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
- The 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_forwardQ.1. A uniform supersonic air flow travelling at a Mach number of 2.5 passes over A wedge which deflects the flow by 15", as shown in the figure. If the pressure and temperature in the uniform flow are 40 kPa and 263 K, respectively, determine the shock wave angle, Mach number, pressure and temperature downstream of the oblique shock wave. Oblique Sheck Waye M= 1.5 T=263 K 15 F- 40 KPaarrow_forwardConsider an oblique shock wave with a wave angle of 30◦ in a Mach 4flow. The upstream pressure and temperature are 2.65 × 104 N/m2 and223.3 K, respectively (corresponding to a standard altitude of 10,000 m).Calculate the pressure, temperature, Mach number, total pressure, and totaltemperature behind the wave and the entropy increase across the wave.arrow_forward
- 4. Determine the upstream Mach number, considering an oblique shock wave with ew = 32° and a pressure ratio, P2/P1 = 3.0.arrow_forwardAir pass through a wind tunnel at 70 kPa and 15 °C and the speed of air is 200 m/s. Mach number is 1.728 2.576 1.701 0.5879arrow_forwardQ.2 Air which enters a diverging duct is slowed by a normal shock wave, as shown in figure. The airstream enters the duct at a Mach number of 3 and leaves it at a Mach number of 0.4. the exit cross-sectional area of the duct is twice the inlet cross- sectional area. Determine the pressure ratio across the normal shock wave, and the ratio of the exit pressure to the inlet pressure. M. = 0.4 M; = 3arrow_forward
- Consider a normal shock wave in a supersonic airstream where the pressure upstream of the shock is 1 atm. Calculate the loss of total pressure across the shock wave when the upstream Mach number is (a) M1 = 2.5, and (b) M1 = 4.5. Compare these two results and comment on their implicationarrow_forwardThe velocity and temperature behind a normal shock wave are 329 m/s and 1500 K, respectively. Calculate the velocity in front of the shock wave.arrow_forwardAir enters a converging- diverging nozzle at a pressure of 830 kPa abs and a temperature of 32°C. Neglecting the entrance velocity and assuming a frictionless process, find the Mach number at the cross-section where the pressure is 240 kPa abs.( for air: k = 1.4 R=287J/kgK)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_forward(a) Write Area-Velocity relation for compressible flows through a supersonic Convergent-Divergent nozzle What is the importance of it? (b) Write Area-density relation for compressible flows through a supersonic Convergent-Divergent nozzle What is the importance of it? (c) Write Area-Mach relation for compressible flows through a supersonic Convergent-Divergent nozzle What is the importance of it? (d) Plot the variation of density, pressure, temperature, velocity and Mach number for compressible flows through a supersonic Convergent-Divergent nozzle Note: Do NOT derive above relations.arrow_forwardAt some section in the convergent-divergent nozzle, in which air is flowing, pressure, velocity, temperature and cross-sectional area are 200 kN/m², 170 m/s, 200°C and 1000 mm² respectively. If the flow conditions are isentropic, determine: (i) Stagnation temperature and stagnation pressure, (ii) Sonic velocity and Mach number at this section, (iii) Velocity, Mach number and flow area at outlet section where pressure is 110 kN/m², (iv) Pressure and temperature at throat of the nozzle. Take for air: R=287 J/kg K, cp = 1.0 kJ/kg K and k = 1.4arrow_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