Fluid Mechanics, 8 Ed
8th Edition
ISBN: 9789385965494
Author: Frank White
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 9, Problem 9.152P
To determine
The drag by shock expansion theory.
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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
sphere rests on a frictionless horizontal surface at a distance of x = 0.5 m from O when it is given a velocity
(V.) in a direction perpendicular to OA. It moves freely until it reach A', when the cord becomes taut. Find
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 9 Solutions
Fluid Mechanics, 8 Ed
Ch. 9 - Prob. 9.1PCh. 9 - Prob. 9.2PCh. 9 - If 8 kg of oxygen in a closed tank at 200°C and...Ch. 9 - P9.4 Consider steady adiabatic airflow in a duct....Ch. 9 - Prob. 9.5PCh. 9 - Prob. 9.6PCh. 9 - Prob. 9.7PCh. 9 - Prob. 9.8PCh. 9 - P9.9 Liquid hydrogen and oxygen are burned in a...Ch. 9 - P9.10 A certain aircraft flics at 609 mi/h at...
Ch. 9 - Prob. 9.11PCh. 9 - Prob. 9.12PCh. 9 - Consider steam at 500 K and 200 kPa. Estimate its...Ch. 9 - Prob. 9.14PCh. 9 - Prob. 9.15PCh. 9 - Prob. 9.16PCh. 9 - Prob. 9.17PCh. 9 - Prob. 9.18PCh. 9 - Prob. 9.19PCh. 9 - Prob. 9.20PCh. 9 - P9.21 N?O expands isentropically through a duct...Ch. 9 - Given the pitot stagnation temperature and...Ch. 9 - Prob. 9.23PCh. 9 - Prob. 9.24PCh. 9 - Prob. 9.25PCh. 9 - Prob. 9.26PCh. 9 - P9.27 A pitot tube, mounted on an airplane flying...Ch. 9 - Prob. 9.28PCh. 9 - Prob. 9.29PCh. 9 - Prob. 9.30PCh. 9 - Prob. 9.31PCh. 9 - Prob. 9.32PCh. 9 - Prob. 9.33PCh. 9 - Prob. 9.34PCh. 9 - Prob. 9.35PCh. 9 - P9.36 An air tank of volume 1.5 m3 is initially at...Ch. 9 - Make an exact control volume analysis of the...Ch. 9 - Prob. 9.38PCh. 9 - Prob. 9.39PCh. 9 - Prob. 9.40PCh. 9 - Prob. 9.41PCh. 9 - Prob. 9.42PCh. 9 - Prob. 9.43PCh. 9 - Prob. 9.44PCh. 9 - It is desired to have an isentropic airflow...Ch. 9 - Prob. 9.46PCh. 9 - Prob. 9.47PCh. 9 - Prob. 9.48PCh. 9 - Prob. 9.49PCh. 9 - Prob. 9.50PCh. 9 - Prob. 9.51PCh. 9 - Prob. 9.52PCh. 9 - Prob. 9.53PCh. 9 - Prob. 9.54PCh. 9 - Prob. 9.55PCh. 9 - Prob. 9.56PCh. 9 - Prob. 9.57PCh. 9 - Prob. 9.58PCh. 9 - Prob. 9.59PCh. 9 - Prob. 9.60PCh. 9 - Prob. 9.61PCh. 9 - Prob. 9.62PCh. 9 - Prob. 9.63PCh. 9 - Prob. 9.64PCh. 9 - Prob. 9.65PCh. 9 - Prob. 9.66PCh. 9 - Prob. 9.67PCh. 9 - Prob. 9.68PCh. 9 - Prob. 9.69PCh. 9 - Prob. 9.70PCh. 9 - A converging-diverging nozzle has a throat area of...Ch. 9 - Prob. 9.72PCh. 9 - Prob. 9.73PCh. 9 - Prob. 9.74PCh. 9 - Prob. 9.75PCh. 9 - Prob. 9.76PCh. 9 - P9.77 A perfect gas (not air) expands...Ch. 9 - Prob. 