Consider an oblique shock wave with a wave angle of
The pressure.
The temperature.
The Mach number.
The total pressure.
The total temperature behind the wave.
The entropy increase.
Answer to Problem 9.2P
The pressure is
The temperature is
The Mach number is
The total pressure is
The total temperature behind the wave is
The entropy increase is
Explanation of Solution
Given:
The upstream temperature is
The upstream pressure is
The wave angle of the shock wave is
The Mach number is
Formula Used:
The expression for the normal component of upstream Mach number is given as,
Here,
The expression for total upstream pressure is given as,
Here,
The expression for the upstream temperature is given as,
The expression for the downstream static pressure is given as,
The expression for the downstream static temperature is given as,
The expression for the downstream normal Mach number is given as,
The expression for the entropy increase across oplique shock wave is given as,
Here,
Calculation:
Thenormal component of upstream Mach number can be calculated as,
The total upstream pressure can be calculated as,
The upstream temperature can be calculated as,
The downstream static pressure can be calculated as,
The downstream static temperature can be calculated as,
The downstream normal Mach number can be calculated as,
The deflection angle can be calculated as,
The angle between downstream flow and oblique shock wave can be calculated as,
The total downstream pressure can be calculated as,
The temperature does not change across shock wave and will be,
The expression for the entropy increase across oplique shock wave is given as,
Conclusion:
Therefore, the pressure is
Therefore, the temperature is
Therefore, the Mach number is
Therefore, the total pressure is
Therefore, the total temperature behind the wave is
Therefore, the entropy increase is
Want to see more full solutions like this?
Chapter 9 Solutions
Fundamentals of Aerodynamics
Additional Engineering Textbook Solutions
Introduction to Heat Transfer
Engineering Mechanics: Dynamics (14th Edition)
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Vector Mechanics for Engineers: Dynamics
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Degarmo's Materials And Processes In Manufacturing
- 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 wavearrow_forwardNitrogen enters a converging–diverging nozzle at 620 kPa and 310 K with a negligible velocity, and it experiences a normal 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. Compare these results to those of air undergoing a normal shock at the same conditions.arrow_forwardAir enters a converging–diverging nozzle of a supersonic wind tunnel at 150 psia and 100°F with a low velocity. The flow area of the test section is equal to the exit area of the nozzle, which is 5 ft2. Calculate the pressure, temperature, velocity, and mass flow rate in the test section for a Mach number Ma = 2. Explain why the air must be very dry for this application.arrow_forward
- The entropy increase across a normal shock wave is 199.5 J/(kg · K). Whatis the upstream Mach number?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_forwardThe Mach number behind a normal shock wave is 0.4752. What is the Mach number in front of the wave? What are the density, pressure, and temperature ratios across the shock?arrow_forward
- Consider a hypersonic vehicle with a spherical nose flying at Mach 20at a standard altitude of 150,000 ft, where the ambient temperature andpressure are 500◦R and 3.06 lb/ft2, respectively. At the point on thesurface of the nose located 20◦ away from the stagnation point, estimatethe: (a) pressure, (b) temperature, (c) Mach number, and (d) velocity ofthe flow.arrow_forwardSupersonic air at Ma1 = 2.0 and 230 kPa flows parallel to a flat wall that suddenly expands by ? = 10° . Ignoring any effects caused by the boundary layer along the wall, calculate downstream Mach number Ma2 and pressure P2.arrow_forwardThe pressure upstream of a normal shock wave is 1 atm. The pressure and temperature downstream of the wave are 10.33 atm and 1,390 °R, respectively. Calculate the Mach number and temperature upstream of the wave.arrow_forward
- vortex generators on the upper surface of a wing will a. decrease the spanwise flow at high Mach numbers b. increase the critical Mach number c. decrease the intensity of the shockwave effects d. increase intensity of the shockwave effectsarrow_forwardAir 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 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_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY