Fundamentals of Aerodynamics
Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.22P

Consider the flow field over a circular cylinder mounted perpendicular to the flow in the test section of a low-speed subsonic wind tunnel. At standard sea level conditions, if the flow velocity at some region of the flow field exceeds about 250 mi/h, compressibility begins to have an effect in that region. Calculate the velocity of the flow in the test section of the wind tunnel above which compressibility effects begin to become important, i.e., above which we cannot accurately assume totally incompressible flow over the cylinder for the wind tunnel tests.

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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.
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.
An 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?

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Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License