Thermodynamics

874 | ThermodynamicsPROBLEMS*Stagnation Properties17–1C A high-speed aircraft is cruising in still air. Howwill the temperature of air at the nose of the aircraft differfrom the temperature of air at some distance from theaircraft?17–2C How and why is the stagnation enthalpy h 0 defined?How does it differ from ordinary (static) enthalpy?17–3C What is dynamic temperature?17–4C In air-conditioning applications, the temperature ofair is measured by inserting a probe into the flow stream.Thus, the probe actually measures the stagnation temperature.Does this cause any significant error?17–5 Determine the stagnation temperature and stagnationpressure of air that is flowing at 44 kPa, 245.9 K, and 470m/s. Answers: 355.8 K, 160.3 kPa17–6 Air at 300 K is flowing in a duct at a velocity of (a) 1,(b) 10, (c) 100, and (d) 1000 m/s. Determine the temperaturethat a stationary probe inserted into the duct will read foreach case.17–7 Calculate the stagnation temperature and pressure forthe following substances flowing through a duct: (a) helium at0.25 MPa, 50°C, and 240 m/s; (b) nitrogen at 0.15 MPa, 50°C,and 300 m/s; and (c) steam at 0.1 MPa, 350°C, and 480 m/s.17–8 Air enters a compressor with a stagnation pressure of100 kPa and a stagnation temperature of 27°C, and it is compressedto a stagnation pressure of 900 kPa. Assuming thecompression process to be isentropic, determine the powerinput to the compressor for a mass flow rate of 0.02 kg/s.Answer: 5.27 kW17–9E Steam flows through a device with a stagnationpressure of 120 psia, a stagnation temperature of 700°F, and avelocity of 900 ft/s. Assuming ideal-gas behavior, determinethe static pressure and temperature of the steam at this state.17–10 Products of combustion enter a gas turbine with astagnation pressure of 1.0 MPa and a stagnation temperatureof 750°C, and they expand to a stagnation pressure of 100kPa. Taking k 1.33 and R 0.287 kJ/kg · K for the productsof combustion, and assuming the expansion process to*Problems designated by a “C” are concept questions, and studentsare encouraged to answer them all. Problems designated by an “E”are in English units, and the SI users can ignore them. Problemswith a CD-EES icon are solved using EES, and complete solutionstogether with parametric studies are included on the enclosed DVD.Problems with a computer-EES icon are comprehensive in nature,and are intended to be solved with a computer, preferably using theEES software that accompanies this text.be isentropic, determine the power output of the turbine perunit mass flow.17–11 Air flows through a device such that the stagnationpressure is 0.6 MPa, the stagnation temperature is 400°C, andthe velocity is 570 m/s. Determine the static pressure and temperatureof the air at this state. Answers: 518.6 K, 0.23 MPaSpeed of Sound and Mach Number17–12C What is sound? How is it generated? How does ittravel? Can sound waves travel in a vacuum?17–13C Is it realistic to assume that the propagation ofsound waves is an isentropic process? Explain.17–14C Is the sonic velocity in a specified medium a fixedquantity, or does it change as the properties of the mediumchange? Explain.17–15C In which medium does a sound wave travel faster:in cool air or in warm air?17–16C In which medium will sound travel fastest for agiven temperature: air, helium, or argon?17–17C In which medium does a sound wave travel faster:in air at 20°C and 1 atm or in air at 20°C and 5 atm?17–18C Does the Mach number of a gas flowing at a constantvelocity remain constant? Explain.17–19 Determine the speed of sound in air at (a) 300 K and(b) 1000 K. Also determine the Mach number of an aircraftmoving in air at a velocity of 280 m/s for both cases.17–20 Carbon dioxide enters an adiabatic nozzle at 1200 Kwith a velocity of 50 m/s and leaves at 400 K. Assuming constantspecific heats at room temperature, determine the Machnumber (a) at the inlet and (b) at the exit of the nozzle.Assess the accuracy of the constant specific heat assumption.Answers: (a) 0.0925, (b) 3.7317–21 Nitrogen enters a steady-flow heat exchanger at 150kPa, 10°C, and 100 m/s, and it receives heat in the amount of120 kJ/kg as it flows through it. Nitrogen leaves the heatexchanger at 100 kPa with a velocity of 200 m/s. Determinethe Mach number of the nitrogen at the inlet and the exit ofthe heat exchanger.17–22 Assuming ideal-gas behavior, determine the speed ofsound in refrigerant-134a at 0.1 MPa and 60°C.17–23 The Airbus A-340 passenger plane has a maximumtakeoff weight of about 260,000 kg, a length of 64 m, a wingspan of 60 m, a maximum cruising speed of 945 km/h, aseating capacity of 271 passengers, maximum cruising altitudeof 14,000 m, and a maximum range of 12,000 km. Theair temperature at the crusing altitude is about 60°C. Determinethe Mach number of this plane for the stated limitingconditions.