Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 12, Problem 85P
To determine
Mach number at the duct exit.
The drop-in stagnation pressure (
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Compressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 560 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 300 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit and the drop in stagnation pressure P01 – P02 during this process. Take the properties of air to be k = 1.4, cp = 1.005 kJ/kg·K, and R = 0.287 kJ/kg·K.
The Mach number at the duct exit is____ .
The drop in stagnation pressure is____ kPa.
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature velocity, Mach number, and stagnation pressure downstream of the shock. Calculate the entropy changes of air and helium across the normal shock wave
A gas at a specified stagnation temperature and pressure is accelerated to Ma = 2 in a converging–diverging nozzle and to Ma = 3 in another nozzle. What can you say about the pressures at the throats of these two nozzles
Chapter 12 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 12 - What is dynamic temperature?Ch. 12 - Calculate the stagnation temperature and pressure...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8EPCh. 12 - Prob. 9PCh. 12 - Products of combustion enter a gas turbine with a...Ch. 12 - Is it possible to accelerate a gas to a supersonic...Ch. 12 - Prob. 72EPCh. 12 - Prob. 73P
Ch. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - For an ideal gas flowing through a normal shock,...Ch. 12 - Prob. 77CPCh. 12 - On a T-s diagram of Raleigh flow, what do the...Ch. 12 - What is the effect of heat gain and heat toss on...Ch. 12 - Prob. 80CPCh. 12 - Prob. 81CPCh. 12 - Prob. 82CPCh. 12 - Argon gas enters a constant cross-sectional area...Ch. 12 - Prob. 84EPCh. 12 - Prob. 85PCh. 12 - Prob. 86PCh. 12 - Prob. 87EPCh. 12 - Prob. 88PCh. 12 - Prob. 89PCh. 12 - Prob. 90PCh. 12 - Prob. 91PCh. 12 - Prob. 93CPCh. 12 - Prob. 94CPCh. 12 - Prob. 95CPCh. 12 - Prob. 96CPCh. 12 - Prob. 97CPCh. 12 - Prob. 98CPCh. 12 - Prob. 99CPCh. 12 - Prob. 100CPCh. 12 - Prob. 101PCh. 12 - Air enters a 5-cm-diameter, 4-m-long adiabatic...Ch. 12 - Helium gas with k=1.667 enters a 6-in-diameter...Ch. 12 - Air enters a 12-cm-diameter adiabatic duct at...Ch. 12 - Prob. 105PCh. 12 - Air flows through a 6-in-diameter, 50-ft-long...Ch. 12 - Air in a room at T0=300k and P0=100kPa is drawn...Ch. 12 - Prob. 110PCh. 12 - Prob. 112PCh. 12 - Prob. 113PCh. 12 - Prob. 114PCh. 12 - Prob. 115PCh. 12 - Prob. 116EPCh. 12 - A subsonic airplane is flying at a 5000-m altitude...Ch. 12 - Prob. 118PCh. 12 - Prob. 119PCh. 12 - Prob. 120PCh. 12 - Prob. 121PCh. 12 - Prob. 122PCh. 12 - Prob. 123PCh. 12 - An aircraft flies with a Mach number Ma1=0.9 at an...Ch. 12 - Prob. 125PCh. 12 - Helium expands in a nozzle from 220 psia, 740 R,...Ch. 12 - Prob. 127PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - Prob. 131PCh. 12 - Prob. 132PCh. 12 - Prob. 133PCh. 12 - Prob. 134PCh. 12 - Prob. 135PCh. 12 - Prob. 136PCh. 12 - Prob. 137PCh. 12 - Prob. 138PCh. 12 - Air is cooled as it flows through a 30-cm-diameter...Ch. 12 - Prob. 140PCh. 12 - Prob. 141PCh. 12 - Prob. 142PCh. 12 - Prob. 145PCh. 12 - Prob. 148PCh. 12 - Prob. 149PCh. 12 - Prob. 150PCh. 12 - Prob. 151PCh. 12 - Prob. 153PCh. 12 - Prob. 154PCh. 12 - Prob. 155PCh. 12 - Prob. 156PCh. 12 - Prob. 157PCh. 12 - Prob. 158PCh. 12 - Prob. 159PCh. 12 - Prob. 160PCh. 12 - Prob. 161PCh. 12 - Prob. 162PCh. 12 - Assuming you have a thermometer and a device to...
