 m/s. The stagnation pressure at the probe insertedinto the flow section is(a) 82 kPa (b) 91 kPa (c) 96 kPa(d) 101 kPa (e) 114 kPa17–153 An aircraft is reported to be cruising in still air at20°C and 40 kPa at a Mach number of 0.86. The velocityof the aircraft is(a) 91 m/s (b) 220 m/s (c) 186 m/s(d) 280 m/s (e) 378 m/s