Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.9P
The entropy increase across a normal shock wave is
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The velocity ratio(v1/v2)of an isentropic flow through a supersonic wind tunnel is 0.915 ifthe velocity and mach number at the exit are 376.95 m/s and 2.60 respectively find the value of speed of sound at the entrance
A supersonic aircraft flies with a velocity
lower by 39 m-s at 7800 m elevation, (T = - 54 C°
at 7800 m) and (T = - 57 C° at 8800 m, M = 2),
determine the difference between Mach no.s.
The angle of the weak oblique shock wave =
The angle of the strong oblique shock wave =
Mach number downstream the weak oblique shock wave (M2)
Pressure downstream the weak oblique shock wave
Temperature downstream the weak oblique shock wave
Chapter 8 Solutions
Fundamentals of Aerodynamics
Ch. 8 - Consider air at a temperature of 230 K. Calculate...Ch. 8 - The temperature in the reservoir of a supersonic...Ch. 8 - At a given point in a flow, T=300K,p=1.2atm, and...Ch. 8 - At a given point in a flow, T=700R,p=1.6atm, and...Ch. 8 - Consider the isentropic flow through a supersonic...Ch. 8 - Consider the isentropic flow over an airfoil. The...Ch. 8 - The flow just upstream of a normal shock wave is...Ch. 8 - The pressure upstream of a normal shock wave is 1...Ch. 8 - The entropy increase across a normal shock wave is...Ch. 8 - The how just upstream of a normal shock wave is...
Ch. 8 - Consider a flow with a pressure and temperature of...Ch. 8 - Consider a flow with a pressure and temperature of...Ch. 8 - Repeat Problems 8.11 and 8.12 using (incorrectly)...Ch. 8 - Derive the Rayleigh Pitot tube formula, Equation...Ch. 8 - On March 16, 1990, an Air Force SR-71 set a new...Ch. 8 - In the test section of a supersonic wind tunnel, a...Ch. 8 - When the Apollo command module returned to earth...Ch. 8 - The stagnation temperature on the Apollo vehicle...Ch. 8 - Prove that the total pressure is constant...
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- 56. A supersonic aircraft flies with a velocity greater by 39 m-s1 at 7600 m elevation, (T = - 51 C° at 7600 m) and (T =- 55 C° at 8600 m, M = 1.9), determine the ratio of Mach no.s.arrow_forwardFor non-isentropic constant-area flow with stagnation temperature change the following relation was determined: Y 1 To _ ²(y + 1)M² (1 + ¹ Z ¹ M²) 2 TO (1+yM²)² It is possible to use the above equation and calculate the downstream Mach number without resorting to iteration for a flow where the upstream Mach number, as well as the upstream and downstream stagnation temperatures, are known. This is a common calculation for flows through engine combustors. Presuming the left side is a known quantity, show that the above equation can be directly solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution. Rewrite the equation as: aM4 + bM² + c = 0, and then M² = (−b ± √b² - 4ac)/2a. Determine the appropriate expressions for a, b, and c.arrow_forwardThe Mach number of an aircraft that travels with a speed of 260 m/s in air at 25° C while it undergoes the compressibility effect will be: (Use speed of sound in air at 0° C: 331 m/s) Select one: a. M = 0.69 b. M= 0.70 c. M= 0.75arrow_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 is flowing in a convergent nozzle. At a particular location within the nozzle the pressure is 280 kPa, the stream temperature is 345 K. and the velocity is 150 m/s. If the cross-sectional area at this location is 9.29 x 103 m², find: (a) The Mach number at this location, (b) The stagnation temperature and pressure. (c) The area, pressure, and temperature at the exit where M-1.0. (d) The mass rate of flow for the nozzle. Indicate any assumptions you may make and the source of data used in the solution.arrow_forward(b) Air flows through a cylindrical duct at a rate of 2.3 kg/s. Friction between air and the duct and friction within air can be neglected. The diameter of the duct is 10cm and the air temperature and pressure at the inlet are T₁ 450 K and P₁ = 200 kPa. If the Mach number at the exit is Ma2 determine the rate of heat transfer and the pressure difference across the duct. The constant pressure specific heat of air is cp = 1.005 kJ/kg-K. The gas constant of air is R = 0.287 kJ/kg-K and assume k = 1.4. -arrow_forward
- aircraft flies at the same Mach number but 50 m/s slower at 8 km compared to its speed at sea level. Find this Mach number a. 1.45 b. 1.55 c. 2.25 d. 1.65 e. 2.50.arrow_forward2. Carbon dioxide gas (CO2) flows adiabatically along a duct. At station 1 the static pressure P₁=120 kPa and the static temperature T1= 120 oC. At station 2 further along the duct the static pressurep2=75 kPa and the velocity C 2= 150 m/s.Determine (1) the Mach number M 2 (2) the stagnation pressure poz (3) stagnationtemperature Toz (4) the Mach number M 1 For CO 2 take R = 188 J/(kg K) and K = 1.30.arrow_forwardQ1: when aircraft is ffying at subsonic velocity, the pressure at its nose i e. the stagnation point is found to be 160 kpa. if the ambient pressure and temperature are 100 kpa and 298k respectively, find the speed and Mach number at which the aircraft is flying.-arrow_forward
- Q4/ Air enters a duct with a Mach number of 2.0, and the temperature and pressure are 170 K and 0.7 bar, respectively. Heat transfer takes place while the flow proceeds down the duct. A converging section (A2/A3 = 1.45) is attached to the outlet as shown in Fig. Q4, and the exit Mach number is 1.0. Assume that the inlet conditions and exit Mach number remain fixed. Find the amount and direction of heat transfer in the duct: (a) If there are no shocks in the system. (b) If there is a normal shock someplace in the duct. M, - 2.0 T,- 170 K P-0.7 bar M, = 1.0 Fig.Q4 AzlA, = 1.45arrow_forwardWhat is the Mach number of an airflow with a velocity of 2000m/s, at 2,000 ft altitude?arrow_forwardFind the velocity of bullet fired in standard air if the Mach angle is 45°. Take R=287.14 J/kg K and k = 1.4 for air. Assume temperature as 27°Carrow_forward
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What is entropy? - Jeff Phillips; Author: TED-Ed;https://www.youtube.com/watch?v=YM-uykVfq_E;License: Standard youtube license