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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Question
Chapter 9, Problem 59P
To determine
(a)
The expression for the velocity component
The expression for the velocity component
To determine
(b)
That the flow field satisfies the in compressible continuity.
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Solve using Euler's law the boundary representation model for the below-mentioned diagram.
Consider steady, incompressible, two-dimensional flow due to a line source at the origin. Fluid is created at the origin and spreads out radially in all directions in the xy-plane. The net volume flow rate of created fluid per unit width is V·/L (into the page of Fig), where L is the width of the line source into the page in Fig Since mass must be conserved everywhere except at the origin (a singular point), the volume flow rate per unit width through a circle of any radius r must also be V·/L. If we (arbitrarily) specify stream function ? to be zero along the positive x-axis (? = 0), what is the value of ? along the positive y-axis (? = 90°)? What is the value of ? along the negative x-axis (? = 180°)?
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FLUID KINEMATICS
Fluid Mechanies
Fundamenteis and Applicationu
acceleration); this term can be nonzero even for steady flows. It accounts
for the effect of the fluid particle moving (advecting or convecting) to a
new location in the flow, where the velocity field is different. For example,
nunan A Çengel | John M. Cinbala
consider steady flow of water through a garden hose nozzle (Fig. 4-8). We
define steady in the Eulerian frame of reference to be when properties at
any point in the flow field do not change with respect to time. Since the
velocity at the exit of the nozzle is larger than that at the nozzle entrance,
fluid particles clearly accelerate, even though the flow is steady. The accel-
eration is nonzero because of the advective acceleration terms in Eq. 4-9.
FLUID MECHANICS
FIGURE 4-8
Flow of water through the nozzle of
a garden hose illustrates that fluid par- Note that while the flow is steady from the…
Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
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