Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 12, Problem 12.8P
The result from Problem 12.6 demonstrates that maximum lift-to-drag ratio decreases as the Mach number increases. This is a fact of nature that progressively causes designers of supersonic airplanes grief as they strive toward aerodynamically efficient airplanes a higher supersonic Mach numbers. What physics is nature using against the airplane designer in this case, and how might the designer meet this challenge?
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Question #2
A supersonic stream leaves a nozzle in parallel flow (region "a") with a Mach
number of 2 and a pressure of 0.67 bar:
The pressure of the atmosphere into which the jet discharges is 1 bar.
(a) Calculate the pressures in regions "b" and “c".
(b) Make a sketch to scale showing stream lines and shock lines.
(c) Assuming the pressure at the nozzle entrance to be maintained constant,
what is the maximum atmospheric pressure for which this general type of
flow configuration is possible? Describe the nature of the flow pattern when
the exhaust-region pressure is raised above the limiting value.
Answer: 1 bar, 1.5 bar, 1.3 bar, 1 bar, 1.328
bar...
A model of a jet fighter aircraft of the military is to be tested in a pressurized helium wind tunnel to identify the effects of flying at supersonic speeds. Which of the following is the primary
criterion to be satisfied such that the model and prototype are dynamically similar?
Select one:
O a. Reynolds Law
O b. Mach Law
О с. Froude Law
O d. Weber Law
1. The pressure in a reservoir of a supersonic wind tunnel is 178.42 KPa, and the density is 1.7 kg/m3. The pressure outside the nozzle is atmospheric, with a Mach number of 1.8 at the exit. The throat has a surface area of 0.15m2 with a Mach Number of 1.0. Solve for the value of the following: (a) Reservoir temperature and speed of sound. (b) Pressure, density, temperature and speed of sound at the throat. (c) Mass flow at the exit.
Chapter 12 Solutions
Fundamentals of Aerodynamics
Ch. 12 - Using the results of linearized theory, calculate...Ch. 12 - For the conditions of Problem 12.1, calculate the...Ch. 12 - Consider a diamond-wedge airfoil such as shown in...Ch. 12 - Equation (12.24). from linear supersonic theory....Ch. 12 - Consider a flat plate at an angle of attack in an...Ch. 12 - Consider a flat plate at an angle of attack in a...Ch. 12 - Using the same flight conditions and the same...Ch. 12 - The result from Problem 12.6 demonstrates that...
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- How to make a good mesh for supersonic airplane simulation?Please explain!arrow_forward5. At 30000ft, estimate the magnitude of transonic drag rise. Using this estimate, calculate the maximum velocity of the airplane at this altitude. Assume drag-divergence Mach number of 0.82 and d(D/D₁)/dM = 14.3 where D₁=1750lb is drag at Mach number 0.9 and D₂ = 4250lb at Mach number 1. 6 Estimate maximum range at 30000€ Also calculate the flight speed to obtain thisarrow_forwardA piston moves along a tube containing air at an initial sound speed of 330 m/s. When the piston velocity is 250 m/s, it drives a shock wave which propagates at a velocity of 500 m/s. When the piston velocity is 100 m/s, it drives a shock at 400 m/s. Use the hypersonic equivalence principle to calculate the shock angles (in degrees) on a flat plate: At an incidence of 6 degrees and a Mach number of 7.2arrow_forward
- A uniform supersonic airflow traveling at Mach 2.0 passes over a wedge (Fig. 10E.1). An oblique shock, making an angle of 40° with the flow direction, is attached to the wedge under these flow conditions. If the static pressure and temperature in the uniform flow are, respectively, 20 kPa and −10 °C, determine the static pressure and temperature behind the wave, the Mach number of the flow passing over the wedge, and the wedge half-angle.arrow_forwardWhat is the mass flow rate of airflow, with a Mach number of 0.230, Area of 10 in^2, Speed of sound of 200 ft/s and a pressure of 0.95 atm?arrow_forwardA supersonic nozzle is used for discharging air from a reservoir. The reservoir pressure and temperature are 0.5 MPa and 500 K. The design Mach number is 2. With back pressure, a normal shock appears at the exit of the nozzle. Determine the Mach number, pressure and temperature of air after the shock. [Ans. M2 = 0.577, p2 = 0.288 MPa, T, = 468.14 K] %3D ||arrow_forward
- 1. Air having a reservoir pressure of 30 psia and density of 0.15 lb/ft is accelerated to a Mach number of 1.6. Find the static pressure, density, and temperature at this Mach number. 2. Consider the flow of air through a supersonic nozzle. The reservoir pressure and temperature are 5 atm and 500 K, respectively. If the Mach number at the nozzle exit is 3, calculate the exit pressure , temperature, and density. 4. A supersonic nozzle is a convergent-divergent duct , which is fed by a large reservoir at the inlet to the nozzle. In the reservoir of the nozzle, the pressure and temperature are 10atm and 550°R , respectively. At the nozzle exit, the pressure is 1 atm. Calculate the temperature and density of the flow at the exit. Assume the flow is isentropic and , of course, compressible. 3. The mass flow of air through a supersonic nozzle is 1.5 lbm/s. The exit velocity is 1,500 ft/sec, and the reservoir temperature and pressure are 1,000 'R and 7 atm , respectively. Calculate the…arrow_forward1. What is the significance of subsonic low-speed wind tunnels?2. Distinguish between Calibrated and True Airspeed.arrow_forward1. An air flow with a Mach number of 2.0 passes through an oblique shock wave inclined at an angle of 45° . Find the flow deflection angle α. 2. An air flow with a Mach number of 8 is deflected by a wedge through an angle α. What is the maximum value of α for an attached oblique shock?arrow_forward
- Q9: A normal shock wave is propagated into still air with a velocity of 722.4 m/s. The still air pressure is 1 atm (1.0133x105 N/m2) and its temperature is 294.4 K. Calculate the Mach number, pressure, temperature and velocity in back of the normal shock wave, relative to a stationary observer. Ans.: M2 = 0.56128, p2 = 5.045 bar,T2 = 521.3 K, M2R = 1.017.arrow_forward70. A supersonic airplane flies at two altitudes, find the temperature of air at second level, (V2 755 m-s, µ1 = 28°, the Mach no. ratio is 1.1). مصطفى لفتة نجم %3Darrow_forwardFor Air: y = 1.4 PART B Question B1 a) With the aid of sketches give a clear account of the operation of convergent nozzles as a function of back pressure. In your answer clearly indicate the critical points (pressure ratios) along the pressure ratio axis. b) Determine the required area ratio A part of the expansion of new teaching and research facilities at QMUL, a new two dimensional blow- down supersonic jet facility is going to be designed, manufactured and installed at our Whitehead Aeronautical Laboratory, Figure QB1. The design Mach number for this facility is M₁ = 2.0. A = A₁ A R=287J/kg K A₁ location at which the area ratio ( A₁ c) What should be the supply pressure to the nozzle (P) in order to have a normal shock wave at a Ax =) is 1.5? A Settling Chamber Po To for this design Mach number. d) For part c, what would be the discharge mass flow rate per unit throat area? You may assume P =105 N/m² and To = 300K. atm Convergent-Divergent Nozzle A AX Schematic of a Supersonic Jet…arrow_forward
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