Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5, Problem 73P
Assume the liquid film in Example 5.9 is horizontal (i.e., θ = 0°) and that the flow is driven by a constant shear stress on the top surface (y = h), τyx = C. Assume that the liquid film is thin enough and flat and that the flow is fully developed with zero net flow rate (flow rate Q = 0). Determine the velocity profile u(y) and the pressure gradient dp=dx.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Q: Consider fully developed laminar flow in the annular space formed by the two concentric cylinders shown
in the below diagram. The outer pipe is stationary, and the inner pipe moves in the x direction with speed V
For pressure gradient, , and the inner cylinder stationary, let ro = R and r = kR, The velocity profile is
ax
given by:
др
+
4μ. θα
Find:
1- Volume flow rate (Q).
2- An expression for the average velocity (V)
3- Fork → 0, find Q and V
6
5.73 Assume the liquid film in Example 5.9 is horizontal (i.e.,
0 = 0°) and that the flow is driven by a constant shear stress
on the top surface (y= h), Tyx= C. Assume that the liquid
film is thin enough and flat and that the flow is fully devel-
oped with zero net flow rate (flow rate Q= 0). Determine the
velocity profile u(y) and the pressure gradient dp/dx.
h = 1 mm
0 = 15°
Width b = 1 m
Hi. Kindly assist with this Fluid Mechanics question.Please answer correctly and show all the steps
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...
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
- Problem 5. The fully-developed velocity profile for laminar flow in a pipe is very different from that for turbulent flow. For laminar flow, the velocity profile is parabolic (where is centerline velocity): = 1 - (1/2)² For turbulent flow, the time averaged velocity profile can be approximated by a power-law profile: v = (1-2) 1/ Find the ratio of average velocity to centerline velocity, V/Vc, and the dimensionless radial location, * = r/R, where you would need to place a Pitot tube if it is to measure the average velocity in the pipe for (a) laminar flow and (b) turbulent flow with n = 6.0 at Rep = 20,000. NOTE: For the integration of the turbulent profile, let * = r/R and y* = 1 − p*.arrow_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_forward= Problem 5. A thin oil film (u 0.80 N·s/m², p = 865 kg/m³) of height h = 5.0 mm is squeezed between two infinite parallel plates (0 ≤ y ≤ h). The bottom plate is stationary, u (y = 0) = 0, and the upper plate drags the flow along in the x-direction with an applied shear stress, Tyx (y = h) = Tw = 100 N/m². Assume fully-developed laminar flow for the oil film. A pressure gradient is applied that results in zero net volumetric flowrate (Q= 0). Find (a) the velocity profile, u (y), (b) the pressure gradient, dp/dx, and (c) plot y* = y/h versus u (on x-axis).arrow_forward
- An incompressible fluid (kinematic viscosity =7.4x10-7 m2/s, specific gravity=0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates,find the shear stress in Pascal on the surface of top plate.arrow_forward6arrow_forwardA 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?arrow_forward
- Required information The rotating-cylinder viscometer in the image shears the fluid in a narrow clearance Ar as shown. Assume a linear velocity distribution in the gaps. ΦΩ Viscous fluid Solid cylinder →Ar<<arrow_forwardA2 A Newtonian fluid with viscosity (Mu) flows upward at a steady rate between two parallel plates that make an angle y with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end, P(0) and P(L), are known and the pressure variations in the y-direction are small. Assume that Vy and Vz = 0 and Vx is a function of y alone. Use the shell balance to approach : - the Total flowrate, QVarrow_forwardQ1\ A crude oil of viscosity 0.85 poise and relative density 0.7 is flowing through a horizontal circular pipe of diameter 126 mm and of length 12 m. Calculate the difference of pressure at the two ends of the pipe, if 125 kg of the oil is collected in a tank in 40 seconds.arrow_forward4. Fluid flows axially in the annular space between a cylinder and a concentric rod. The radius of the rod is r; and that of the cylinder is ro. Fluid motion in the annular space is driven by an axial pressure gradient dp/dz. The cylinder is maintained at uniform temperature To. Assume incompressible laminar axisymmetric flow and neglect gravity and end effects. Show that the axial velocity is given by: _1-(r; /r, )? In(r, / r; ) r dp |(r/r,)? Au dz - In(r / r, ) – 1arrow_forwardHelp me plsarrow_forwardQuestion 4 du Water flows past a flat plate that has a length L = 5 m and a width w = 2 m, as shown in Figure Q4. The shear stress at the wall is given by Tw = μ- When the flow is laminar the shear stress at the wall is given by the equation: dy Tw = 0.0644 PU² The viscosity of water is μ = 1 mPa.s. 8(x) = 5 - Where p = 1000 kg/m³ is the water density and U.. = 5 m/s is the velocity of the water. The height of the boundary layer is 8, and can be approximated by μx puo X 1arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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
8.01x - Lect 27 - Fluid Mechanics, Hydrostatics, Pascal's Principle, Atmosph. Pressure; Author: Lectures by Walter Lewin. They will make you ♥ Physics.;https://www.youtube.com/watch?v=O_HQklhIlwQ;License: Standard YouTube License, CC-BY
Dynamics of Fluid Flow - Introduction; Author: Tutorials Point (India) Ltd.;https://www.youtube.com/watch?v=djx9jlkYAt4;License: Standard Youtube License