Thermodynamics

876 | Thermodynamicsvelocities at the nozzle exit, how would it affect the massflow rate through the nozzle?17–49C How does the parameter Ma* differ from the Machnumber Ma?17–50C What would happen if we attempted to deceleratea supersonic fluid with a diverging diffuser?17–51C What would happen if we tried to further acceleratea supersonic fluid with a diverging diffuser?17–52C Consider the isentropic flow of a fluid through aconverging–diverging nozzle with a subsonic velocity at thethroat. How does the diverging section affect (a) the velocity,(b) the pressure, and (c) the mass flow rate of the fluid?17–53C Is it possible to accelerate a fluid to supersonicvelocities with a velocity other than the sonic velocity at thethroat? Explain.17–54 Explain why the maximum flow rate per unit areafor a given gas depends only on P 0 / 1T 0 . For an ideal gaswith k 1.4 and R 0.287 kJ/kg · K, find the constant asuch that ṁ/A* aP 0 / 1T 0 .17–55 For an ideal gas obtain an expression for the ratio ofthe velocity of sound where Ma 1 to the speed of soundbased on the stagnation temperature, c*/c 0 .17–56 An ideal gas flows through a passage that first convergesand then diverges during an adiabatic, reversible,steady-flow process. For subsonic flow at the inlet, sketch thevariation of pressure, velocity, and Mach number along thelength of the nozzle when the Mach number at the minimumflow area is equal to unity.17–57 Repeat Prob. 17–56 for supersonic flow at the inlet.17–58 Air enters a nozzle at 0.2 MPa, 350 K, and a velocityof 150 m/s. Assuming isentropic flow, determine the pressureand temperature of air at a location where the airvelocity equals the speed of sound. What is the ratio of thearea at this location to the entrance area?Answers: 0.118 MPa, 301 K, 0.62917–59 Repeat Prob. 17–58 assuming the entrance velocityis negligible.17–60E Air enters a nozzle at 30 psia, 630 R, and a velocityof 450 ft/s. Assuming isentropic flow, determine the pressureand temperature of air at a location where the airvelocity equals the speed of sound. What is the ratio of thearea at this location to the entrance area?Answers: 17.4 psia, 539 R, 0.57417–61 Air enters a converging–diverging nozzle at 0.5 MPawith a negligible velocity. Assuming the flow to be isentropic,determine the back pressure that will result in an exitMach number of 1.8. Answer: 0.087 MPa17–62 Nitrogen enters a converging–diverging nozzle at 700kPa and 450 K with a negligible velocity. Determine the criticalvelocity, pressure, temperature, and density in the nozzle.17–63 An ideal gas with k 1.4 is flowing through a nozzlesuch that the Mach number is 2.4 where the flow area is25 cm 2 . Assuming the flow to be isentropic, determine theflow area at the location where the Mach number is 1.2.17–64 Repeat Prob. 17–63 for an ideal gas with k 1.33.17–65 Air at 900 kPa and 400 K enters a convergingnozzle with a negligible velocity. The throat areaof the nozzle is 10 cm 2 . Assuming isentropic flow, calculateand plot the exit pressure, the exit velocity, and the mass flowrate versus the back pressure P b for 0.9 P b 0.1 MPa.17–66 Reconsider Prob. 17–65. Using EES (or other)software, solve the problem for the inlet conditionsof 1 MPa and 1000 K.17–67E Air enters a converging–diverging nozzle of asupersonic wind tunnel at 150 psia and 100°F with a lowvelocity. The flow area of the test section is equal to the exitarea of the nozzle, which is 5 ft 2 . Calculate the pressure, temperature,velocity, and mass flow rate in the test section for aMach number Ma 2. Explain why the air must be very dryfor this application. Answers: 19.1 psia, 311 R, 1729 ft/s,1435 lbm/sShock Waves and Expansion Waves17–68C Can a shock wave develop in the converging sectionof a converging–diverging nozzle? Explain.17–69C What do the states on the Fanno line and theRayleigh line represent? What do the intersection points ofthese two curves represent?17–70C Can the Mach number of a fluid be greater than 1after a shock wave? Explain.17–71C How does the normal shock affect (a) the fluidvelocity, (b) the static temperature, (c) the stagnation temperature,(d) the static pressure, and (e) the stagnation pressure?17–72C How do oblique shocks occur? How do obliqueshocks differ from normal shocks?17–73C For an oblique shock to occur, does the upstreamflow have to be supersonic? Does the flow downstream of anoblique shock have to be subsonic?17–74C It is claimed that an oblique shock can be analyzedlike a normal shock provided that the normal component ofvelocity (normal to the shock surface) is used in the analysis.Do you agree with this claim?17–75C Consider supersonic airflow approaching the noseof a two-dimensional wedge and experiencing an obliqueshock. Under what conditions does an oblique shock detachfrom the nose of the wedge and form a bow wave? What isthe numerical value of the shock angle of the detached shockat the nose?17–76C Consider supersonic flow impinging on the roundednose of an aircraft. Will the oblique shock that forms in frontof the nose be an attached or detached shock? Explain.