Connect with LearnSmart for Anderson: Fundamentals of Aerodynamics, 6e
6th Edition
ISBN: 9781259683268
Author: Anderson, John
Publisher: Mcgraw-hill Higher Education (us)
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Chapter 9, Problem 9.16P
Consider a circular cylinder (oriented with its axis perpendicular to the flow) and a symmetric diamond-wedge airfoil with a half-angle of
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A shaft is loaded in bending and torsion such that Ma = 70 N·m, T₁ = 45 N · m, M =
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corrected endurance limit of S₂ = 210 MPa is assumed. Let K = 2.2 and K = 1.8. With a
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design factor of 2.0 determine the minimum acceptable diameter of the shaft using the
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Chapter 9 Solutions
Connect with LearnSmart for Anderson: Fundamentals of Aerodynamics, 6e
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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- An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.arrow_forwardProblem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forward
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