Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5, Problem 17P
A viscous liquid is sheared between two parallel disks of radius R, one of which rotates while the other is fixed. The velocity field is purely tangential, and the velocity varies linearly with z from Vθ = 0 at z = 0 (the fixed disk) to the velocity of the rotating disk at its surface (z = h). Derive an expression for the velocity field between the disks.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A VISCOUS FLUID FLOWS BETWEEN TWO PARALLEL AND INFINITELY LARGE PLATES KEPT AT A DISTANCE 2H FROM EACH OTHER. THE UPPER PLATE IS AT Y = H AND THE LOWE...
A viscous fluid flows between two parallel and infinitely large plates kept at a distance 2h from each other. The upper plate is at y = h and the lower plate is at y = - h. The considered
fluid flows mono directionally along the x-direction under a constant pressure gradient K = -dP/dx. The transverse profile of velocity is given by :
U(y) = K (h² - y²)
U (y) = (h-y)
U(y) = (h² - y²)
U(y) = (y²)
U(y) = K (h-y)
2h
EU(y)
The velocity components in the x and y
directions are given by
3
u = Axy3 - x2y, v = xy2 --
The value of a for a possible flow field
involving an incompressible fluid is
A viscous incompressible liquid of density p and of dynamic viscosity n is
carried upwards against gravity with the aid of moving side walls. This
laminar flow is steady and fully developed in z-direction and there is no
applied pressure gradient. The coordinate is fixed in the midway between
the walls as shown below.
2d
g=-gk
liquid
P, n
x=-d
x=d
I. The velocity profile in z-direction is
pg
w(x) =
(x2 – d) + U.
2n
II. To be able to carry a net amount of liquid upwards, the wall velocities
need to be greater than pgd²/(2n).
III. If one of the walls stops, increasing the speed of the other wall to 3/2U
would carry the same amount of liquid upwards.
Which of the above statements are true?
Chapter 5 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 5 - Which of the following sets of equations represent...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - In an incompressible three-dimensional flow field,...Ch. 5 - In a two-dimensional incompressible flow field,...Ch. 5 - The three components of velocity in a velocity...Ch. 5 - The x component of velocity in a steady,...Ch. 5 - The y component of velocity in a steady...Ch. 5 - The velocity components for an incompressible...Ch. 5 - The radial component of velocity in an...Ch. 5 - A crude approximation for the x component of...
Ch. 5 - A useful approximation for the x component of...Ch. 5 - A useful approximation for the x component of...Ch. 5 - For a flow in the xy plane, the x component of...Ch. 5 - Consider a water stream from a jet of an...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - For an incompressible flow in the r plane, the r...Ch. 5 - A viscous liquid is sheared between two parallel...Ch. 5 - A velocity field in cylindrical coordinates is...Ch. 5 - Determine the family of stream functions that...Ch. 5 - The stream function for a certain incompressible...Ch. 5 - Determine the stream functions for the following...Ch. 5 - Determine the stream function for the steady...Ch. 5 - Prob. 23PCh. 5 - A parabolic velocity profile was used to model...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - Prob. 27PCh. 5 - A flow field is characterized by the stream...Ch. 5 - In a parallel one-dimensional flow in the positive...Ch. 5 - Consider the flow field given by V=xy2i13y3j+xyk....Ch. 5 - Prob. 31PCh. 5 - The velocity field within a laminar boundary layer...Ch. 5 - A velocity field is given by V=10ti10t3j. Show...Ch. 5 - The y component of velocity in a two-dimensional,...Ch. 5 - A 4 m diameter tank is filled with water and then...Ch. 5 - An incompressible liquid with negligible viscosity...Ch. 5 - Sketch the following flow fields and derive...Ch. 5 - Consider the low-speed flow of air between...Ch. 5 - As part of a pollution study, a model...Ch. 5 - As an aircraft flies through a cold front, an...Ch. 5 - Wave flow of an incompressible fluid into a solid...Ch. 5 - A steady, two-dimensional velocity field is given...Ch. 5 - A velocity field is represented by the expression...Ch. 5 - A parabolic approximate velocity profile was used...Ch. 5 - A cubic approximate velocity profile was used in...Ch. 5 - The velocity field for steady inviscid flow from...Ch. 5 - Consider the incompressible flow of a fluid...Ch. 5 - Consider the one-dimensional, incompressible flow...Ch. 5 - Expand (V)V in cylindrical coordinates by direct...Ch. 5 - Determine the velocity potential for (a) a flow...Ch. 5 - Determine whether the following flow fields are...Ch. 5 - The velocity profile for steady flow between...Ch. 5 - Consider the velocity field for flow in a...Ch. 5 - Consider the two-dimensional flow field in which u...Ch. 5 - Consider a flow field represented by the stream...Ch. 5 - Fluid passes through the set of thin, closely...Ch. 5 - A two-dimensional flow field is characterized as u...Ch. 5 - A flow field is represented by the stream function...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the velocity field given by V=Ax2i+Bxyj,...Ch. 5 - Consider again the viscometric flow of Example...Ch. 5 - The velocity field near the core of a tornado can...Ch. 5 - A velocity field is given by V=2i4xjm/s. Determine...Ch. 5 - Consider the pressure-driven flow between...Ch. 5 - Consider a steady, laminar, fully developed,...Ch. 5 - Assume the liquid film in Example 5.9 is not...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - A linear velocity profile was used to model flow...Ch. 5 - A cylinder of radius ri rotates at a speed ...Ch. 5 - The velocity profile for fully developed laminar...Ch. 5 - Assume the liquid film in Example 5.9 is...Ch. 5 - The common thermal polymerase chain reaction (PCR)...Ch. 5 - A tank contains water (20C) at an initial depth y0...Ch. 5 - For a small spherical particle of styrofoam...Ch. 5 - Use Excel to generate the progression to an...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
What is the purpose of low-stress grinding?
