Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
The laminar flow of a fluid with viscosity µ and density ρ in a circular pipe of radius R has a velocity distribution described by where UCL is the velocity on the centerline where r = 0. (a) Using a control volume analysis, find τw, the shear stress at the wall, in terms of R and the pressure gradient dp/dx. (b) Using the expression for the velocity profile, find τw, the shear stress at the wall, in terms of µ, R, and UCL. (c) Find the average velocity  in terms of UCL. (d) Using the results from parts (a)-(c), show that where Re is the Reynolds number based on the diameter D.

The laminar flow of a fluid with viscosity µ and density ρ in a circular pipe of radius R has a velocity distribution described by where UCL is the velocity on the centerline where r = 0. (a) Using a control volume analysis, find τw, the shear stress at the wall, in terms of R and the pressure gradient dp/dx. (b) Using the expression for the velocity profile, find τw, the shear stress at the wall, in terms of µ, R, and UCL. (c) Find the average velocity  in terms of UCL. (d) Using the results from parts (a)-(c), show that where Re is the Reynolds number based on the diameter D.

Elements Of Electromagnetics
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
See similar textbooks
icon
Related questions
Question

The laminar flow of a fluid with viscosity µ and density ρ in a circular pipe of radius R has a velocity distribution described by

where UCL is the velocity on the centerline where r = 0.

(a) Using a control volume analysis, find τw, the shear stress at the wall, in terms of R and the pressure gradient dp/dx.

(b) Using the expression for the velocity profile, find τw, the shear stress at the wall, in terms of µ, R, and UCL.

(c) Find the average velocity  in terms of UCL.

(d) Using the results from parts (a)-(c), show that

where Re is the Reynolds number based on the diameter D.

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Dimensional Analysis
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS