Explanation Given information: The case of flow is Couette flow between a moving and a fixed plate. There is slip condition on both the wall and the simple slip condition we know here is ( δ u ) w a l l = l d u d y | w a l l where l is the mean free path of the fluid. Consider the moving plate have velocity in x-direction is V . And consider upper plate is placed at + h and lower plate at − h . Calculation: We know the continuity equation for two dimensional (x,y) flow is ∂ u ∂ x + ∂ v ∂ y = 0 But we are considering the Couette flow which is here a axial flow u ≠ 0 , v = w = 0 , so the continuity equation reduced and become, ∂ u ∂ x = 0 , u = u ( y ) this is the conclusion from continuity equation. Now we know that the Navier-Stokes momentum equation for two-dimensional flow is: ρ ( u ∂ u ∂ x + v ∂ u ∂ y ) = − ∂ p ∂ x + ρ g x + μ ( ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 ) ρ ( 0 + 0 ) = 0 + 0 + μ ( 0 + ∂ 2 u ∂ y 2 ) ∂ 2 u ∂ y 2 = 0 , We get, u = c 1 y + c 2 ------- equation A Where c 1 , c 2 are the constants of integration and for the value of these two, we have to use boundary condition

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 4, Problem 4.97P

To determine

Velocity distribution when there is slip at both walls.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 4.96P

Chapter 4, Problem 4.98P

Chapter 4 Solutions

Fluid Mechanics

Ch. 4 - Prob. 4.1P Ch. 4 - Flow through the converging nozzle in Fig. P4.2...Ch. 4 - Prob. 4.3P Ch. 4 - Prob. 4.4P Ch. 4 - Prob. 4.5P Ch. 4 - Prob. 4.6P Ch. 4 - Prob. 4.7P Ch. 4 - P4.8 When a valve is opened, fluid flows in...Ch. 4 - An idealized incompressible flow has the proposed...Ch. 4 - A two-dimensional, incompressible flow has the...