9.78PCh. 9 - P9.79 A large tank, at 400 kPa and 450 K, supplies...Ch. 9 - Prob. 9.80PCh. 9 - Prob. 9.81PCh. 9 - Prob. 9.82PCh. 9 - 1*9.83 When operating at design conditions (smooth...Ch. 9 - Prob. 9.84PCh. 9 - A typical carbon dioxide tank for a paintball gun...Ch. 9 - Prob. 9.86PCh. 9 - Prob. 9.87PCh. 9 - Prob. 9.88PCh. 9 - Prob. 9.89PCh. 9 - Prob. 9.90PCh. 9 - Prob. 9.91PCh. 9 - Prob. 9.92PCh. 9 - Prob. 9.93PCh. 9 - Prob. 9.94PCh. 9 - Prob. 9.95PCh. 9 - Prob. 9.96PCh. 9 - Prob. 9.97PCh. 9 - Prob. 9.98PCh. 9 - Prob. 9.99PCh. 9 - Prob. 9.100PCh. 9 - Prob. 9.101PCh. 9 - Prob. 9.102PCh. 9 - Prob. 9.103PCh. 9 - Prob. 9.104PCh. 9 - Prob. 9.105PCh. 9 - Prob. 9.106PCh. 9 - Prob. 9.107PCh. 9 - Prob. 9.108PCh. 9 - P9.109 A jet engine at 7000-m altitude takes in 45...Ch. 9 - Prob. 9.110PCh. 9 - Prob. 9.111PCh. 9 - Prob. 9.112PCh. 9 - Prob. 9.113PCh. 9 - Prob. 9.114PCh. 9 - Prob. 9.115PCh. 9 - Prob. 9.116PCh. 9 - P9.117 A tiny scratch in the side of a supersonic...Ch. 9 - Prob. 9.118PCh. 9 - Prob. 9.119PCh. 9 - Prob. 9.120PCh. 9 - Prob. 9.121PCh. 9 - Prob. 9.122PCh. 9 - Prob. 9.123PCh. 9 - Prob. 9.124PCh. 9 - Prob. 9.125PCh. 9 - Prob. 9.126PCh. 9 - Prob. 9.127PCh. 9 - Prob. 9.128PCh. 9 - Prob. 9.129PCh. 9 - Prob. 9.130PCh. 9 - Prob. 9.131PCh. 9 - Prob. 9.132PCh. 9 - Prob. 9.133PCh. 9 - P9.134 When an oblique shock strikes a solid wall,...Ch. 9 - Prob. 9.135PCh. 9 - Prob. 9.136PCh. 9 - Prob. 9.137PCh. 9 - Prob. 9.138PCh. 9 - Prob. 9.139PCh. 9 - Prob. 9.140PCh. 9 - Prob. 9.141PCh. 9 - Prob. 9.142PCh. 9 - Prob. 9.143PCh. 9 - Prob. 9.144PCh. 9 - Prob. 9.145PCh. 9 - Prob. 9.146PCh. 9 - Prob. 9.147PCh. 9 - Prob. 9.148PCh. 9 - Prob. 9.149PCh. 9 - Prob. 9.150PCh. 9 - Prob. 9.151PCh. 9 - Prob. 9.152PCh. 9 - Prob. 9.153PCh. 9 - Prob. 9.154PCh. 9 - Prob. 9.155PCh. 9 - Prob. 9.156PCh. 9 - The Ackeret airfoil theory of Eq. (9.104) is meant...Ch. 9 - Prob. 9.1WPCh. 9 - Prob. 9.2WPCh. 9 - Prob. 9.3WPCh. 9 - Prob. 9.4WPCh. 9 - Prob. 9.5WPCh. 9 - Prob. 9.6WPCh. 9 - Prob. 9.7WPCh. 9 - Prob. 9.8WPCh. 9 - FE9.1 For steady isentropic flow, if the absolute...Ch. 9 - FE9.2 For steady isentropic flow, if the density...Ch. 9 - Prob. 9.3FEEPCh. 9 - Prob. 9.4FEEPCh. 9 - Prob. 9.5FEEPCh. 9 - Prob. 9.6FEEPCh. 9 - Prob. 9.7FEEPCh. 9 - Prob. 9.8FEEPCh. 9 - Prob. 9.9FEEPCh. 9 - Prob. 9.10FEEPCh. 9 - Prob. 9.1CPCh. 9 - Prob. 9.2CPCh. 9 - Prob. 9.3CPCh. 9 - Prob. 9.4CPCh. 9 - Prob. 9.5CPCh. 9 - Prob. 9.6CPCh. 9 - Professor Gordon Holloway and his student, Jason...Ch. 9 - Prob. 9.8CPCh. 9 - Prob. 9.1DPCh. 9 - Prob. 9.2DP
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