Fluid Mechanics, 8 Ed
8th Edition
ISBN: 9789385965494
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 8, Problem 8.112P
To determine
The equivalencies of the given expressions.
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3.) 13.152* - A sphere (m = 2 kg) is connected to a fixed point O by an inextensible cord (L = 1.2 m). The
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the maximum possible velocity v. if the impulse of the force exerted on the cord is not to exceed F = 3Ns.
4.) 13.165* - Two billiard balls A & B (same mass m & diameter d = 2.37") are as shown. Ball A has velocity
V₁ = 3 ft/s when it strikes B, which is at rest. B then moves in the x direction after impact. Find (a) angle 0,
(b) the velocity of B after impact (VB'). Positional variables are x = 6" and y = 10", and e = 0.9.
We will consider a linear system and a nonlinear system under uncertainty, each expressed in the form
of a set of stochastic differential equation (SDE) as follows:
=
da (Ax+ Bu)dt + Gdw,
dx = f(x,u,t)dt+Gdw,
(1)
(2)
where x is the state, u is the control, and dw is a differential increment of standard Brownian motion, i.e.,
E[dw] = 0 and E [dw(t)dw(t)] = dt-1.
In this problem, we consider the linear SDE, Eq. (1), with a very simple model where x = R², u = [0,0]
(no control), and dw R². The matrices A, B, and G are given as follows:
A=02x2, B=02x2; G = [000]
(3)
where σp Є R represents the degree of the uncertainty, and let us take σ₁ = 2 and σ2 = 3. Assume that the
initial state is deterministic and e(t = 0) = [0,0]. Take the following steps to simulate the given SDE for
1 € [0, 1]:
(a): Consider the increments of w between each time interval [+1). Derive the analytical expression
of Aw using w~N(02, 12), where Aw, w(tk+1) — w(tk).
(c): Derive the approximate continuous-time EoM from…
Chapter 8 Solutions
Fluid Mechanics, 8 Ed
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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