Thermodynamics

17–115E Steam enters a converging nozzle at 450 psia and900°F with a negligible velocity, and it exits at 275 psia. Fora nozzle exit area of 3.75 in 2 , determine the exit velocity,mass flow rate, and exit Mach number if the nozzle (a) isisentropic and (b) has an efficiency of 90 percent. Answers:(a) 1847 ft/s, 18.7 lbm/s, 0.900, (b) 1752 ft/s, 17.5 lbm/s, 0.84917–116 Steam enters a converging–diverging nozzle at 1 MPaand 500°C with a negligible velocity at a mass flow rate of 2.5kg/s, and it exits at a pressure of 200 kPa. Assuming the flowthrough the nozzle to be isentropic, determine the exit area andthe exit Mach number. Answers: 31.5 cm 2 , 1.73817–117 Repeat Prob. 17–116 for a nozzle efficiency of 95percent.Review Problems17–118 Air in an automobile tire is maintained at a pressureof 220 kPa (gauge) in an environment where the atmosphericpressure is 94 kPa. The air in the tire is at theambient temperature of 25°C. Now a 4-mm-diameter leakdevelops in the tire as a result of an accident. Assuming isentropicflow, determine the initial mass flow rate of air throughthe leak. Answer: 0.554 kg/min17–119 The thrust developed by the engine of a Boeing 777is about 380 kN. Assuming choked flow in the nozzles, determinethe mass flow rate of air through the nozzle. Take theambient conditions to be 265 K and 85 kPa.17–120 A stationary temperature probe inserted into a ductwhere air is flowing at 250 m/s reads 85°C. What is theactual temperature of air? Answer: 53.9°C17–121 Nitrogen enters a steady-flow heat exchanger at150 kPa, 10°C, and 100 m/s, and it receives heat in theamount of 125 kJ/kg as it flows through it. The nitrogenleaves the heat exchanger at 100 kPa with a velocity of 180m/s. Determine the stagnation pressure and temperature ofthe nitrogen at the inlet and exit states.17–122 Derive an expression for the speed of sound basedon van der Waals’ equation of state P RT(v b) a/v 2 .Using this relation, determine the speed of sound in carbondioxide at 50°C and 200 kPa, and compare your result to thatobtained by assuming ideal-gas behavior. The van der Waalsconstants for carbon dioxide are a 364.3 kPa · m 6 /kmol 2and b 0.0427 m 3 /kmol.17–123 Obtain Eq. 17–10 by starting with Eq. 17–9 andusing the cyclic rule and the thermodynamic property relationsc pT a 0s0T b Pandc vT a 0s0T b .v17–124 For ideal gases undergoing isentropic flows, obtainexpressions for P/P*, T/T*, and r/r* as functions of k and Ma.17–125 Using Eqs. 17–4, 17–13, and 17–14, verify that forthe steady flow of ideal gases dT 0 /T dA/A (1 Ma 2 )Chapter 17 | 879dV/V. Explain the effect of heating and area changes on thevelocity of an ideal gas in steady flow for (a) subsonic flowand (b) supersonic flow.17–126 A subsonic airplane is flying at a 3000-m altitudewhere the atmospheric conditions are 70.109 kPa and 268.65 K.A Pitot static probe measures the difference between the staticand stagnation pressures to be 35 kPa. Calculate the speed ofthe airplane and the flight Mach number. Answers: 257 m/s,0.78317–127 Plot the mass flow parameter ṁ 1RT 0 /(AP 0 ) versusthe Mach number for k 1.2, 1.4, and 1.6 in the range of 0 Ma 1.17–128 Helium enters a nozzle at 0.8 MPa, 500 K, anda velocity of 120 m/s. Assuming isentropic flow, determinethe pressure and temperature of helium at a locationwhere the velocity equals the speed of sound. What is theratio of the area at this location to the entrance area?17–129 Repeat Prob. 17–128 assuming the entrance velocityis negligible.17–130 Air at 0.9 MPa and 400 K enters a convergingnozzle with a velocity of 180 m/s. The throatarea is 10 cm 2 . Assuming isentropic flow, calculate and plotthe mass flow rate through the nozzle, the exit velocity, theexit Mach number, and the exit pressure–stagnation pressureratio versus the back pressure–stagnation pressure ratio for aback pressure range of 0.9 P b 0.1 MPa.17–131 Steam at 6.0 MPa and 700 K enters a convergingnozzle with a negligible velocity. Thenozzle throat area is 8 cm 2 . Assuming isentropic flow, plotthe exit pressure, the exit velocity, and the mass flow ratethrough the nozzle versus the back pressure P b for 6.0 P b 3.0 MPa. Treat the steam as an ideal gas with k 1.3, c p 1.872 kJ/kg · K, and R 0.462 kJ/kg · K.17–132 Find the expression for the ratio of the stagnationpressure after a shock wave to the static pressure before theshock wave as a function of k and the Mach number upstreamof the shock wave Ma 1 .17–133 Nitrogen enters a converging–diverging nozzle at 700kPa and 300 K with a negligible velocity, and it experiences anormal shock at a location where the Mach number is Ma 3.0. Calculate the pressure, temperature, velocity, Mach number,and stagnation pressure downstream of the shock. Comparethese results to those of air undergoing a normal shockat the same conditions.17–134 An aircraft flies with a Mach number Ma 1 0.8 atan altitude of 7000 m where the pressure is 41.1 kPa and thetemperature is 242.7 K. The diffuser at the engine inlet hasan exit Mach number of Ma 2 0.3. For a mass flow rate of65 kg/s, determine the static pressure rise across the diffuserand the exit area.