Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.19P
Repeat Problem 9.18, except with
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By using the expression for the shear stress derived in class (and in BSL), show that the shear force on asphere spinning at a constant angular velocity in a Stokes’ flow, is zero.This means that a neutrally buoyant sphere (weight equal buoyancy force) that is made to spin in aStokes’ flow, will neither rise nor fall, nor translate in any preferential direction in the (x-y) plane.
expressions for velocity are:
v_r (r,θ)= U_∞ [1-3R/2r+R^3/(2r^3 )] cosθ
v_θ (r,θ)= -U_∞ [1-3R/4r-R^3/(4r^3 )] sinθ
Where v_r and v_θ are the radial and angle velocity, U_∞ is the velocity of fluid coming to sphere which very faar away from the sphere. And R is the radius of sphere.
If a body with a linear dimension of 1 ft is moving in a fluid with
velocity q, find the Froude number and the Reynolds number for the follow-
ing cases: (a) when the fluid is air and has 4 100 ft/sec; (b) when the
1
fluid is water and has q
-
5 ft/sec.
Chapter 9 Solutions
Fundamentals of Aerodynamics
Ch. 9 - A slender missile is flying at Mach 1.5 at low...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Equation (8.80) does not hold for an oblique shock...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Consider the flow over a 22.2 half-angle wedge. If...Ch. 9 - Consider a flat plate at an angle of attack a to a...Ch. 9 - A 30.2 half-angle wedge is inserted into a...Ch. 9 - Consider a Mach 4 airflow at a pressure of 1 atm....Ch. 9 - Consider an oblique shock generated at a...Ch. 9 - Consider the supersonic flow over an expansion...
Ch. 9 - A supersonic flow at M1=1.58 and p1=1atm expands...Ch. 9 - A supersonic flow at M1=3,T1=285K, and p1=1atm is...Ch. 9 - Consider an infinitely thin flat plate at an angle...Ch. 9 - Consider a diamond-wedge airfoil such as shown in...Ch. 9 - Consider sonic flow. Calculate the maximum...Ch. 9 - Consider a circular cylinder (oriented with its...Ch. 9 - Consider the supersonic flow over a flat plate at...Ch. 9 - (The purpose of this problem is to calculate a...Ch. 9 - Repeat Problem 9.18, except with =30. Again, we...Ch. 9 - Consider a Mach 3 flow at 1 atm pressure initially...Ch. 9 - The purpose of this problem is to explain what...
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- Consider the boundary layer over a flat plate at 45° angle as shown. The exact flow field in this configuration is described by the Falkner-Skan similarity solution with n = 1/3 (see Figure 10.8 of the textbook, the Falkner-Skan profile chart). The objective is to find the approximate solution to this problem using the Thwaites method and calculate its error. Ve 11/4 Assume that for this approximate solution the free stream velocity is U₂(x) = ax" where a is an unknown constants and n = 1/3. Use the Thwaites method to find the momentum 0/x and 8*/x displacement thicknesses as well as the friction coefficient cf = 0.5, as functions of Re₂ = Uer/v, where is the shear stress at the wall. (No need to interpolate the Thwaites method table values; you can pick the nearest numbers.) Using the Falkner-Skan profile chart approximate the friction coefficient c; (by estimating the slope of the corresponding velocity profile at the wall). How does this value compare with your prediction in part…arrow_forwardPlot the streamlines and potential lines of the fl ow due to aline source of strength m at (a, 0) plus a source 3m at(2a, 0). What is the fl ow pattern viewed from afar?arrow_forward5arrow_forward
- i need answer quicklyarrow_forwardPlease answer with detailarrow_forwardProblem 1: Consider a uniform flow (U. ) past a 2D cylinder (1) Derive analytical expression for the the drag and lift forces exerted on a 2D cylinder in an inviscid flow, using either the stream function w or velocity potential ø provided below: y =U_r 1-: sin0, ø =l 1+ cos0. (2) Plot the streamlines around the cylinder. Discuss its differences in the vortex structures comparing with the other cases at finite Reynolds numbers. (a) Re << 1 (b) Re= 10 (c) Re 60 (d) Re 1000arrow_forward
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