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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Textbook Question
Chapter 8, Problem 7P
Viscous oil flows steadily between parallel plates. The flow is fully developed and laminar. The pressure gradient is 1.25 kPa/m and the channel half-width is h = 1.5 mm. Calculate the magnitude and direction of the wall shear stress at the upper plate surface. Find the volume flow rate through the channel (μ = 0.50 N · s/m2).
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Question3
Explain briefly what is meant by fully developed laminar flow. The velocity u at any radius r in
fully developed laminar flow through a straight horizontal pipe of internal radius ro is given by
u= (1/4µ)(ro2 - r2)dp/dx
dp/dx is the pressure gradient in the direction of flow and u is the dynamic viscosity.
Show that the pressure drop over a length L is given by the following formula.
Ap = 32µLu/D?
The wall skin friction coefficient is defined as Cr = 2t( pum2).
Show that C= 16/Re where Re = pumD/u and p is the density, um is the mean velocity and t, is
the wall shear stress.
3. Explain briefly what is meant by fully developed laminar flow. The velocity u at any
radius r in fully developed laminar flow through a straight horizontal pipe of internal
radius ro is given by
u= (1/4µ)(ro2-r2)dp/dx
dp/dx is the pressure gradient in the direction of flow and u is the dynamic viscosity.
Show that the pressure drop over a length L is given by the following formula.
Ap=32μLu/D²
The wall skin friction coefficient is defined as C = 21/(pum²).
Show that C= 16/Re where Re = pumD/μ and p is the density, um is the mean velocity
and to is the wall shear stress.
Water is flowing in the pipe at a flow rate of 0.736 m^3/s. There are four 45-degree elbows in the pipe. Surface illumination: 0.0001524 m. Find the diameter of the pipe. Coefficient of water kinematic viscosity: 1.12*10^-6 m^2/s.
Chapter 8 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 8 - Consider incompressible flow in a circular...Ch. 8 - What is the maximum flow rate of air that may...Ch. 8 - For flow in circular tubes, transition to...Ch. 8 - An incompressible fluid flows between two infinite...Ch. 8 - Oil is confined in a 4-in.-diameter cylinder by a...Ch. 8 - Viscous oil flows steadily between parallel...Ch. 8 - Calculate for the flow in this two-dimensional...Ch. 8 - The velocity profile in a two-dimensional open...Ch. 8 - A large mass is supported by a piston of diameter...Ch. 8 - A hydraulic jack supports a load of 9000 kg. The...
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