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- An air stream with a Mach number of (3.04) a pressure of (302 kPa) and a temperature of (502 K) enters a diverging channel. If the ratio of the exit cross- sectional area to the inlet cross- sectional area is (3). Determine the back pressure which is necessary to produce a normal shock wave in the channel with a cross-sectional area equal to twice the inlet cross-sectional area. Assume steady, one-dimensional isentropic flow except through the normal shock wave. Ax=2Ai , Ae=3Aiarrow_forwardD5. A converging-diverging nozzle operates with air and subsonic flow at the inlet and supersonic flow at the outlet with no shacks inside the nozzle. Determine the mach number and static pressure at the outlet if the area of the outlet is 0.900 m2, the area of the throat is 0.490m2, and the stagnation pressure is 215 kPa.arrow_forwardIn compressible flow, velocity measurements with a Pitot probe can be grossly in error if relations developed for incompressible flow are used. Therefore, it is essential that compressible flow relations be used when evaluating flow velocity from Pitot probe measurements. Consider supersonic flow of air through a channel. A probe inserted into the flow causes a shock wave to occur upstream of the probe, and it measures the stagnation pressure and temperature to be 620 kPa and 340 K, respectively. If the static pressure upstream is 110 kPa, determine the flow velocity.arrow_forward
- Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.arrow_forwardAn ideal isentropic nozzle is attached to an infinite reservoir that has stagnation conditions 3 MPa and 2250 K, and a constant specific heat of 1.2. If the nozzle's static exit pressure is 38.871 kPa, what is the exit static temperature? Also determine the nozzle's exit Mach number, stagnation pressure, and stagnation temperature.arrow_forwardConsider gas flow through a converging–diverging nozzle. Of the five following statements, select the one that is incorrect: (a) The fluid velocity at the throat can never exceed the speed of sound. (b) If the fluid velocity at the throat is below the speed of sound, the diversion section will act like a diffuser. (c) If the fluid enters the diverging section with a Mach number greater than one, the flow at the nozzle exit will be supersonic. (d ) There will be no flow through the nozzle if the back pressure equals the stagnation pressure. (e) The fluid velocity decreases, the entropy increases, and stagnation enthalpy remains constant during flow through a normal shock.arrow_forward
- Air enters a converging–diverging nozzle at a pressure of 1200 kPa with negligible velocity. What is the lowest pressure that can be obtained at the throat of the nozzle?arrow_forwardAir enters a diffuser with a velocity of 200m/s. Determine the speed of sound in m/s at the diffuser inlet at 30°C. Determine the speed of sound Mach number at the diffuser inlet at 30°C.arrow_forwardExample: Carbon dioxide flows steadily at a mass flow rate of 3 kg/s and pressure of 1400 kPa and 200°C with a low velocity. It expands after the nozzle to a pressure of 200 kPa. The duct is designed so that the flow can be approximated as isentropic. Determine the density, velocity, flow area, and Mach number at each location along the duct that corresponds to a pressure drop of 200 kPaarrow_forward
- Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.arrow_forwardAir flows from a large tank where the pressure and temperature are 600 kPa and 800 K, respectively, through a converging nozzle with an exit area of 0.0005 m2 and discharges to the atmosphere with a pressure of 100 kPa. The flow Is lsentroplc throughout the nozzle. Determine the Mach number, temperature, pressure and velocity at the exit section, and also calculate the mass flow rate.arrow_forwardIn air-conditioning applications, the temperature of air is measured by inserting a probe into the flow stream. Thus, the probe actually measures the stagnation temperature. Does this cause any significant error?arrow_forward
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