Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.2WP
To determine
Justification for the use of superposition in inviscid flow analysis.
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Chapter 8 Solutions
Fluid Mechanics
Ch. 8 - Prob. 8.1PCh. 8 - The steady plane flow in Fig. P8.2 has the polar...Ch. 8 - P8.3 Using cartesian coordinates, show that each...Ch. 8 - P8.4 Is the function 1/r a legitimate velocity...Ch. 8 - Prob. 8.5PCh. 8 - An incompressible plane flow has the velocity...Ch. 8 - Prob. 8.7PCh. 8 - For the velocity distribution u=By,=+Bx , evaluate...Ch. 8 - Prob. 8.9PCh. 8 - Prob. 8.10P
Ch. 8 - Prob. 8.11PCh. 8 - Prob. 8.12PCh. 8 - P8.13 Starting at the stagnation point in Fig....Ch. 8 - P8.14 A tornado may be modeled as the circulating...Ch. 8 - Hurricane Sandy, which hit the New Jersey coast on...Ch. 8 - Prob. 8.16PCh. 8 - P8.17 Find the position (x, y) on the upper...Ch. 8 - Prob. 8.18PCh. 8 - Prob. 8.19PCh. 8 - Plot the streamlines of the flow due to a line...Ch. 8 - P8.21 At point A in Fig. P8.21 is a clockwise line...Ch. 8 - P8.22 Consider inviscid stagnation flow, (see...Ch. 8 - P8.23 Sources of strength m = 10 m2/s are placed...Ch. 8 - P8.24 Line sources of equal strength m = Ua, where...Ch. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Prob. 8.27PCh. 8 - Sources of equal strength m are placed at the four...Ch. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - A Rankine half-body is formed as shown in Fig....Ch. 8 - Prob. 8.32PCh. 8 - P8.33 Sketch the streamlines, especially the body...Ch. 8 - Prob. 8.34PCh. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - Prob. 8.37PCh. 8 - Consider potential flow of a uniform stream in the...Ch. 8 - A large Rankine oval, with a = 1 m and h = 1 m, is...Ch. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Prob. 8.42PCh. 8 - P8.43 Water at 20°C flows past a 1-rn-diameter...Ch. 8 - Prob. 8.44PCh. 8 - Prob. 8.45PCh. 8 - P8.46 A cylinder is formed by bolting two...Ch. 8 - Prob. 8.47PCh. 8 - Prob. 8.48PCh. 8 - Prob. 8.49PCh. 8 - It is desired to simulate flow past a...Ch. 8 - Prob. 8.51PCh. 8 -
P8.52 The Flettner rotor sailboat in Fig. E8.3...Ch. 8 - P8.52 The Flettner rotor sailboat in Fig. E8.3 has...Ch. 8 - Prob. 8.54PCh. 8 - Prob. 8.55PCh. 8 - Prob. 8.56PCh. 8 - Prob. 8.57PCh. 8 - Prob. 8.58PCh. 8 - Prob. 8.59PCh. 8 - Prob. 8.60PCh. 8 - Prob. 8.61PCh. 8 - Prob. 8.62PCh. 8 - The superposition in Prob. P8.62 leads to...Ch. 8 - Consider the polar-coordinate stream function...Ch. 8 - Prob. 8.65PCh. 8 - Prob. 8.66PCh. 8 - Prob. 8.67PCh. 8 - Prob. 8.68PCh. 8 - Prob. 8.69PCh. 8 - Prob. 8.70PCh. 8 - Prob. 8.71PCh. 8 - Prob. 8.72PCh. 8 - Prob. 8.73PCh. 8 - Prob. 8.74PCh. 8 - Prob. 8.75PCh. 8 - Prob. 8.76PCh. 8 - Prob. 8.77PCh. 8 - Prob. 8.78PCh. 8 - Prob. 8.79PCh. 8 - Prob. 8.80PCh. 8 - Prob. 8.81PCh. 8 - Prob. 8.82PCh. 8 - Prob. 8.83PCh. 8 - Prob. 8.84PCh. 8 - Prob. 8.85PCh. 8 - Prob. 8.86PCh. 8 - Prob. 8.87PCh. 8 - Prob. 8.88PCh. 8 - Prob. 8.89PCh. 8 - NASA is developing a swing-wing airplane called...Ch. 8 - Prob. 8.91PCh. 8 - Prob. 8.92PCh. 8 - Prob. 8.93PCh. 8 - Prob. 8.94PCh. 8 - Prob. 8.95PCh. 8 - Prob. 8.96PCh. 8 - Prob. 8.97PCh. 8 - Prob. 8.98PCh. 8 - Prob. 8.99PCh. 8 - Prob. 8.100PCh. 8 - Prob. 8.101PCh. 8 - Prob. 8.102PCh. 8 - Prob. 8.103PCh. 8 - Prob. 8.104PCh. 8 - Prob. 8.105PCh. 8 - Prob. 8.106PCh. 8 - Prob. 8.107PCh. 8 - P8.108 Consider two-dimensional potential flow...Ch. 8 - Prob. 8.109PCh. 8 - Prob. 8.110PCh. 8 - Prob. 8.111PCh. 8 - Prob. 8.112PCh. 8 - Prob. 8.113PCh. 8 - Prob. 8.114PCh. 8 - Prob. 8.115PCh. 8 - Prob. 8.1WPCh. 8 - Prob. 8.2WPCh. 8 - Prob. 8.3WPCh. 8 - Prob. 8.4WPCh. 8 - Prob. 8.5WPCh. 8 - Prob. 8.6WPCh. 8 - Prob. 8.7WPCh. 8 - Prob. 8.1CPCh. 8 - Prob. 8.2CPCh. 8 - Prob. 8.3CPCh. 8 - Prob. 8.4CPCh. 8 - Prob. 8.5CPCh. 8 - Prob. 8.6CPCh. 8 - Prob. 8.7CPCh. 8 - Prob. 8.1DPCh. 8 - Prob. 8.2DPCh. 8 - Prob. 8.3DP
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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.arrow_forwardAn 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_forward
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