Ch. 4 - Prob. 4.11P Ch. 4 - Prob. 4.12P Ch. 4 - Prob. 4.13P Ch. 4 - Prob. 4.14P Ch. 4 - What is the most general form of a purely radial...Ch. 4 - Prob. 4.16P Ch. 4 - An excellent approximation for the two-dimensional...Ch. 4 - Prob. 4.18P Ch. 4 - A proposed incompressible plane flow in polar...Ch. 4 - Prob. 4.20P Ch. 4 - Prob. 4.21P Ch. 4 - Prob. 4.22P Ch. 4 - Prob. 4.23P Ch. 4 - Prob. 4.24P Ch. 4 - An incompressible flow in polar coordinates is...Ch. 4 - Prob. 4.26P Ch. 4 - Prob. 4.27P Ch. 4 - P4.28 For the velocity distribution of Prob. 4.10,...Ch. 4 - Prob. 4.29P Ch. 4 - Prob. 4.30P Ch. 4 - Prob. 4.31P Ch. 4 - Prob. 4.32P Ch. 4 - Prob. 4.33P Ch. 4 - Prob. 4.34P Ch. 4 - P4.35 From the Navier-Stokes equations for...Ch. 4 - A constant-thickness film of viscous liquid flows...Ch. 4 - Prob. 4.37P Ch. 4 - Prob. 4.38P Ch. 4 - Reconsider the angular momentum balance of Fig....Ch. 4 - Prob. 4.40P Ch. 4 - Prob. 4.41P Ch. 4 - Prob. 4.42P Ch. 4 - Prob. 4.43P Ch. 4 - Prob. 4.44P Ch. 4 - Prob. 4.45P Ch. 4 - Prob. 4.46P Ch. 4 - Prob. 4.47P Ch. 4 - Consider the following two-dimensional...Ch. 4 - Prob. 4.49P Ch. 4 - Prob. 4.50P Ch. 4 - Prob. 4.51P Ch. 4 - Prob. 4.52P Ch. 4 - Prob. 4.53P Ch. 4 - P4.54 An incompressible stream function is...Ch. 4 - Prob. 4.55P Ch. 4 - Prob. 4.56P Ch. 4 - A two-dimensional incompressible flow field is...Ch. 4 - P4.58 Show that the incompressible velocity...Ch. 4 - Prob. 4.59P Ch. 4 - Prob. 4.60P Ch. 4 - An incompressible stream function is given by...Ch. 4 - Prob. 4.62P Ch. 4 - Prob. 4.63P Ch. 4 - Prob. 4.64P Ch. 4 - Prob. 4.65P Ch. 4 - Prob. 4.66P Ch. 4 - A stream function for a plane, irrotational, polar...Ch. 4 - Prob. 4.68P Ch. 4 - A steady, two-dimensional flow has the following...Ch. 4 - A CFD model of steady two-dimensional...Ch. 4 - Consider the following two-dimensional function...Ch. 4 - Prob. 4.72P Ch. 4 - Prob. 4.73P Ch. 4 - Prob. 4.74P Ch. 4 - Given the following steady axisymmetric stream...Ch. 4 - Prob. 4.76P Ch. 4 - Prob. 4.77P Ch. 4 - Prob. 4.78P Ch. 4 - Prob. 4.79P Ch. 4 - Oil, of density and viscosity , drains steadily...Ch. 4 - Prob. 4.81P Ch. 4 - Prob. 4.82P Ch. 4 - P4.83 The flow pattern in bearing Lubrication can...Ch. 4 - Consider a viscous film of liquid draining...Ch. 4 - Prob. 4.85P Ch. 4 - Prob. 4.86P Ch. 4 - Prob. 4.87P Ch. 4 - The viscous oil in Fig. P4.88 is set into steady...Ch. 4 - Oil flows steadily between two fixed plates that...Ch. 4 - Prob. 4.90P Ch. 4 - Prob. 4.91P Ch. 4 - Prob. 4.92P Ch. 4 - Prob. 4.93P Ch. 4 - Prob. 4.94P Ch. 4 - Two immiscible liquids of equal thickness h are...Ch. 4 - Prob. 4.96P Ch. 4 - Prob. 4.97P Ch. 4 - Prob. 4.98P Ch. 4 - For the pressure-gradient flow in a circular tube...Ch. 4 - W4.1 The total acceleration of a fluid particle is...Ch. 4 - Is it true that the continuity relation, Eq....Ch. 4 - Prob. 4.3WP Ch. 4 - Prob. 4.4WP Ch. 4 - W4.5 State the conditions (there are more than...Ch. 4 - Prob. 4.6WP Ch. 4 - W4.7 What is the difference between the stream...Ch. 4 - Under what conditions do both the stream function...Ch. 4 - Prob. 4.9WP Ch. 4 - Consider an irrotational, incompressible,...Ch. 4 - Prob. 4.1FEEP Ch. 4 - Prob. 4.2FEEP Ch. 4 - Prob. 4.3FEEP Ch. 4 - Given the steady, incompressible velocity...Ch. 4 - Prob. 4.5FEEP Ch. 4 - Prob. 4.6FEEP Ch. 4 - C4.1 In a certain medical application, water at...Ch. 4 - Prob. 4.2CP

Knowledge Booster

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.

Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY

Elements Of Electromagnetics

Mechanical Engineering

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:9780134319650

Author:Russell C. Hibbeler

Publisher:PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:9781259822674

Author:Yunus A. Cengel Dr., Michael A. Boles

Publisher:McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:9781118170519

Author:Norman S. Nise

Publisher:WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:9781118807330

Author:James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:WILEY

SEE MORE TEXTBOOKS

Physics 33 - Fluid Statics (1 of 10) Pressure in a Fluid; Author: Michel van Biezen;https://www.youtube.com/watch?v=mzjlAla3H1Q;License: Standard YouTube License, CC-BY