Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 1, Problem 1.3P
Consider an infinitely thin flat plate of chord c at an angle of attack
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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 tank is filled with air at 20°C and 139 kPa in stationary condition. Air is leaving the tank with flowing in a
nozzle under steady-state condition. The flow is under isentropic and subsonic condition. The nozzle exit area is
18,59 cm?. After leaving from the nozzle, air strikes a vertical plate. Define the force [N] required to hold the plate
stationary. (Note: Assume Pe=1 atm, kair=1.4, Rair=287 J/kg.K)
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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.
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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- Consider a circular cylinder in a hypersonic flow, with its axisperpendicular to the flow. Let φ be the angle measured between radiidrawn to the leading edge (the stagnation point) and to any arbitrary pointon the cylinder. The pressure coefficient distribution along the cylindricalsurface is given by Cp = 2 cos2 φ for 0 ≤ φ ≤ π/2 and 3π/2 ≤ φ ≤ 2πand Cp = 0 for π/2 ≤ φ ≤ 3π/2. Calculate the drag coefficient for thecylinder, based on projected frontal area of the cylinder.arrow_forwardOne type of supersonic wind tunnel is a blow-down tunnel, where air is stored in a high-pressure reservoir, and then, upon the opening of a valve, exhausted through the tunnel into a vacuum tank or simply into the open atmosphere at the downstream end of the tunnel. For this example, weconsider just the high-pressure reservoir as a storage tank that is being charged with air by a high-pressure pump. As air is being pumped into the constant-volume reservoir, the air pressure inside the reservoir increases. The pump continues to charge the reservoir until the desired pressure is achieved.Consider a reservoir with an internal volume of 30 m3. As air is pumped into the reservoir, the air pressure inside the reservoir continually increases with time. Consider the instant during the charging process when the reservoir pressure is 10 atm. Assume the air temperature inside the reservoir is held constant at 300 K by means of a heat exchanger.Air is pumped into the reservoir at the rate of 1…arrow_forwardConsider a low-speed open-circuit subsonic wind tunnel. The tunnel is turned on, and the pressure difference between the inlet (the settling chamber) and the test section is read as a height difference of 10 cm on a U-tube mercury manometer. (The density of liquid mercury is 1.36 × 104 kg/m3.) Assume that a Pitot tube is inserted into the test-section flow of the wind tunnel. The tunnel test section is completely sealed from the outside ambient pressure. Calculate the total pressure measured by the Pitot tube, assuming the static pressure at the tunnel inlet is atmospheric. Given that A2/A1 = 1/12. (Round the final answer to two decimal places.) The total pressure measured by the Pitot tube is × 105 N/m2.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_forward1 atm = 2116 lb/ft2 = 1.01 × 105 N/m2. Consider the isentropic flow over an airfoil. The freestream conditions areT∞ = 245 K and p∞ = 4.35 × 104 N/m2. At a point on the airfoil, thepressure is 3.6 × 104 N/m2. Calculate the density at this point.arrow_forwardConsider a flat plate with a chord length (from leading to trailing edge) of 1 m. The free-stream flow properties are M1 = 3, p1 = 1 atm, and T, = 270 K. Using shock-expansion theory, tabulate and plot on graph paper these properties as functions of angle of attack from 0 to 30° (use increments of 5°): a. Pressure on the top surface b. Pressure on the bottom surface c. Temperature on the top surface d. Temperature on the bottom surface e. Lift per unit span f. Drag per unit span g. Lift/drag ratio (Note: The results from this problem will be used for comparison with linear supersonic theory in Chap. 9.)arrow_forward
- The instrument fairing on an aircraft is shown below, consisting of a forward ramp at30◦, a horizontal section, and a rear ramp at 25◦. During a flight in air at Mach 5.5,the static pressure is 42.6 kPa and the static temperature is 250 K. An oblique shockforms at the turn of the forward ramp, two expansion fans form at the front and rear ofthe horizontal section, and a second oblique shock forms at the turn of the rear ramp. (a) Calculate the Mach numbers and pressures at regions 2, 3, 4, and 5. (b) Determine stagnation pressure ratio p05/p01. (c) Tabulate the angles of all oblique shocks waves leading/trailing expansion waves relative to horizontal (not relative to flow angle). Gamma = 1.4, R=287 J/kgK PLEASE SHOW ALL WORKarrow_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 supersonic flow with M = 2, p = 1 atm, and T = 288 K. This flow isdeflected at a compression corner through 20◦. Calculate M, p, T , p0, and T0 behind the resulting oblique shock wave.arrow_forward
- Consider a wing mounted in the test-section of a subsonic wind tunnel. The velocity of the airflow is 160 ft/s. If the velocity at a point on the wing is 195 ft/s, what is the pressure coefficient at this point?arrow_forwardIn your own words, write a summary of the differences between incompressible flow, subsonic flow, and supersonic flow.arrow_forwardAir flows isentropically from a large reservoir maintained at 597°C and 1.0 MPa absolute into a converging-diverging duct. The flow at the exit plane of diverging duct is supersonic. The duct is 2 m long and has a circular cross sectional area with radius, r in m that varies in axial distance, x along the duct that is defined by r = 0.03x² +0.02 where x extends from -1.0 m to 1.0 m. (a) Sketch a 2D diagram of the above system on a graph of duct radius against axial distance with appropriate labelling. (b) Using the isentropic table provided, determine (i) the Mach number, pressure and temperature at the exit plane, and (ii) the mass flow rate through the duct. E.Q2 (c) If the radius of the duct as specified in E.Q2 is doubled, would the Mach number on the exit plane be increased, decreased or remain unchanged? Explain your answer briefly. Take heat specific ratio of 1.4 and specific gas constant of 0.287 kJ/(kg-K) for air.arrow_forward
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