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 3.12P

Consider the flow over a semi-infinite body as discussed in Section 3.11. If V is the velocity of the uniform stream, and the stagnation point is 1 ft upstream of the source:

a. Draw the resulting semi-infinite body to scale on graph paper.

b. Plot the pressure coefficient distribution over the body; that is, plot C p , versus distance along the centerline of the body.

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A two-dimensional flow field has an x-component of velocity given in Cartesian coordinates by u = 2x − 3y. (a) Find v, the y-component of velocity, if the flow is incompressible and v = 0 when x = 0. (b) If the flow follows the Bernoulli equation, find an expression for the pressure distribution as a function of x and y, given that the pressure is p0 at the stagnation point.  
3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
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