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 35P
A 4 m diameter tank is filled with water and then rotated at a rate of ω = 2π(1 − e−t)rad/s. At the tank walls, viscosity prevents relative motion between the fluid and the wall. Determine the speed and acceleration of the fluid particles next to the tank walls as a function of time.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
a flat plate of area 1.5×106 mm 2 is pulled with speed of 0.4 m/s relative to another plate located at a distance of 0.15 mm from it. find the force required to maintain this speed, if the fluid separating them is having viscosity 1 poise
Two concentric cylinders of radii a and b respectively (a > b) have their common axislying along the z-axis. The space between them b < r < a contains fluid of viscosity µ.A flow is generated by moving the outer cylinder with constant speed U parallel to itsaxis whilst the inner cylinder remains at rest.
1. Use cylindrical polar coordinates (r, θ, z) and consider an elementary fluid elementof lengths dr and dz and angle dθ (measured from the z-axis). Draw a diagramshowing the forces acting on the surfaces of the fluid element.
2. Determine the velocity distribution u in thez-direction, stating any assumptions you make.
An infinite plate is moving at a constant velocity of 3m/s over a second stationary plate. A thin layer of the liquid with viscosity of 0.65 centipoises and specific gravity of 0.88 separates the moving plate from the stationary plate. The fluid velocity varies linearly with the distance from the stationary plate. If the length between the two plates is 0.3mm, determine:
The absolute viscosity of the liquid in s
The kinematic viscosity of the liquid stokes
The shear stress on the fluid layer
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
The programmer intends for this pseudocode to display three random numbers in the range of 1 through 7. Accordi...
Starting Out with Programming Logic and Design (5th Edition) (What's New in Computer Science)
What populates the Smalltalk world?
Concepts Of Programming Languages
For the circuit shown, use the node-voltage method to find v1, v2, and i1.
How much power is delivered to the c...
Electric Circuits. (11th Edition)
Thetakes the .class files containing the programs bytecodes and transfers them to primary memory.
Java How to Program, Early Objects (11th Edition) (Deitel: How to Program)
ICA 8-49
The specific heats of aluminum and iron are 0.214 and 0.107 calories per gram degree Celsius [cal/(g °...
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
The ______ member function moves a files write position to a specified byte in the file.
Starting Out with C++: Early Objects (9th Edition)
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
- Two parallel flat plates are spaced 2 in. apart. One plate is moving at a velocity of 10 ft/min and the other is moving in the opposite direction at 35 ft/min. The viscosity of the fluid between the plates is constant at 363 lb/ft-hr. Calculate the stress on each plate. Calculate the fluid velocity profile expression for the system and fluid velocities at ½ in. intervals from plate to plate.arrow_forwardbetween two infinite surfaces with lateral cross-section It is coated with glycerin with an absolute viscosity of μ = 1.025 Ns / m2. This a cube parallel to two surfaces and with sides of c x c x c cm slides downwards. If the density of the cube is ρ = 254 kg / m3 then U Find the velocity (m / s). (g = 9.81 m / s2)arrow_forwardA liquid with kinematic viscosity of 3 centi stokes and specific weight 9 kN/m3 fills the space between a large stationary plate and a parallel plate of 475 mm square, the film thickness being 1 mm. If the smaller plate is to be pulled with uniform velocity of 4 m/s, determine the force required if the liquid film is maintained all through.arrow_forward
- ۱۵ Q3/ A dash pot is 0.2 m in diameter and 0.25 m long and it slides down in a vertical cylinder of diameter 0.21 m. The lubricating oil filled in the annular space has a viscosity of 0.5 poise and has a linear velocity profile. When the load on the piston is 25 N, find the speed with which the piston slides down. سرعة الله Dash pot Oil Cylinder- 0.2 m 25 N 0.21 m T 0.25 marrow_forwardDarrow_forwardFluidarrow_forward
- A cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. If the diameter and height of the cylinder are D and L, respectively, derive an expression for the velocity of the cylinder as a function of time, t. Discuss what will happen as t → ∞. Can this device serve as a viscometer?arrow_forwardThe sliding plate viscometer is used to measure fluid viscosity. The top plate (100 mm × 50 mm) is moving to the right with a constant velocity of 22 m/s in response to a force of 1 N. The bottom plate is stationary and separated by a vertical distance of 1 mm from the upper plate. What is the viscosity of the fluid? W h F L moving plate stationary plate fluid Varrow_forwardThe velocity profile for the course of a Newtonian substance between two wide, parallel plates is given by the equation: 3V U= 2 where V is the mean velocity. The fluid has a viscosity of 0.04lb-s/ft2. When V = 2 ft/s and h = 0.2in. Determine: (a) the shearing stress acting on the bottom wall, and; (b) the shearing stress acting on a plane parallel to the walls and passing through the centreline (Mid distribution).arrow_forward
- 5.Some oil is full of the space by two parallel plates. The lower plate is stationary, while the upper one moves parallel to it with a velocity U=2.5m/s due to a force F=98.1N corresponding to a square with length L= 60cm. h=12.5mm. Determine the dynamic viscosity of oil. y → U > F harrow_forwardA flat plate of area 2x10¹ cm² is pulled with a speed of 0.5 m/s relative to another plate located at a distance of 0.2 mm from it. If the fluid separated the two plates has a viscosity of 1.0 poise, find the force required to maintain the speed.arrow_forwardAn infinite plate is moving at a constant velocity of 0.3m/s over a second stationary plate. A thin layer of the liquid with viscosity of 0.65 centipoises and specific gravity of 0.88 separates the moving plate from the stationary plate. The fluid velocity varies linearly with the distance from the stationary plate. If the length between the two plates is 0.3mm, determine: The absolute viscosity of the liquid in s The kinematic viscosity of the liquid stokes The shear stress on the fluid layer A centrifuge bowl with internal diameter of 150mm is turning at 8000r/min is used to separate chlorobenzene, with a density of 1109 kgm3, from an aqueous wash liquid having a density of 1020 kgm3. The free liquid surface inside the bowl is 40mm from the axis of rotation. If the centrifugal bowl is to contain equal volumes of the two liquids, what should be the radial…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
Understanding Thermal Radiation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=FDmYCI_xYlA;License: Standard youtube license