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 25P
A flow field is characterized by the stream function ψ = 3x2y – y3. Demonstrate that the flow field represents a two- dimensional incompressible flow. Show that the magnitude of the velocity depends only on the distance from the origin of the coordinates. Plot the stream line ψ = 2.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine the two-dimensional stream function corresponding to o = Aln(r/ro),
where A is a constant. What is the flow pattern? Plot the velocity field, potential field, and
3.
streamlines
velocity field is given by:
A two-dimensional
V = (x - 2y) i- (2x + y)Ĵj
a. Show that the flow is incompressible and irrotational.
b. Derive the expression for the velocity potential, (x,y).
c. Derive the expression for the stream function, 4(x,y).
1. 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.
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
- Consider a velocity field where the x and y components of velocity aregiven by u = cx and v = −cy, where c is a constant. Assuming the velocity field given is pertains to an incompressible flow, calculate the stream function and velocity potential.Using your results, show that lines of constant φ are perpendicular to linesof constant ψ.arrow_forwardby the velocity components u=2V A two-dimensional incompressible flow field is defined y -21 (2-2) V-212 L L == L where V and L are constants. If they exist, find the stream function and velocity potential.arrow_forwardThe 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 isarrow_forward
- The 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_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_forwardWhat is the flow pattern? Plot the velocity field, potential field, and streamlines. Please explain it in detail.arrow_forward
- need urgent help, thanks the question is related to advanced fluid mechanicsarrow_forwardFor the stream function Y = r5/² sin (), calculate the pressure field and sketch the streamlines of this flow.arrow_forwardQ3 The stream function for a given 2D flow fields is V = 5a²y – (s/3)y Determine the corresponding velocity potential.arrow_forward
- The stream function in a two dimensional flow field is given by sie= x2 - y2 .find the magnitude of the velocity at point (1. 1) .arrow_forwardA velocity field is specified as shown, the coordinates are measured in meters. Is the flow field one-, two-, or three-dimensional? Why? Calculate the velocity components at the points (2, 1/2). Develop an equation for the streamline passing through this point. Plot several streamlines in the first quadrant including the one that passes through the point (2, 1/2)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
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