Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.57P
To determine

(a)

To calculate:

The pressure in the tank.

To determine

(b)

To calculate:

The mass flow.

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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass. Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.  Discuss the positive definiteness of V (x, x_dot). Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0. Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1. Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Homework#5

Chapter 9 Solutions

Fluid Mechanics

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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