Q: Consider the laminar flow near a flat, solid wall, as illustrated in Fig. 2.1. The momentum equation for this flow involves the competition among three effects: inertia, pressure gradient, and friction [see eq. (2.26)]. For the purpose of scale analysis, consider a flow region of length L and thickness L. Show that in this region, the ratio of inertia to friction is of order Re,, where Re, is the Reynolds number based on wall length. Note that the region selected for analysis is not the boundary layer region discussed in Chapter 2. In a certain flow, the value of Re̟ is 10³. What force balance rules the L × L region: inertia ~ pressure, inertia ~ friction, or pressure ~ friction? Um, Tm, Pao Use Solid wall du du I dP, (2.26) dy Figure 2.1 Velocity and temperature boundary layers near a plate parallel to a uniform flow.
Q: Consider the laminar flow near a flat, solid wall, as illustrated in Fig. 2.1. The momentum equation for this flow involves the competition among three effects: inertia, pressure gradient, and friction [see eq. (2.26)]. For the purpose of scale analysis, consider a flow region of length L and thickness L. Show that in this region, the ratio of inertia to friction is of order Re,, where Re, is the Reynolds number based on wall length. Note that the region selected for analysis is not the boundary layer region discussed in Chapter 2. In a certain flow, the value of Re̟ is 10³. What force balance rules the L × L region: inertia ~ pressure, inertia ~ friction, or pressure ~ friction? Um, Tm, Pao Use Solid wall du du I dP, (2.26) dy Figure 2.1 Velocity and temperature boundary layers near a plate parallel to a uniform flow.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![Q: Consider the laminar flow near a flat, solid wall, as illustrated in Fig. 2.1.
The momentum equation for this flow involves the competition among
three effects: inertia, pressure gradient, and friction [see eq. (2.26)]. For
the purpose of scale analysis, consider a flow region of length L and
thickness L. Show that in this region, the ratio of inertia to friction is
of order Re,, where Re, is the Reynolds number based on wall length.
Note that the region selected for analysis is not the boundary layer region
discussed in Chapter 2. In a certain flow, the value of Re, is 10. What
force balance rules the L × L region: inertia
or pressure friction?
Um, Tm, Poo
T
pressure, inertia ~ friction,
y
Solid wall
| dP,
+ v
(2.26)
p dx
Figure 2.1 Velocity and temperature boundary layers near a plate parallel to a uniform flow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33c1b6f8-ca92-4ab2-88ae-aa100f4ff9bf%2F89372ced-6498-42f2-b7bb-d1e91c38b4da%2Fmxk0mqo_processed.png&w=3840&q=75)
Transcribed Image Text:Q: Consider the laminar flow near a flat, solid wall, as illustrated in Fig. 2.1.
The momentum equation for this flow involves the competition among
three effects: inertia, pressure gradient, and friction [see eq. (2.26)]. For
the purpose of scale analysis, consider a flow region of length L and
thickness L. Show that in this region, the ratio of inertia to friction is
of order Re,, where Re, is the Reynolds number based on wall length.
Note that the region selected for analysis is not the boundary layer region
discussed in Chapter 2. In a certain flow, the value of Re, is 10. What
force balance rules the L × L region: inertia
or pressure friction?
Um, Tm, Poo
T
pressure, inertia ~ friction,
y
Solid wall
| dP,
+ v
(2.26)
p dx
Figure 2.1 Velocity and temperature boundary layers near a plate parallel to a uniform flow.
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