Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 71P
A cylinder of radius ri rotates at a speed ω coaxially inside a fixed cylinder of radius ro. A viscous fluid fills the space between the two cylinders. Determine the velocity profile in the space between the cylinders and the shear stress on the surface of each cylinder. Explain why the shear stresses are not equal.
P5.71
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5.71 A cylinder of radius r; rotates at a speed w coaxially inside a fixed cylinder of radius ro. A viscous
fluid fills the space between the two cylinders. Determine the velocity profile in the space between the
cylinders and the shear stress on the surface of each cylinder. Explain why the shear stresses are not
equal.
5. A linear velocity profile is formed in a fluid between two plates as shown in the figure when
one of the plates is moved parallel to the other and there is no externally imposed pressure
gradient (i.e. there is no pump). If the top plate is travels at U = 0.3 m/s and the bottom
plate is held fixed and the two plates are separated by a distance d = 0.3 m/s, derive an
equation for the velocity profile u(y). Assume that the fluid in contact with either plate
moves at the same speed as the plate (this is called the no-slip condition).
U=0.3 m/s
d=0.3 m
(3) The cart shown below is restrained from moving by a cable connected to a fixed wall. The
tank has a circular cross section of diameter D and the flow exit has a circular cross section of
diameter Do. Do not assume that H(t) is constant. The fluid has density p and the exit is open to
the atmosphere.
Wall
H
D-
Do
Cable
Vo
(1) Determine H(t) and the exit velocity Vo(t).
(2) Determine the tension in the cable as a function of time
Your answers should be in terms of given parameters (D, Do, p, g)
о,
Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 5 - Which of the following sets of equations represent...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - In an incompressible three-dimensional flow field,...Ch. 5 - In a two-dimensional incompressible flow field,...Ch. 5 - The three components of velocity in a velocity...Ch. 5 - The x component of velocity in a steady,...Ch. 5 - The y component of velocity in a steady...Ch. 5 - The velocity components for an incompressible...Ch. 5 - The radial component of velocity in an...Ch. 5 - A crude approximation for the x component of...
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