Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 12, Problem 12.3P
Consider a diamond-wedge airfoil such as shown in Figure 9.26, with a half-angle
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1. A flat plate airfoil with a chord length of 1 m and a width of 6 m is required to generate a lift of 40, 000 N when flying in air at a Mach number of 2.0, a temperature of −20°C and a pressure of 105 P a. What is the required angle of attack? What is the wave drag at this angle of attack? 2. A symmetrical diamond-shaped airfoil is placed at an angle of attack of 2° in a flow at Mach 2 and static pressure of 2×103 P a. The half-angle at the leading and trailing edges is 3° . If its total surface area (top and bottom) is 4 m2 , find the forces due to lift and wave drag acting on the airfoil.
Consider a low-speed subsonic wind tunnel designed with a reservoir cross-sectional area of 2 m2 and a test-section cross-sectional area of 0.5 m2. The pressure in the test section is 1 atm. Assume constant density equal to standard sea level density, calculate the pressure (in Pa) required in the reservoir necessary to achieve a flow velocity of 40 m/s in the test section.
A straight-tapered flying-wing aircraft has the following characteristics: span, 20 ft; area, 100 ft2 ; root chord, 6 ft; tip chord, 4 ft; leading-edge sweep angle, 40 deg; sweep angle of line of maximum thickness, 24 deg; and Airfoil NACA 2412. Determine the wing's lift-curve slope and induced drag k value. Assume the flight Mach number is 0.25 in standard sea-level conditions.
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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- Consider a flat plate at an angle of attack in an inviscid supersonic flow.From linear theory, what is the value of the maximum lift-to-drag ratio,and at what angle of attack does it occur?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_forwardIn the test section of a high-speed subsonic wind tunnel operating at Mach number of 0.75, a NACA 2415 airfoil is mounted. The compressible lift coefficient measured for that airfoil is 0.7. Determine the equivalent incompressible lift coefficient and the angle of attack at which the airfoil is flying.arrow_forward
- The Boeing 747 has a wingspan of 65 meters and AR of 7.7. (a)Assuming take off weight of 910,000 pounds and a take off velocity 160 knots, calculate the lift coefficient at take off for standard sea-level conditions.(b) Compare the above result with the lift coefficient for cruise at Mach number of 92% of the speed of sound.arrow_forwardFor a given airfoil, the critical Mach number is 0.8. Calculate the value ofp/p∞ at the minimum pressure point when M∞ = 0.8.arrow_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
- Consider the isentropic flow through a supersonic wind-tunnel nozzle. The reservoir properties are T0= 500 K and p0 = 10 atm. If p (corresponds to your assigned altitude) at the nozzle exit, calculate the exit temperature and density.ASSIGNED ALTITUDE = 9522 ftarrow_forwardConsider an infinitely thin flat plate with a 1 m chord at an angle of attackof 10◦ in a supersonic flow. The pressure and shear stress distributions onthe upper and lower surfaces are given by pu = 4 × 104(x − 1)2 +5.4 × 104, pl = 2 × 104(x − 1)2 + 1.73 × 105, τu = 288x−0.2, andτl = 731x−0.2, respectively, where x is the distance from the leading edgein meters and p and τ are in newtons per square meter. Calculate thenormal and axial forces, the lift and drag, moments about the leadingedge, and moments about the quarter chord, all per unit span. Also,calculate the location of the center of pressure.arrow_forwardConsider a diamond-wedge airfoil such as shown , with ahalf-angle ε = 10◦. The airfoil is at an angle of attack α = 15◦ to a Mach3 freestream. Using linear theory, calculate the lift and wave-dragcoefficients for the airfoil. Compare these approximate results with thosefrom the exact shock-expansion theory obtained.arrow_forward
- 1. Consider a low-speed subsonic wind tunnel designed with a reservoir cross-sectional area A, = 2 m2 and a test-section cross-sectional area A2 = 0.5 m2. The pressure in the test section is P2 = 1 atm. Assume constant density equal to standard sea level density, calculate the pressure (in kPa) required in the reservoir, P1, necessary to achieve a flow velocity V2: 40 m/s in the test section. a. From item no. 1, calculate the mass flow rate (in kg/s) through the wind tunnel. b. Calculate the Mach number of the vehicle in air. c. Calculate the Mach number of the vehicle in hydrogen.arrow_forwardConsider the supersonic flow over a flat plate at an angle of attack, assketched . As stated , the flow direction downstream of the trailing edge of the plate, behind the trailing edge shock and expansion waves, is not precisely in the freestream direction.Why? Outline a method to calculate the strengths of the trailing edgeshock and expansion waves, and the direction of the flow downstream ofthe trailing edge.arrow_forward10 Consider a diamond-shaped airfoil. The maximum thickness is 0.04 and occurs at mid-chord. The freestream Mach number is 2.0, and the airfoil is operating at a 5 degree angle of attack. a)Find the expressions for the lift coefficient, drag coefficient, and lift to drag ratio using shock-expansion theory Cl= 0.2286, Cd= 0.0302, and L/D= 7.57 Please show workarrow_forward
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