Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 8, Problem 22P
Consider steady, incompressible, and fully developed laminar flow of a viscous liquid down an incline with no pressure gradient. The velocity profile was derived in Example 5.9. Plot the velocity profile. Calculate the kinematic viscosity of the liquid if the film thickness on a 30° slope is 0.8 mm and the maximum velocity is 15.7 mm/s.
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liquid (density 800kg/m3, viscosity 10−3 kg/ms) has to be supplied at a mean speed of 2m/s through a pipe of diameter 12.5mm with a surface roughness equivalent to that for structural steel. What is the magnitude of the pressure gradient necessary to achieve this flow? Your answer should have a positive sign and be to the nearest 10 Pa/m. You may wish to use the Moody diagram.
Problem 4: Differential Analysis
Water flows in a thin layer between a wall and a vertical plate separated by a distance h = 1 mm.
The wall is stationary while the plate moves upwards with a velocity Vplate = 1 m/s. Assume
p=1000 kg/m³, v = 10-6 m²/s.
1. Assuming that the flow is laminar, steady, and fully developed, use differential analysis
(Navier-Stokes) to calculate the velocity profile.
2. Calculate the flow rate per unit width.
3. Compute the Reynolds number in the water and air flow and determine if the conditions are
laminar or turbulent.
b-1 mm
g-10
Pam
Zoomed-in fully-developed region
V-1 m/s
Figure 4: Flow between stationary wall and moving plate.
The velocity distribution in a fully developed laminar pipe flow is given by where UCL is the velocity at the centerline, and R is the pipe radius. The fluid density is ρ, and its viscosity is µ. (a) Find the average velocity . (b) Write down the Reynolds number Re based on average velocity and pipe diameter. At what approximate value of this Reynolds number would you expect the flow to become turbulent? Why is this value only approximate? (c) Assume that the stress/strain rate relationship for the fluid is Newtonian. Find the wall shear stress τw in terms of µ, R and UCL. Express the local skin friction coeffient Cf in terms of the Reynolds number Re.
Chapter 8 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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