Fluid Mechanics Fundamentals And Applications
3rd Edition
ISBN: 9780073380322
Author: Yunus Cengel, John Cimbala
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Textbook Question
Chapter 4, Problem 22P
Consider steady flow of air through the diffuser portion of a wind tunnel (Fig. P4-21). Along the centerline of the diffuser, the air speed decreases from uentranceto uexitas sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x=0 to x=L
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Fy = 100 N
Fx = 100 N
Z
a = 500 mm
F₂ = 500 N
b = 1000 mm
Figure 2: Schematics for problem 3.
1. Draw the moment (M), axial (N), and shear (S) diagrams. Please note that this is a 3D problem and you
will have moment (M) and shear (S) along two different axes. That means that you will have a total of 5
diagrams.
I tried solving this one but have no idea where I went wrong can you please help me out with this?
Question 1.
A tube rotates in the horizontal xy plane with a constant angular velocity w about the z-axis. A
particle of mass m is released from a radial distance R when the tube is in the position shown.
This problem is based on problem 3.2 in the text.
y
ω
R
m
2R
Figure 1
X
a) Draw a free body diagram of the particle if the tube is frictionless.
b) Draw a free body diagram of the particle if the coefficient of friction between the sides of the
tube and the particle is μs = flk = fl.
c) For the case where the tube is frictionless, what is the radial speed at which the particle
leaves the tube?
d) For the case where there is friction, derive a differential equation that would allow you to
solve for the radius of the particle as a function of time. I'm only looking for the differential
equation. DO NOT solve it.
e) If there is no friction, what is the angle of the tube when the particle exits?
• Hint: You may need to solve a differential equation for the last part. The "potentially…
Chapter 4 Solutions
Fluid Mechanics Fundamentals And Applications
Ch. 4 - What does the word kinematics mean? Explain what...Ch. 4 - Briefly discuss the difference between derivative...Ch. 4 - Consider steady flow of water through an...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - -5 A steady, two-dimensional velocity field is...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - What is the Eulerian description of fluid motion?...Ch. 4 - Is the Lagrangian method of fluid flow analysis...Ch. 4 - Prob. 9CPCh. 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 - List at least three oiler names for the material...Ch. 4 - A weather balloon is hunched into the atmosphere...Ch. 4 - A Pilot-stalk probe can often be seen protruding...Ch. 4 - Is the Eulerian method of fluid flow analysis more...Ch. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Prob. 19PCh. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - The velocity field for a flow is given by...Ch. 4 - Consider steady flow of air through the diffuser...Ch. 4 - For the velocity field of Prob. 422, calculate the...Ch. 4 - A steady, incompressible, two-dimensional (in the...Ch. 4 - For the velocity field of Prob. 4-6, calculate the...Ch. 4 - Prob. 26CPCh. 4 - Prob. 27CPCh. 4 - What is the definition of a streamline? What do...Ch. 4 - Prob. 29CPCh. 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 - What is the definition of a timeline? How can...Ch. 4 - Consider a cross-sectional slice through an array...Ch. 4 - Prob. 35PCh. 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 held for a line vartex in the r...Ch. 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 - Conversing duct flow is modeled by the steady,...Ch. 4 - Prob. 48CPCh. 4 - Name and briefly describe the four fundamental...Ch. 4 - Converging duct flow (Fig. P4—16) is modeled by...Ch. 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 - Prob. 57PCh. 4 - Prob. 58PCh. 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. 62PCh. 4 - Prob. 63PCh. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Prob. 65PCh. 4 - Consider the steady, incompressible,...Ch. 4 - Prob. 67PCh. 4 - Prob. 68PCh. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - A cylindrical lank of water rotates in solid-body...Ch. 4 - Prob. 74PCh. 4 - A cylindrical tank of radius rrim= 0.354 m rotates...Ch. 4 - Prob. 76PCh. 4 - Prob. 77PCh. 4 - Consider the following steady, three-dimensional...Ch. 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 - A steady, three-dimensional velocity field is...Ch. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Prob. 88CPCh. 4 - Briefly explain the purpose of the Reynolds...Ch. 4 - True or false: For each statement, choose whether...Ch. 4 - Consider the integral ddtt2tx2. Solve it two ways:...Ch. 4 - Prob. 92PCh. 4 - Consider the general form of the Reynolds...Ch. 4 - Consider the general form of the Reynolds...Ch. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - Prob. 98PCh. 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 - The velocity field for an incompressible flow is...Ch. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 111PCh. 4 - Prob. 112PCh. 4 - Prob. 114PCh. 4 - In a steady, two-dimensional flow field in the...Ch. 4 - Prob. 116PCh. 4 - Prob. 117PCh. 4 - Prob. 119PCh. 4 - Based on your results of Prob. 4—116, discuss the...Ch. 4 - Prob. 121PCh. 4 - Prob. 122PCh. 4 - Water is flowing in a 3-cm-diameter garden hose at...Ch. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Prob. 126PCh. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - The actual path traveled by an individual fluid...Ch. 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 - Prob. 136PCh. 4 - A steady, two-dimensional velocity field is given...Ch. 4 - Prob. 138PCh. 4 - Prob. 139PCh. 4 - Prob. 140PCh. 4 - Prob. 141PCh. 4 - Prob. 142P
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