Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 11, Problem 11.4P
In low-speed incompressible flow, the peak pressure coefficient (at the minimum pressure point) on an airfoil 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.
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Chapter 11 Solutions
Fundamentals of Aerodynamics
Ch. 11 - Consider a subsonic compressible flow in cartesian...Ch. 11 - Using the Prandtl-Glauert rule, calculate the lift...Ch. 11 - Under low-speed incompressible flow conditions,...Ch. 11 - In low-speed incompressible flow, the peak...Ch. 11 - For a given airfoil, the critical Mach number is...Ch. 11 - Consider an airfoil in a Mach 0.5 freestream. At a...Ch. 11 - Prob. 11.7PCh. 11 - Consider the flow over a circular cylinder; the...Ch. 11 - In Problem 11.8, the critical Mach number for a...
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- 5. 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_forwardThe 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_forward(a) The maximum speed achieved by the X-15A-2 rocket-powered research craft was 6630 ft/s at 99,000 ft. Assuming standard day conditions, whatwas its Mach number?(b) An SR-71 is traveling at Mach 3.2 in standard day 80,000-ft conditions.What is its velocity in nautical miles per hour?arrow_forward
- MA The Mach number at the maximum velocity point on the upper surface of an airfoil is 0.6 for the freestream conditions of M = 0.5. Calculate the Mach MA = 0.6 number at the same point for the freestream conditions of M = 0.7. Use the convenient similarity rule. М,- 0.7 M= 0.5arrow_forwardConsider the flow over a circular cylinder; the incompressible flow oversuch a cylinder . Consider also the flow over a sphere; the incompressible flow over a sphere .The subsonic compressible flow over both the cylinder and the sphere isqualitatively similar but quantitatively different from their incompressiblecounterparts. Indeed, because of the “bluntness” of these bodies, theircritical Mach numbers are relatively low. In particular: For a cylinder: Mcr = 0.404 For a sphere: Mcr = 0.57Explain on a physical basis why the sphere has a higher Mcr than thecylinder.arrow_forwardConsider a flat plate at an angle of attack α to a Mach 2.4 airflow at 1 atmpressure. What is the maximum pressure that can occur on the platesurface and still have an attached shock wave at the leading edge? At whatvalue of α does this occur?arrow_forward
- Under low-speed incompressible flow conditions, the pressure coefficientat a given point on an airfoil is −0.54. Calculate Cp at this point when thefreestream Mach number is 0.58, usinga. The Prandtl-Glauert ruleb. The Karman-Tsien rulec. Laitone’s rulearrow_forwardA normal shock occurs in a stream of oxygen. The oxygen flows at Ma=1.8 and the upstream pressure and temperature are 40 psia and 85 degrees Fahrenheit. a) Calculate the following on the downstream side of the shock: static pressure, stagnation pressure, static temperature, stagnation temperature, static density, and velocity. b)If the Mach number is doubled to 3.6, what will be the resulting values of the parameters listed in part (a)?arrow_forwardA pitot tube, mounted on an airplane fl ying at 8000 m standardaltitude, reads a stagnation pressure of 57 kPa.Estimate the plane’s (a) velocity and (b) Mach number.arrow_forward
- For a converging-diverging nozzle that is choked what is the ratio of nozzle area divided by the throat area for a Mach number of 2.1? (Assume isentropic flow for an ideal gas and k = 1.4.) Enter your answer to the fourth decimal place.arrow_forwardAssume that a supersonic converging-diverging nozzle operating isentropically delivers air to a receiver with pressure of 1175 kPa. The entrance conditions are 1500 kPa abs, 327 °C, and near-zero Mach number. Use the isentropic table only. (a) What is the exit Mach number? Mention the operation mode. (b) What is the exit temperature? (c) Determine the area ratio A/A2, A3, and the mass flow rate if D-100 mm. (d) If the entire diverging portion of the nozzle were suddenly detached, what would the Mach number and rh /A be at the new outlet? Pt Preceiver Trarrow_forwardare 3000 ft/s and 500°R, respectively Calculate the Mach number M and the characteristic Mach number M* at this point 3.4. Consider a normal shock wave in air The upstream conditions are given by M = 3; P1 1 atm, and p, = 1 23 kg/m' Calculate the downstream values of p2, T, P24 M2, u2, Poz, and Tmarrow_forward
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