Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
1. Consider an annulus flow. Two long cylinders are concentrically aligned as shown in Figure Q1. A viscous fluid filled up the space in between. The inner cylinder of radius R4 is stationary while the outer eylinder of radius R, rotates with an angular velocity w. Neglect gravitational effect. (a) Simplify the momentum equations. State all assumptions. (b) Apply the boundary conditions and determine the velocity. (c) Plot velocity against r and sketch the velocity profile for R, < r < Ro. (d) What is the wall shear stress at the wall of the inner cylinder? 1 dv, av, 2u- ar +- r a0 + ar az e. 1dv, (dve +- [Trr Tre Trz T= Ter Tee Tez 1 Tze Tz a ve +- r a0 2µ az r a0 ae (av, av (ave 1dv, + 24 az ar az r a0 az Figure Q1

1. Consider an annulus flow. Two long cylinders are concentrically aligned as shown in Figure Q1. A viscous fluid filled up the space in between. The inner cylinder of radius R4 is stationary while the outer eylinder of radius R, rotates with an angular velocity w. Neglect gravitational effect. (a) Simplify the momentum equations. State all assumptions. (b) Apply the boundary conditions and determine the velocity. (c) Plot velocity against r and sketch the velocity profile for R, < r < Ro. (d) What is the wall shear stress at the wall of the inner cylinder? 1 dv, av, 2u- ar +- r a0 + ar az e. 1dv, (dve +- [Trr Tre Trz T= Ter Tee Tez 1 Tze Tz a ve +- r a0 2µ az r a0 ae (av, av (ave 1dv, + 24 az ar az r a0 az Figure Q1

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
Unless otherwise stated, given: Properties of air, p = 1.18kg/m³, µ = 1.85 x 10-2mPa·s. Properties of water, p = 997kg/m³, µ = 0.89mPa · s. 1. Consider an annulus flow. Two long cylinders are concentrically aligned as shown in Figure Q1. A viscous fluid filled up the space in between. The inner cylinder ofradius R; is stationary while the outer cylinder of radius R, rotates with an angular velocity w. Neglect gravitational effect. (a) Simplify the momentum equations. State all assumptions. (b) Apply the boundary conditions and determine the velocity. (c) Plot velocity against r and sketch the velocity profile for R; <r< R,. (d) What is the wall shear stress at the wall of the inner cylinder? av, 2µ- ar a ve 1 dv, r a0 + ar az Tre Trz 1dv, r a0 2µ "ag ae T= Ter Tee Tez az r a0 Tze + az ar Fag 2µ- + az r a0 az Figure Q1
Transcribed Image Text:Unless otherwise stated, given: Properties of air, p = 1.18kg/m³, µ = 1.85 x 10-2mPa·s. Properties of water, p = 997kg/m³, µ = 0.89mPa · s. 1. Consider an annulus flow. Two long cylinders are concentrically aligned as shown in Figure Q1. A viscous fluid filled up the space in between. The inner cylinder ofradius R; is stationary while the outer cylinder of radius R, rotates with an angular velocity w. Neglect gravitational effect. (a) Simplify the momentum equations. State all assumptions. (b) Apply the boundary conditions and determine the velocity. (c) Plot velocity against r and sketch the velocity profile for R; <r< R,. (d) What is the wall shear stress at the wall of the inner cylinder? av, 2µ- ar a ve 1 dv, r a0 + ar az Tre Trz 1dv, r a0 2µ "ag ae T= Ter Tee Tez az r a0 Tze + az ar Fag 2µ- + az r a0 az Figure Q1
Expert Solution
steps

Step by step

Solved in 6 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Fluid Kinematics
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