Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.10P
Consider the supersonic flow over an expansion corner, such as given in Figure 9.25. The deflection angle
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Air is flowing in a convergent nozzle. The stagnation pressure is 350 KPa ,
the stagnation temperature is 400 K and Mach number is 0.7. If the cross
sectional area at this location is 10 × 10-3 m² , find
1) The static temperature and static pressure
2) The velocity at this location.
3) The area and static temperature and static pressure at the exit where Mach
number =1
Q2) Uniform airflow at Mach 3 passes into a concave corner of angle 15°, as shown in
Figure. The pressure and temperature in the supersonic flow are, respectively, 72 kPa and
290K. Determine the tangential and normal components of velocity and Mach number
upstream and downstream of the wave for the weak shock solution. Also find the static and
stagnation pressure ratios across the wave.
M1 = 3
Q1. A turbojet aircraft flying at speed of 1645 km/h and altitude of 9000 m.
A supersonic intake was designed with a conical center body, which generated one
oblique shock wave and normal shock wave at the inlet of the aircraft. The
deflection of the conical center body is a 10°. Calculate the fluid flow properties
and velocity at the aircraft inlet of the intake. Assume a weak solution.
Take: R= 0.287 kJ/kg K, and Cp=0.9 kJ/kg K.
Chapter 9 Solutions
Fundamentals of Aerodynamics
Ch. 9 - A slender missile is flying at Mach 1.5 at low...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Equation (8.80) does not hold for an oblique shock...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Consider the flow over a 22.2 half-angle wedge. If...Ch. 9 - Consider a flat plate at an angle of attack a to a...Ch. 9 - A 30.2 half-angle wedge is inserted into a...Ch. 9 - Consider a Mach 4 airflow at a pressure of 1 atm....Ch. 9 - Consider an oblique shock generated at a...Ch. 9 - Consider the supersonic flow over an expansion...
Ch. 9 - A supersonic flow at M1=1.58 and p1=1atm expands...Ch. 9 - A supersonic flow at M1=3,T1=285K, and p1=1atm is...Ch. 9 - Consider an infinitely thin flat plate at an angle...Ch. 9 - Consider a diamond-wedge airfoil such as shown in...Ch. 9 - Consider sonic flow. Calculate the maximum...Ch. 9 - Consider a circular cylinder (oriented with its...Ch. 9 - Consider the supersonic flow over a flat plate at...Ch. 9 - (The purpose of this problem is to calculate a...Ch. 9 - Repeat Problem 9.18, except with =30. Again, we...Ch. 9 - Consider a Mach 3 flow at 1 atm pressure initially...Ch. 9 - The purpose of this problem is to explain what...
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- A rocket motor is designed to give 10, 000 N thrust at 10, 000 m altitude. The combustion chamber pressure and temperature are 2 × 106 P a and 2800°K, respectively. The gases exit the combustion chamber through a Laval nozzle. Find the exit Mach number, and the cross-sectional areas of the exit and the throat of the nozzle. Assume the nozzle flow is isentropic and one-dimensional, and that the ratio of specific heats γ for the combustion gases is 1.32.arrow_forwardThe stagnation chamber of a wind tunnel is connected to a high pressure air bottle farm which is outside the laboratory building. The two are connected by a long pipe which has a inside diameter of 4 inches. If the static pressure ratio between the bottle farm and the stagnation chamber is 10 and the bottle farm static pressure is 100 atm, how long can the pipe be without choking and what is the change in entropy? Assume adiabatic,subsonic, one-dimensional flow with a friction coefficient of 0.005.arrow_forward3. Assume a supersonic flow with M=2, P=1 atm, and T=288 K that is deflected via 15° at a compression corner. Determine M, P, T, as well as PO and TO behind the associated oblique shock wave.arrow_forward
- A normal shock wave exists in air flow with up stream M=2, and a pressure of 20 kpa and temperature of 15c. find The mach number, pressure, stagnation pressure temperature stagnation temperature and air velocity down stream of the shock wave.arrow_forwardAQ1) Uniform air flow at Mach 3 passes into a concave corner of angle 15°, as shown in Figure P6.1. The pressure and temperature in the supersonic flow are, respectively. 72 kPa and 290 K. Determine the tangential and normal components of velocity and Mach number upstream and downstream of the wave. Also, find the static and stagnation pressure ratios across the wave. How great would the corner angle have to be before the shock would detach from the corner? L SPR 15°arrow_forwardThe velocity ratio (v1/v2) of an isentropic flow through a supersonic wind tunnel is 0.615. if the mach number at the tunnels entry section is 0.95 find the value of mach number at the exitarrow_forward
- Nozzle is assuming steady one-dimensional flow. M = 2.731. This is the the supersonic flow of air through a convergent-divergent nozzle. The stagnation temperature = 300K, stagnation pressure at the inlet = 107500Pa, static pressure at the exit=4400Pa, C1 is a constant = 0.1097 for calculating circular cross-sectional area of a convergent-divergent nozzle: A = C1 + x^2 and x (axial distance from the throat) =1m. γ = 1.4 and R=287. Calculate the mass flow rate of air through the nozzle. Thank You.arrow_forward2. An air tank with a nozzle has a pressure of 196.32 KPa and density of 1.9 Kg/m³. Outside the converging- diverging nozzle, the pressure is atmospheric and designed to have a Mach No. of 1.0 and 1.5 at the throat and exit respectively. The area at the throat is 0.11m2. Calculate the following: (a) Temperature and speed of sound at the tank. (b) Pressure, density, temperature and speed of sound at the throat. (c) Mass flow at the exit.arrow_forwardQ4/ 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_forward
- Q.5 A supersonic wind tunnel, which is shown in the figure, is fed from a large tank. The air is discharged to the atmosphere. The Mach number in the test section is 2.65 and a normal shock wave stands at the exit of the wind tunnel. The pressure at section 3 immediately after the normal shock wave is 100 kPa. The flow is isentropic except through the normal shock wave. Find: 1. Po, P1, P2 and M3. 2. If a Pitot tube is placed in the exit jet, then calculate the pressure measured by the Pitot tube. Po Test section Normal shock wave Exit Jet Pitot tubearrow_forwardIn the test section of a supersonic wind tunnel, a Pitot tube in the flowreads a pressure of 1.13 atm. A static pressure measurement (from apressure tap on the sidewall of the test section) yields 0.1 atm. Calculatethe Mach number of the flow in the test section.arrow_forwardThe pressure ratio across a normal shock wave that occurs in air is 1.25. Ahead of the shock wave, the pressure is 100 kPa and the temperature is 15 C. Find the velocity, pressure, and temperature of the air behind the shock wave.arrow_forward
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