Package: Loose Leaf For Fluid Mechanics With 1 Semester Connect Access Card
8th Edition
ISBN: 9781259638848
Author: White
Publisher: MCG
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Chapter 7, Problem 7.18P
Air at 20°C and 1 atm flows at 5 m/s past a flat plate. At x = 60 cm and y = 2.95 mm, use the Blasius solution, Table 7.1, to find (a) the velocity u; and (b) the wall shear stress. (c) For extra credit, find a Blasius formula for the shear stress away from the wall.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
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.
Chapter 7 Solutions
Package: Loose Leaf For Fluid Mechanics With 1 Semester Connect Access Card
Ch. 7 - Prob. 7.1PCh. 7 - A gas at 20°C and 1 atm flows at 6 ft/s past a...Ch. 7 - Prob. 7.3PCh. 7 - Prob. 7.4PCh. 7 - SAE 30 oil at 20°C flows at 1.8 ft3/s from a...Ch. 7 - Prob. 7.6PCh. 7 - P7.7 Air at 20°C and 1 atm enters a 40-cm-square...Ch. 7 - P7.8 Air, p = 1.2 kg/m3 and E-5 kg/(m .s), flows...Ch. 7 - P7.9 Repeat the flat-plate momentum analysis of...Ch. 7 - Repeat Prob. P7.9, using a trigonometric profile...
Ch. 7 - Prob. 7.11PCh. 7 - Prob. 7.12PCh. 7 - Prob. 7.13PCh. 7 - Prob. 7.14PCh. 7 - Prob. 7.15PCh. 7 - A thin flat plate 55 by 110 cm is immersed in a...Ch. 7 - Consider laminar flow past a sharp flat plate of...Ch. 7 - Air at 20°C and 1 atm flows at 5 m/s past a flat...Ch. 7 - Prob. 7.19PCh. 7 - Air at 20°C and I atm flows at 20 m/s past the...Ch. 7 - Prob. 7.21PCh. 7 - Prob. 7.22PCh. 7 - Prob. 7.23PCh. 7 - Prob. 7.24PCh. 7 - Prob. 7.25PCh. 7 - P7.26 Consider laminar boundary layer flow past...Ch. 7 - Prob. 7.27PCh. 7 - Prob. 7.28PCh. 7 - Prob. 7.29PCh. 7 - Prob. 7.30PCh. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - P7.39 A hydrofoil 50 cm long and 4 m wide moves...Ch. 7 - Prob. 7.40PCh. 7 - Prob. 7.41PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - P7.45 A thin sheet of fiberboard weighs 90 N and...Ch. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.48PCh. 7 - Based strictly on your understanding of flat-plate...Ch. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.53PCh. 7 - *P7.54 If a missile takes off vertically from sea...Ch. 7 - Prob. 7.55PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57PCh. 7 - Prob. 7.58PCh. 7 - Prob. 7.59PCh. 7 - Prob. 7.60PCh. 7 - Prob. 7.61PCh. 7 - A sea-level smokestack is 52 m high and has a...Ch. 7 - For those who think electric cars are sissy, Keio...Ch. 7 - Prob. 7.64PCh. 7 - Prob. 7.65PCh. 7 - Prob. 7.66PCh. 7 - The Toyota Prius has a drag coefficient of 0.25, a...Ch. 7 - Prob. 7.68PCh. 7 - Prob. 7.69PCh. 7 - P7.70 The Army’s new ATPS personnel parachute is...Ch. 7 - Prob. 7.71PCh. 7 - Prob. 7.72PCh. 7 - Prob. 7.73PCh. 7 - Prob. 7.74PCh. 7 - Prob. 7.75PCh. 7 - P7.76 The movie The World’s Fastest Indian tells...Ch. 7 - Prob. 7.77PCh. 7 - Prob. 7.78PCh. 7 - Prob. 7.79PCh. 7 - Prob. 7.80PCh. 7 - Prob. 7.81PCh. 7 - Prob. 7.82PCh. 7 - Prob. 7.83PCh. 7 - P7.84 A Ping-Pong ball weighs 2.6 g and has a...Ch. 7 - Prob. 7.85PCh. 7 - Prob. 7.86PCh. 7 - P7.87 A tractor-trailer truck has a drag area CA =...Ch. 7 - P7.88 A pickup truck has a clean drag area CDA of...Ch. 7 - Prob. 7.89PCh. 7 - Prob. 7.90PCh. 7 - Prob. 7.91PCh. 7 - Prob. 7.92PCh. 7 - A hot-film probe is mounted on a cone-and-rod...Ch. 7 - Baseball drag data from the University of Texas...Ch. 7 - Prob. 7.95PCh. 7 - Prob. 7.96PCh. 7 - Prob. 7.97PCh. 7 - A buoyant ball of specific gravity SG 1 dropped...Ch. 7 - Prob. 7.99PCh. 7 - Prob. 7.100PCh. 7 - Prob. 7.101PCh. 7 - Prob. 7.102PCh. 7 - Prob. 7.103PCh. 7 - Prob. 7.104PCh. 7 - Prob. 7.105PCh. 7 - Prob. 7.106PCh. 7 - Prob. 7.107PCh. 7 - Prob. 7.108PCh. 7 - Prob. 7.109PCh. 7 - Prob. 7.110PCh. 7 - Prob. 7.111PCh. 7 - Prob. 7.112PCh. 7 - Prob. 7.113PCh. 7 - Prob. 7.114PCh. 7 - Prob. 7.115PCh. 7 - Prob. 7.116PCh. 7 - Prob. 7.117PCh. 7 - Suppose that the airplane of Prob. P7.116 is...Ch. 7 - Prob. 7.119PCh. 7 - Prob. 7.120PCh. 7 - Prob. 7.121PCh. 7 - Prob. 7.122PCh. 7 - Prob. 7.123PCh. 7 - Prob. 7.124PCh. 7 - Prob. 7.125PCh. 7 - Prob. 7.126PCh. 7 - Prob. 7.127PCh. 7 - Prob. 7.1WPCh. 7 - Prob. 7.2WPCh. 7 - Prob. 7.3WPCh. 7 - Prob. 7.4WPCh. 7 - Prob. 7.5WPCh. 7 - Prob. 7.6WPCh. 7 - Prob. 7.7WPCh. 7 - Prob. 7.8WPCh. 7 - Prob. 7.9WPCh. 7 - How does the concept of drafting, in automobile...Ch. 7 - Prob. 7.11WPCh. 7 - Prob. 7.12WPCh. 7 - Prob. 7.1FEEPCh. 7 - Prob. 7.2FEEPCh. 7 - Prob. 7.3FEEPCh. 7 - Prob. 7.4FEEPCh. 7 - Prob. 7.5FEEPCh. 7 - Prob. 7.6FEEPCh. 7 - Prob. 7.7FEEPCh. 7 - Prob. 7.8FEEPCh. 7 - Prob. 7.9FEEPCh. 7 - Prob. 7.10FEEPCh. 7 - Prob. 7.1CPCh. 7 - Prob. 7.2CPCh. 7 - Prob. 7.3CPCh. 7 - Prob. 7.4CPCh. 7 - Prob. 7.5CPCh. 7 - It is desired to design a cup anemometer for wind...
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