Using the results of linearized theory, calculate the lift and wave-drag coefficients for an infinitely thin flat plate in a Mach 2.6 freestream at angles of attack of
(a)
Compare these approximate results with those from the exact shock- expansion theory obtained in Problem 9.13. What can you conclude about the accuracy of linearized theory in this case?
(a)
The lift and wave drag coefficients and comparison of accuracy.
Answer to Problem 12.1P
The lift and drag coefficients are
Explanation of Solution
Given:
The angle of attack is
The Mach number is
Formula used:
The expression for lift is given as,
The expression for drag is given as,
Calculation:
The coefficient of lift can be calculated as,
Refer to problem 9.13, the error can be calculated as,
The coefficient of drag can be calculated as,
Refer to problem 9.13, the error can be calculated as,
Conclusion:
Therefore, the lift and drag coefficients are
(b)
The lift and wave drag coefficients and comparison of accuracy.
Answer to Problem 12.1P
The lift and drag coefficients are
Explanation of Solution
Given:
The angle of attack is
The Mach number is
Formula used:
The expression for lift is given as,
The expression for drag is given as,
Calculation:
The coefficient of lift can be calculated as,
Refer to problem 9.13, the error can be calculated as,
The coefficient of drag can be calculated as,
Refer to problem 9.13, the error can be calculated as,
Conclusion:
The lift and drag coefficients in first case are
(c)
The lift and wave drag coefficients and comparison of accuracy.
Answer to Problem 12.1P
The lift and drag coefficients are
Explanation of Solution
Given:
The angle of attack is
The Mach number is
Formula used:
The expression for lift is given as,
The expression for drag is given as,
Calculation:
The coefficient of lift can be calculated as,
Refer to problem 9.13, the error can be calculated as,
The coefficient of drag can be calculated as,
Refer to problem 9.13, the error can be calculated as,
Conclusion:
Therefore, the lift and drag coefficients are
Want to see more full solutions like this?
Chapter 12 Solutions
Fundamentals of Aerodynamics
Additional Engineering Textbook Solutions
Applied Fluid Mechanics (7th Edition)
Fundamentals Of Thermodynamics
Vector Mechanics for Engineers: Statics, 11th Edition
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Fluid Mechanics Fundamentals And Applications
Applied Statics and Strength of Materials (6th Edition)
- 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.arrow_forwardConsider the same Lockheed F-104 supersonic fighter shown, with the same flight conditions of Mach 2 at an altitude of 11 km. For these conditions the wing angle of attack is α = 0.035 rad = 1.98◦. Assume the chord length of the airfoil is 2.2 m, which is approximately the mean chord length for the wing. Also, assume fully turbulent flow over the airfoil. Calculate: (a) the airfoil skin friction drag coefficient, and (b) the airfoil wave-drag coefficient. Compare the two values of drag.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
- Starting from the basic principles, drive an expression to compute the lift coefficient when the free stream Mach number equals (0.8)arrow_forwardConsider a flat plate at α = 20◦ in a Mach 20 freestream. Using straightnewtonian theory, calculate the lift- and wave-drag coefficients. Comparethese results with exact shock-expansion theory.arrow_forwardAn infinitely thin flat plate is operating at a given freestream Mach number of 2.4 where ambient pressure is 0.53 atm. Calculate Lift per unit span for an given angle of attack of 4 degrees using both shock-expansion theory and linearized theoryarrow_forward
- The pressure ratio across a normal shock wave in air is 4.5. What are the Mach numbers in front of and behind the wave? What are the density and temperature ratios across the wave?arrow_forwardA 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.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_forward
- A normal shock wave was formed on the surface of a supersonic aircraft at a velocity of 1,600 m/s into still atmospheric air at standard seal level conditions. Calculate: a) M₁ b) M₂ c) P₂ d) T₂ e) V₂arrow_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_forwardAn infinitely thin flat plate is operating at a given freestream Mach number of 2.4 where ambient pressure is 0.53 atm. Calculate Lift to drag ratio for an given angle of attack of 4 degrees using both shock-expansion theory and linearized theoryarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning