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
Videos
Textbook Question
Chapter 5, Problem 71P
A cylinder of radius ri rotates at a speed ω coaxially inside a fixed cylinder of radius ro. A viscous fluid fills the space between the two cylinders. Determine the velocity profile in the space between the cylinders and the shear stress on the surface of each cylinder. Explain why the shear stresses are not equal.
P5.71
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The entrance flow between two parallel plates (gap h) has a velocity that varies linearly at the entrance and develops into a fully parabolic profile at the exit. What is the relationship between the maximum velocity at the entrance and that at the exit? You can show by symmetry that the maximum velocity is attained at the mid-plane between the two plates.
5. 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 m
Fluid mechanics.
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
Determine the normal stress in each member of the truss structure. All joints are ball joint, and the material ...
Introduction To Finite Element Analysis And Design
1.1 What is the difference between an atom and a molecule? A molecule and a crystal?
Manufacturing Engineering & Technology
A loading causes the wires to elongate into the dashed shape. Explain how to determine the normal strain AB in ...
Mechanics of Materials
The surface temperature of transmission.
Introduction to Heat Transfer
Consider refrigerant R-134a flowing in a smooth, horizontal, tube of wall thickness 2 mm. The refrigerant is at...
Fundamentals of Heat and Mass Transfer
What parts are included in the vehicle chassis?
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
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
- P4.8 When a valve is opened, fluid flows in the expansion duct of Fig. P4.8 according to the approximation Ut V=iU(1- v=iU (1-7) tanh L Find (a) the fluid acceleration at (x, t) = (L, L/U) and (b) the time for which the fluid acceleration at x = L is zero. Why does the fluid acceleration become negative after condition (b)? 1 I u(x, t) 1 1 (X=0 1x = L Fig. P4.8arrow_forwardH.W.2/: The bottom quarter of a vertical cylindrical tank of total height 0.4 m and diameter 0.3 m is filled with a liquid (SG > 1, like glycerin) and the rest with water, as shown in the figure below. The tank is now rotated about its vertical axis at a constant angular speed of v. Determine (a) the value of the angular speed when the point P on the axis at the liquid-liquid interface touches the bottom of the tank and (b) the amount of water that would be spilled out at this angular speed? 3h h = 0.1 m D = 0.3 marrow_forwardThe waterwheel in Fig. is being driven at 200 r/minby a 150-ft/s jet of water at 20 ° C. The jet diameter is 2.5 in.Assuming no losses, what is the horsepower developed bythe wheel? For what speed Ω r/min will the horsepowerdeveloped be a maximum? Assume that there are manybuckets on the waterwheel.arrow_forward
- Consider a steady, two-dimensional, incompressible fl owof a newtonian fl uid in which the velocity fi eld isknown: u = - 2 xy , υ = y 2 - x 2 , w = 0. ( a ) Does thisfl ow satisfy conservation of mass? ( b ) Find the pressurefi eld, p ( x , y ) if the pressure at the point ( x = 0, y = 0) isequal to p a .arrow_forwardA jet of air having velocity V₁ and cross-sectional area A₁ strikes an inclined plate as shown in the figure. Neglect any effects of viscosity. V₁ (a) Find V₂ and V3 in terms of V₁. Note that the pressure is patm everywhere. (b) Because viscous effects are negligible, there is no way for the air to exert a force on the plate in the tangential (z) direction. Using the coordinate system in the figure, find A₂ and A3 in terms of A₁ and 0. (c) For V₁ = 50 m/s, A₁ = 5 x 10-4 m², and 0 = 60°, find the force required to hold the plate in place. Neglect the weight of the plate. Recall that pair = 1.225 kg/m³.arrow_forwardFluid 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_forward
- Consider a sphere of radius R immersed in a uniform stream Uo, as shown in Fig. P4.7. According to the theory of Chap. 8, the fluid velocity along streamline AB is given by V = ui = U, (1+ Find (a) the position of maximum fluid acceleration along AB and (b) the time required for a fluid particle to travel from A to B. B(Sphere *=-4R P4.7arrow_forwardQ⁴arrow_forwardConsider a viscous fi lm of liquid draining uniformly downthe side of a vertical rod of radius a , as in Fig. P4.84. Atsome distance down the rod the fi lm will approach a terminalor fully developed draining fl ow of constant outer radiusb , with υ z = υ z ( r ), υ θ = υ r = 0. Assume that the atmosphereoffers no shear resistance to the fi lm motion. Derivea differential equation for υ z , state the proper boundaryconditions, and solve for the fi lm velocity distribution.How does the fi lm radius b relate to the total fi lm volumefl ow rate Q ?arrow_forward
- Water in a vertical (i.e., gravitational force of the fluid in the nozzle plays a role, and the elevation change in the Bernoulli's Equation, if needed, should be considered) pipe is charging from an attached bend nozzle into the atmosphere as shown in Fig. 5. The nozzle's weight is 20 kg. The pipe and the nozzle are connected by a flange. The gage pressure of the flow at the flange is 35 kPa when the discharge rate is 0.1 m³/s. The volume of the bending nozzle is 0.012 m³. Calculate the vertical component of the anchoring forcing required to hold the nozzle in place and determine its direction. G= 9.81 m/s². The density of water is 1000 kg/m³. ChatGPT solution: Nozzle 1 Area -0.01 m² P-35 kPa Area -0.025 m² 0.10 ms Figure 5: Q5 35 degreearrow_forward(b) if Vr = U, thên vg J(r). Q2 Determine the velocity profile in a fluid situated between two coaxial rotating cylinders. Let the inner cylinder have radius R1, and angular velocity N1; let the outer cylinder have radius R2 and angular velocity N2.arrow_forwardDerive an expression for the capillary- height change h, as shown, for a fluid of surface tension Y and contact angle 0 be- tween two parallel plates W apart. Evaluate for water at 20°C if W = 0.5 mm.arrow_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
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