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 41P
Wave flow of an incompressible fluid into a solid surface follows a sinusoidal pattern. Flow is axisymmetric about the z axis, which is normal to the surface. The z component of the flow follows the pattern
Determine (a) the radial component of flow (Vr) and (b) the convective and local components of the acceleration
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
navier stokes
The velocity vector in a flow is given by :V=-3xi-4yj-7zk Determine the stream equation passing through a point L(4,2,3)
The velocity component in the y-direction is given as v = 3x - 4y for the steady, inviscid and two-
dimensional flow of an incompressible fluid. The only body force is the gravity, g, and it acts in the negative
y-direction. The density of the fluid is p. For an irrotational flow, determine
a) The velocity component in the x-direction, if it is zero at the origin
b) The acceleration vector:
) and
c) The pressure field, if the pressure is Po at the origin
d) The stream function(
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
- A flow can be described by the following equations. u =x cos y and v= -2x siny. Then the flow is (A) Rotational (B) Irrotational (C) Either rotational or irrotational (D) None of thesearrow_forward6. For a two-dimensional flow, the velocity field is ū = 1²+y • jwhere i and j are the basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from below. (1) The flow is incompressible. (2) The flow is unsteady. -y (3) y-component of acceleration, ay (z²+y²)² -(z+y) (4) x-component of acceleration,az (2²+y?)² (A) (2) and (3) (B) (1) and (3) (C) (1) and (2) (D) (3) and (4)arrow_forwardFlow through a converging nozzle can be approximated by a one-dimensional velocity distribution u=vo (1+2). For the nozzle shown below, assume that the velocity varies linearly from u = vo at the entrance to u = 3v, at the exit. Compute the acceleration at the entrance and exit if vo=10m/s and L = 1m. x=0 X u= :326 x=Larrow_forward
- Derive the Eulerian acceleration of a fluid particle in a flow field given by 1 V = xy²i -y'j + xykarrow_forward5. Determine the 1, in order that the velocity constants т, and m x+lr y+mr z + nr where r = x² +y² +z° may satisfy the equation of V = r(x+r)'r(x+r)´ r(x+r)] continuity for a fluid motion.arrow_forwardA flow of a liquid is described by the velocity field V = (Ax – B)î – Ayĵ where x and y are in meters and A = 1/s and B = 2 m/s. Consider the streamlines that pass through the locations (x y) = (3,4) and ( -3, 4). What is the speed of flow at (3,4)? a. 1.38 m/s ОБ.3.27 m/s О с. 4.12 m/s O d. 5.70 m/s e. 6.40 m/sarrow_forward
- 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.arrow_forwardConsider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forward(c) The 3-plane pattern of a flow is given by w= 3(z + %). Determine the velocity V W = and the direction of flow, a at the point z= 4 +5i. Repeat above calculation for w = 3(z +%)+4i In zarrow_forward
- Q1) One dimensional steady fluid flow along x axis is shown in figure. The velocities at point O and X2 as from uo= 3 m/s and u2= 12 m/s. Assuming that the velocity is varying linearly with the distance through x axis, Uo= 3 m/s U2= 12 m/s X, +0.10 m- a) Calculate accelerations at O, X, and X2 points. (15) b) Determine the flow is incompressible or not. (10) 0.20 m-arrow_forwardy x = r cos 0 V = Or y = r sine r = √x² + y² χ Flow in "solid body rotation" acts like a solid spinning around an axis. The streamlines are circular, the velocity is purely tangential, and the velocity magnitude is V = r, where is the angular velocity (positive counter-clockwise) and r is the radius. (a) Express the velocity vector V as a function of x and y. (b) Calculate the curl of the velocity vector V × V, indicating clearly the direction of the resulting vector.arrow_forwardp) A mass of fluid is in motion so that the lines of motion lie on the surface of coaxial cylinders. Show that the equation of continuity is partial differential ap 1 a 5(pvo) + əz - (ρυ.) 0 r d0 where (v,, vg, vz) are the components of velocity in cylindrical co-ordinates and p is the density.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