Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 10, Problem 66P
In an irrotational region of flow, we wtite the velocitv
* ¦"
From Chap. 9. we also vmte the components of the vorticitv vector in cylindrical coordinates as £r 7 -W- -p- >it --- -zr ^^ i- 7 *; l^s) 7 "d1 - Substitute the velocity components into the vorticitv cc-rnpc-nente tc- show that all three components of the voracity vector are indeed zero in an irtotatlona] reaic-n of flow.
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Ius A fluid flow situation depends on the Nelocity (V), the
density several lineor dimension, 4shi, h2.pressure drep
(DO > gravity (9) , Viscosity , Susface tension ). and bulk
mo dulus of elasticity k. Apply dimen sional analysis. to
these variables td A s*
Qus A fluid flow situatton depends
the Velocity (V), the
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density several lineor dimension, tsh, L2, pressure drop
(PP) » gravity (o),Viscosity Ms Susface tension (), and bulk
mo dulus of elasticity k. Apply dimen sional analysis. to
these variables ed MKEA
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Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A
Water responds to shear stress by continuously yielding in angular deformation in the
direction of the shear.
IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear
Istress, as shown in Figure 1.1.
do
dt
dx
,and v =
dy
dx
Angular deformation (Shear strain), 0 =
dt
do
Rate of shear strain =
dt
dx
dv
(Velocity gradient)
dy
dy dt
dv
Therefore, to
dv
T = constant
dy
dv
T = -
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The proportionally constant, u, is called the absolute viscosity of the flyid
Example
A flat plate of 50 cm² is being pulled over a fixed
flat surface at a constant velocity of 45 cm/sec
(Figure 1.1). An oil film of unknown viscosity
separates the plate and the fixed surface by a
distance of 0.1 cm. The force (T) required to pull
the plate is measured to be 31.7 N, and the viscosity
E of the fluid is constant. Determine the viscosity
(absolute).
22
Example
A flat…
Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
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Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
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Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
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