Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.52P
To determine
To estimate the value of W when the flow rate is 12 m3 s.
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Problem 1 (30 Points)
Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In
scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no
friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in
both scenarios, there is one generalized coordinate, .
R
Scenario 1
R
m
R
g
Scenario 2
m
HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the
bowl (scenario 1), or the pivot point of the pendulum (scenario 2).
Part I
a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points)
b) What can you say about the systems based on the Lagrangian? (2 points)
c) Solve for the equations of motion for both systems. (8 points)
Part II
Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to
determine the normal force acting on the mass.
a)…
Chapter 10 Solutions
Fluid Mechanics
Ch. 10 - Prob. 10.1PCh. 10 - P10.2 Water at 20°C flows in a 30-cm-wide...Ch. 10 - Prob. 10.3PCh. 10 - Prob. 10.4PCh. 10 - Prob. 10.5PCh. 10 - Prob. 10.6PCh. 10 - Prob. 10.7PCh. 10 - Prob. 10.8PCh. 10 - Equation (10.10) is for a single disturbance wave....Ch. 10 - Prob. 10.10P
Ch. 10 - Prob. 10.11PCh. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Prob. 10.16PCh. 10 - Prob. 10.17PCh. 10 - Prob. 10.18PCh. 10 - Prob. 10.19PCh. 10 - An unfinished concrete sewer pipe, of diameter 4...Ch. 10 - Prob. 10.21PCh. 10 - Prob. 10.22PCh. 10 - Prob. 10.23PCh. 10 - Prob. 10.24PCh. 10 - Prob. 10.25PCh. 10 - Prob. 10.26PCh. 10 - Prob. 10.27PCh. 10 - Prob. 10.28PCh. 10 - Prob. 10.29PCh. 10 - Prob. 10.30PCh. 10 - Prob. 10.31PCh. 10 - Prob. 10.32PCh. 10 - Prob. 10.33PCh. 10 - Prob. 10.34PCh. 10 - Prob. 10.35PCh. 10 - Prob. 10.36PCh. 10 - Prob. 10.37PCh. 10 - Prob. 10.38PCh. 10 - Pl0.39 A trapezoidal channel has n = 0.022 and Sn...Ch. 10 - Prob. 10.40PCh. 10 - Prob. 10.41PCh. 10 - Prob. 10.42PCh. 10 - Prob. 10.43PCh. 10 - Prob. 10.44PCh. 10 - Prob. 10.45PCh. 10 - Prob. 10.46PCh. 10 - Prob. 10.47PCh. 10 - Prob. 10.48PCh. 10 - Prob. 10.49PCh. 10 - Prob. 10.50PCh. 10 - Prob. 10.51PCh. 10 - Prob. 10.52PCh. 10 - Prob. 10.53PCh. 10 - A clay tile V-shaped channel has an included angle...Ch. 10 - Prob. 10.55PCh. 10 - Prob. 10.56PCh. 10 - Prob. 10.57PCh. 10 - Prob. 10.58PCh. 10 - Prob. 10.59PCh. 10 - Prob. 10.60PCh. 10 - P10.59 Uniform water flow in a wide brick channel...Ch. 10 - P10.62 Consider the flow in a wide channel over a...Ch. 10 - Prob. 10.63PCh. 10 - Prob. 10.64PCh. 10 - Prob. 10.65PCh. 10 - Prob. 10.66PCh. 10 - Prob. 10.67PCh. 10 - Prob. 10.68PCh. 10 - Given is the flow of a channel of large width b...Ch. 10 - Prob. 10.70PCh. 10 - Prob. 10.71PCh. 10 - Prob. 10.72PCh. 10 - Prob. 10.73PCh. 10 - Prob. 10.74PCh. 10 - Prob. 10.75PCh. 10 - Prob. 10.76PCh. 10 - Prob. 10.77PCh. 10 - Prob. 10.78PCh. 10 - Prob. 10.79PCh. 10 - Prob. 10.80PCh. 10 - Prob. 10.81PCh. 10 - Prob. 10.82PCh. 10 - Prob. 10.83PCh. 10 - Prob. 10.84PCh. 10 - Pl0.85 The analogy between a hydraulic jump and a...Ch. 10 - Prob. 10.86PCh. 10 - Prob. 10.87PCh. 10 - Prob. 10.88PCh. 10 - Prob. 10.89PCh. 10 - Prob. 10.90PCh. 10 - Prob. 10.91PCh. 10 - Prob. 10.92PCh. 10 - Prob. 10.93PCh. 10 - Prob. 10.94PCh. 10 - Prob. 10.95PCh. 10 - Prob. 10.96PCh. 10 - Prob. 10.97PCh. 10 - Prob. 10.98PCh. 10 - Prob. 10.99PCh. 10 - Prob. 10.100PCh. 10 - Prob. 10.101PCh. 10 - Prob. 10.102PCh. 10 - Prob. 10.103PCh. 10 - Prob. 10.104PCh. 10 - Prob. 10.105PCh. 10 - Prob. 10.106PCh. 10 - Prob. 10.107PCh. 10 - Prob. 10.108PCh. 10 - Prob. 10.109PCh. 10 - Prob. 10.110PCh. 10 - Prob. 10.111PCh. 10 - Prob. 10.112PCh. 10 - Prob. 10.113PCh. 10 - Prob. 10.114PCh. 10 - Prob. 10.115PCh. 10 - Prob. 10.116PCh. 10 - Prob. 10.117PCh. 10 - Prob. 10.118PCh. 10 - Prob. 10.119PCh. 10 - The rectangular channel in Fig. P10.120 contains a...Ch. 10 - Prob. 10.121PCh. 10 - Prob. 10.122PCh. 10 - Prob. 10.123PCh. 10 - Prob. 10.124PCh. 10 - Prob. 10.125PCh. 10 - Prob. 10.126PCh. 10 - Prob. 10.127PCh. 10 - Prob. 10.128PCh. 10 - Prob. 10.1WPCh. 10 - Prob. 10.2WPCh. 10 - Prob. 10.3WPCh. 10 - Prob. 10.4WPCh. 10 - Prob. 10.5WPCh. 10 - Prob. 10.6WPCh. 10 - Prob. 10.7WPCh. 10 - Prob. 10.8WPCh. 10 - Prob. 10.9WPCh. 10 - Prob. 10.10WPCh. 10 - Prob. 10.11WPCh. 10 - Prob. 10.12WPCh. 10 - Prob. 10.13WPCh. 10 - Prob. 10.1FEEPCh. 10 - Prob. 10.2FEEPCh. 10 - Prob. 10.3FEEPCh. 10 - Prob. 10.4FEEPCh. 10 - Prob. 10.5FEEPCh. 10 - Prob. 10.6FEEPCh. 10 - Prob. 10.7FEEPCh. 10 - February 1998 saw the failure of the earthen dam...Ch. 10 - Prob. 10.2CPCh. 10 - Prob. 10.3CPCh. 10 - Prob. 10.4CPCh. 10 - Prob. 10.5CPCh. 10 - Prob. 10.6CPCh. 10 - Prob. 10.7CPCh. 10 - Prob. 10.1DPCh. 10 - Prob. 10.2DP
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