Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 1, Problem 1.16P
Consider a flat plate at zero angle of attack in a hypersonic flow at Mach10 at standard sea level conditions. At a point 0.5 m downstream from the leading edge, the local shear stress at the wall is
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Consider a cone at zero angle of attack in a hypersonic flow. (Hypersonic flow is very high-speed flow, generally defined as any flow above a Mach number of 5.) The half-angle of the cone is θc, as shown inthe figure. An approximate expression for the pressure coefficient on the surface of ahypersonic body is given by the newtonian sine-squared law : Cp = 2 sin2 θcNote that Cp, hence, p, is constant along the inclined surface of the cone. Along the base of the body, we assume that p = p∞. Neglecting the effect of friction, obtain an expression for the drag coefficient of the cone, where CD is based on the area of the base Sb.
The shock waves on a vehicle in supersonic flight cause a component ofdrag called supersonic wave drag Dw. Define the wave-drag coefficient asCD,w = Dw/q∞S, where S is a suitable reference area for the body. Insupersonic flight, the flow is governed in part by its thermodynamicproperties, given by the specific heats at constant pressure cp and atconstant volume cv. Define the ratio cp/cv ≡ γ . Using Buckingham’spi theorem, show that CD,w = f (M∞, γ ). Neglect the influence of friction.
Consider a Lear jet flying at a velocity of 250 m/s at an altitude of 10 km,where the density and temperature are 0.414 kg/m3 and 223 K,respectively. Consider also a one-fifth scale model of the Lear jet beingtested in a wind tunnel in the laboratory. The pressure in the test section ofthe wind tunnel is 1 atm = 1.01 × 105 N/m2. Calculate the necessaryvelocity, temperature, and density of the airflow in the wind-tunnel testsection such that the lift and drag coefficients are the same for thewind-tunnel model and the actual airplane in flight.
Chapter 1 Solutions
Fundamentals of Aerodynamics
Ch. 1 - For most gases at standard or near standard...Ch. 1 - Starting with Equations (1.7),(1.8), and (1.11),...Ch. 1 - Consider an infinitely thin flat plate of chord c...Ch. 1 - Consider an infinitely thin flat plate with a 1 m...Ch. 1 - Consider an airfoil at 12 angle of attack. The...Ch. 1 - Consider an NACA 2412 airfoil (the meaning of the...Ch. 1 - The drag on the hull of a ship depends in part on...Ch. 1 - The shock waves on a vehicle in supersonic flight...Ch. 1 - Consider two different flows over geometrically...Ch. 1 - Consider a Lear jet flying at a velocity of 250...
Ch. 1 - A U-tube mercury manometer is used to measure the...Ch. 1 - The German Zeppeins of World War I were dirigibles...Ch. 1 - Consider a circular cylinder in a hypersonic flow,...Ch. 1 - Derive Archimedes principle using a body of...Ch. 1 - Consider a light, single-engine, propeller-driven...Ch. 1 - Consider a flat plate at zero angle of attack in a...Ch. 1 - Consider the Space Shuttle during its atmospheric...Ch. 1 - The purpose of this problem is to give you a feel...Ch. 1 - For the design of their gliders in 1900 and 1901,...Ch. 1 - Consider the existence of a forward-facing axial...
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- The stagnation pressure in a Mach 2 wind tunnel operating with air is 750 kPa. A 4-cm-diameter sphere positioned in the wind tunnel has a drag coefficient of 0.95. Calculate the drag force on the sphere. FD Narrow_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_forwardConsider 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_forward
- Consider a normal shockwave in air where the upstream flowproperties are u1 = 680 m/s, T1 = 288 K, and p1 = 1 atm. Calculate the velocity, temperature, and pressure downstream of the shock.arrow_forwardAn explosion occurs which creates a plane normal shock wave propagating into a region of air that is at rest (stagnation pressure po=1.0135×105Pa) and (stagnation temperature of To=290K). The speed of the shock is 1700 m/s. The air is modelled as an inviscid fluid, specific heat ratio γ=1.4 and gas constant R=287~J/kg⋅K. Calculate the air speed in m/s, relative to a stationary observer in the region behind the shock?arrow_forwardAn aircraft is flying at 440 km/hr at 3 km on a standard day. What is the aircraft Mach Number?arrow_forward
- Consider 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_forwarda balloon is 4 m in diameter and contains helium at 125 kpa and 15°c. balloon material and payload weigh 200 n, not including the helium. estimate (a) the terminal ascent velocity in sea-level standard air, (b) the final standard altitude (neglecting winds) at which the balloon will come to rest, and (c) the minimum diameter (< 4 m) for which the balloon will just barely begin to rise in sea-level standard air.arrow_forwardAn engineer is designing a subsonic wind tunnel. The test section is to have a cross-sectional area of 4 m2 and an airspeed of 60 m/s. The air density is 1.2 kg/m3. The area of the tunnel exit is 10 m2. The head loss through the tunnel is given by hL=0.025VT2/2g, where VT is the airspeed in the test section. Calculate the power needed to operate the wind tunnel. Hint: Assume negligible energy loss for the flow approaching the tunnel in region A, and assume atmospheric pressure at the outlet section of the tunnel. Assume α = 1.0 at all locations.arrow_forward
- 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.arrow_forwardConsider an aerofoil in a free stream with a velocity of 50 m/s at standard sea-level conditions. At a point on the aerofoil, the pressure is 9.5 x 104 N/m². What is the pressure coefficient at this point?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_forward
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