Water flows through a circular pipe with diameter d. The velocity profile of the water is given as: u(r)= (4-²) where the radius of the pipe, u is the viscosity, and a is a constant. a) Show that this velocity profile satisfies the boundary conditions of a fully developed is laminar flow. b) Which units must the constant a have for u (r) to express velocity in m/s? c) Find an expression for the shear stress at the point derr = d/4 d) Find an expression for the shear force acting on a piece of pipe of length L. e) What is the difference between a turbulent and a laminar flow?
Water flows through a circular pipe with diameter d. The velocity profile of the water is given as: u(r)= (4-²) where the radius of the pipe, u is the viscosity, and a is a constant. a) Show that this velocity profile satisfies the boundary conditions of a fully developed is laminar flow. b) Which units must the constant a have for u (r) to express velocity in m/s? c) Find an expression for the shear stress at the point derr = d/4 d) Find an expression for the shear force acting on a piece of pipe of length L. e) What is the difference between a turbulent and a laminar flow?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Water flows through a circular pipe with diameter d. The velocity profile of the water is given as:
u(r) = (-1²)
4μ 4
where the radius of the pipe, u is the viscosity, and a is a constant.
a) Show that this velocity profile satisfies the boundary conditions of a fully developed is laminar flow.
b) Which units must the constant a have for u (r) to express velocity in m/s?
c) Find an expression for the shear stress at the point derr = d / 4
d) Find an expression for the shear force acting on a piece of pipe of length L.
e) What is the difference between a turbulent and a laminar flow?
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