Degarmo's Materials And Processes In Manufacturing
If a class is named Student, what name can you use for a constructor for this class?
Java: An Introduction to Problem Solving and Programming (8th Edition)
Modify the Product_T table by adding an attribute QtyOnHand that can be used to track the finished goods invent...
Modern Database Management
The ____________ is always transparent.
Web Development and Design Foundations with HTML5 (8th Edition)
7.13* For a bearing
DE = NUS 5 53’56 ”WT and angles to the right, compute the bearing of PG if angle
DEF 2 88°...
Elementary Surveying: An Introduction To Geomatics (15th Edition)
Why does the following pseudocode not perform as indicated in the comments? // This program gets a dollar amoun...
Starting Out with Programming Logic and Design (5th Edition) (What's New in Computer Science)
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.Similar questions
- 2. In a two dimensional incompressible fluid flow, the velocity components are given by: u=(x-4y) and v=-(y+4x). If possible show that the potential exists and determine its form. Also determine whether the flow is irrotational?arrow_forwardConsider a three-dimensional, steady velocity field given by V = (u, v, w) = (3.2 + 1.4x)i + (2.4 – 2.1y)j + (w)k. If the w-velocity is only a function of z, and the magnitude of w-velocity at z = 0 is 5, find the velocity field of w if the flow is known to be incompressible.arrow_forwardThe components of a two-dimensional velocity field are u = 4 + y³ and v = 16. The equation for a streamline can be written as y++ Ay + Bx + C = 0. Determine the values of the coefficients for the streamline passing through (3, 1). A = i B = i C= iarrow_forward
- Fluid Mechanics There is an incompressible Newtoniel fluid between the parallel plates whose bottom plate is fixed and the top plate is moved at V speed.The velocity field is u = V (y / h) i, where V is the velocity of the moving plate and h is the distance between plates. Find the stresses in such a flow. What can the momentum equation tell us about this flow?arrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forwardA two-dimensional flow field is given by the equations: u = ax + by V = Cx + dy Give one possible combination of constants a, b, c and d (none of which are zero) for which this describes the flow of an incompressible fluid. a = b = C = d=arrow_forward
- 3. Consider a viscous flow between two flat plates separated by a distance H. The bottom plate is located at y = 0 and moves to the right with speed Uplate. The top plate is located at y = H and moves to the left with speed 2Uplate. The pressure in the flow is constant. The fluid between the plates has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, two dimensional, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity between the plates in terms of Uplate, H, and y. b. Determine the average velocity between the plates in terms of Uplate and H. C. Determine the shear stress acting on the bottom plate in terms of Uplate, H, and µ. 2Uplate y fluid H Uplatearrow_forwardConsider the flow field V = (ay+dx)i + (bx-dy)j + ck, where a(t), b(t), c(t), and d(t) are time dependent coefficients. Prove the density is constant following a fluid particle, then find the pressure gradient vector gradP, Γ for a circular contour of radius R in the x-y plane (centered on the origin) using a contour integral, and Γ by evaluating the Stokes theorem surface integral on the hemisphere of radius R above the x-y plane bounded by the contour.arrow_forwardIn three-dimensional fluid flow, the velocity component an u = * + y z, v = - (xy + yz + zx). Determine the %3D satisfy the continuity equation.arrow_forward
- For the flow of an incompressible fluid, the velocity in x-direction u = ax + by and velocity in z-direction is zero. Find velocity component in y-direction such that v = 0 at y = 0. O atarrow_forward5. A linear velocity profile is formed in a fluid between two plates as shown in the figure when one of the plates is moved parallel to the other and there is no externally imposed pressure gradient (i.e. there is no pump). If the top plate is travels at U = 0.3 m/s and the bottom plate is held fixed and the two plates are separated by a distance d = 0.3 m/s, derive an equation for the velocity profile u(y). Assume that the fluid in contact with either plate moves at the same speed as the plate (this is called the no-slip condition). U=0.3 m/s d=0.3 marrow_forwardA fluid of density ρ and viscosity μ flows from left to right through the horizontal pipe of radius a and lengthL, shown in the figure below. The pressures at the centers of the inlet and exit are P1 and P2 ,respectively. You may assume that the only non-zero velocity component is vz and that it is not afunction of the angular coordinate, θ.(a) Simplify the continuity equation and show that vz = vz(r), i.e., it is a function of r only.(b) Simplify the momentum balance equation in the z-direction and show that it equals equation a in the image (c) Assuming that (dP/dz)=-delta P/L , solve the above equation with appropriate boundaryconditions and show that it equals equation c in the image(d) Show that the volumetric flow rate equals equation d in the imagearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher: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
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license