FLUID MECHANICS FUND. (LL)-W/ACCESS
4th Edition
ISBN: 9781266016042
Author: CENGEL
Publisher: MCG CUSTOM
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Chapter 4, Problem 71P
To determine
The magnitude of the rate of rotation (angular velocity) about point
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The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
A linear system is one that satisfies the principle of superposition. In other words, if an input u₁
yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-
bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.
Using this fact, determine the output y(t) of the following linear system:
given the input:
P(s) =
=
Y(s)
U(s)
=
s+1
s+10
u(t) = e−2+ sin(t)
=e
Chapter 4 Solutions
FLUID MECHANICS FUND. (LL)-W/ACCESS
Ch. 4 - What does the word kinematics mean? Explain what...Ch. 4 - Briefly discuss the difference between derivative...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - -5 A steady, two-dimensional velocity field is...Ch. 4 - Consider steady flow of water through an...Ch. 4 - What is the Eulerian description of fluid motion?...Ch. 4 - Is the Lagrangian method of fluid flow analysis...Ch. 4 - A stationary probe is placed in a fluid flow and...Ch. 4 - A tiny neutrally buoyant electronic pressure probe...
Ch. 4 - Define a steady flow field in the Eulerian...Ch. 4 - Is the Eulerian method of fluid flow analysis more...Ch. 4 - A weather balloon is hunched into the atmosphere...Ch. 4 - A Pilot-stalk probe can often be seen protruding...Ch. 4 - List at least three oiler names for the material...Ch. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - For the velocity field of Prob. 4-6, calculate the...Ch. 4 - Consider steady flow of air through the diffuser...Ch. 4 - For the velocity field of Prob. 4-21, calculate...Ch. 4 - A steady, incompressible, two-dimensional (in the...Ch. 4 - The velocity field for a flow is given by...Ch. 4 - Prob. 25CPCh. 4 - What is the definition of a timeline? How can...Ch. 4 - What is the definition of a streamline? What do...Ch. 4 - Prob. 28CPCh. 4 - Consider the visualization of flow over a 15°...Ch. 4 - Consider the visualization of ground vortex flow...Ch. 4 - Consider the visualization of flow over a sphere...Ch. 4 - Prob. 32CPCh. 4 - Consider a cross-sectional slice through an array...Ch. 4 - A bird is flying in a room with a velocity field...Ch. 4 - Conversing duct flow is modeled by the steady,...Ch. 4 - The velocity field of a flow is described by...Ch. 4 - Consider the following steady, incompressible,...Ch. 4 - Consider the steady, incompressible,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - The velocity field for a line some in the r plane...Ch. 4 - A very small circular cylinder of radius Rtis...Ch. 4 - Consider the same two concentric cylinders of...Ch. 4 - The velocity held for a line vartex in the r...Ch. 4 - Prob. 47PCh. 4 - Name and briefly describe the four fundamental...Ch. 4 - Prob. 49CPCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Using the results of Prob. 4—57 and the...Ch. 4 - Converging duct flow (Fig. P4—16) is modeled by...Ch. 4 - Prob. 60PCh. 4 - For the velocity field of Prob. 4—60, what...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Prob. 67PCh. 4 - Consider the steady, incompressible,...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - A cylindrical lank of water rotates in solid-body...Ch. 4 - Prob. 75PCh. 4 - A cylindrical tank of radius rrim= 0.354 m rotates...Ch. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - For the Couette flow of Fig. P4—79, calculate the...Ch. 4 - Combine your results from Prob. 4—80 to form the...Ch. 4 - Consider a steady, two-dimensional, incompressible...Ch. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Consider the following steady, three-dimensional...Ch. 4 - Prob. 85PCh. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Briefly explain the purpose of the Reynolds...Ch. 4 - Prob. 88CPCh. 4 - True or false: For each statement, choose whether...Ch. 4 - Consider the integral ddtt2tx2. Solve it two ways:...Ch. 4 - Prob. 91PCh. 4 - Consider the general form of the Reynolds...Ch. 4 - Consider the general form of the Reynolds...Ch. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - The velocity field for an incompressible flow is...Ch. 4 - Consider fully developed two-dimensional...Ch. 4 - For the two-dimensional Poiseuille flow of Prob....Ch. 4 - Combine your results from Prob. 4—100 to form the...Ch. 4 - Prob. 103PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 116PCh. 4 - Based on your results of Prob. 4—116, discuss the...Ch. 4 - Prob. 118PCh. 4 - In a steady, two-dimensional flow field in the...Ch. 4 - A steady, two-dimensional velocity field in the...Ch. 4 - A velocity field is given by u=5y2,v=3x,w=0 . (Do...Ch. 4 - The actual path traveled by an individual fluid...Ch. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Water is flowing in a 3-cm-diameter garden hose at...Ch. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - An array of arrows indicating the magnitude and...Ch. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135PCh. 4 - A steady, two-dimensional velocity field is given...Ch. 4 - Prob. 137PCh. 4 - Prob. 138PCh. 4 - Prob. 139PCh. 4 - Prob. 140PCh. 4 - Prob. 141P
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