FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 37P
Consider the following steady, incompressible, two-dimensional velocity field:
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
4. A steady, incompressible, and two-dimensional velocity field is given by the following
components in the xy-plane:
Vxu = 2.65 + 3.12x + 5.46y
=
Vy=
=v=0.8+ 5.89x² + 1.48y
=
Calculate the acceleration field (find expressions for acceleration components ax and ay and
calculate the acceleration at the point (x,y) = (-1,3).
a. Derive an equation for the material acceleration vector.b. Obtain the vorticity vector for the velocity field.c. Is the flow rotational or irrotational? Show through your derivation.d. Is the flow incompressible or compressible? Show through your derivation.
Q: A flow field is given by:
V = (x'y)i+(y°z)j–-(2x*yz+ yz*)k
Prove that it is a case of possible steady incompressible fluid flow. Calculate the
velocity and acceleration at the point (3,2.4).
Chapter 4 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
Ch. 4 - What does the word kinematics mean? Explain what...Ch. 4 - Briefly discuss the difference between derivative...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - Consider the following steady, two-dimensional...Ch. 4 - -5 A steady, two-dimensional velocity field is...Ch. 4 - Consider steady flow of water through an...Ch. 4 - What is the Eulerian description of fluid motion?...Ch. 4 - Is the Lagrangian method of fluid flow analysis...Ch. 4 - A stationary probe is placed in a fluid flow and...Ch. 4 - A tiny neutrally buoyant electronic pressure probe...
Ch. 4 - Define a steady flow field in the Eulerian...Ch. 4 - Is the Eulerian method of fluid flow analysis more...Ch. 4 - A weather balloon is hunched into the atmosphere...Ch. 4 - A Pilot-stalk probe can often be seen protruding...Ch. 4 - List at least three oiler names for the material...Ch. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - For the velocity field of Prob. 4-6, calculate the...Ch. 4 - Consider steady flow of air through the diffuser...Ch. 4 - For the velocity field of Prob. 4-21, calculate...Ch. 4 - A steady, incompressible, two-dimensional (in the...Ch. 4 - The velocity field for a flow is given by...Ch. 4 - Prob. 25CPCh. 4 - What is the definition of a timeline? How can...Ch. 4 - What is the definition of a streamline? What do...Ch. 4 - Prob. 28CPCh. 4 - Consider the visualization of flow over a 15°...Ch. 4 - Consider the visualization of ground vortex flow...Ch. 4 - Consider the visualization of flow over a sphere...Ch. 4 - Prob. 32CPCh. 4 - Consider a cross-sectional slice through an array...Ch. 4 - A bird is flying in a room with a velocity field...Ch. 4 - Conversing duct flow is modeled by the steady,...Ch. 4 - The velocity field of a flow is described by...Ch. 4 - Consider the following steady, incompressible,...Ch. 4 - Consider the steady, incompressible,...Ch. 4 - A steady, incompressible, two-dimensional velocity...Ch. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - The velocity field for a line some in the r plane...Ch. 4 - A very small circular cylinder of radius Rtis...Ch. 4 - Consider the same two concentric cylinders of...Ch. 4 - The velocity held for a line vartex in the r...Ch. 4 - Prob. 47PCh. 4 - Name and briefly describe the four fundamental...Ch. 4 - Prob. 49CPCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Converging duct flow is modeled by the steady,...Ch. 4 - Using the results of Prob. 4—57 and the...Ch. 4 - Converging duct flow (Fig. P4—16) is modeled by...Ch. 4 - Prob. 60PCh. 4 - For the velocity field of Prob. 4—60, what...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - For the velocity field of Prob. 4—60, calculate...Ch. 4 - Prob. 64PCh. 4 - Prob. 65PCh. 4 - Consider steady, incompressible, two-dimensional...Ch. 4 - Prob. 67PCh. 4 - Consider the steady, incompressible,...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - A cylindrical lank of water rotates in solid-body...Ch. 4 - Prob. 75PCh. 4 - A cylindrical tank of radius rrim= 0.354 m rotates...Ch. 4 - Prob. 77PCh. 4 - Prob. 78PCh. 4 - Prob. 79PCh. 4 - For the Couette flow of Fig. P4—79, calculate the...Ch. 4 - Combine your results from Prob. 4—80 to form the...Ch. 4 - Consider a steady, two-dimensional, incompressible...Ch. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Consider the following steady, three-dimensional...Ch. 4 - Prob. 85PCh. 4 - A steady, three-dimensional velocity field is...Ch. 4 - Briefly explain the purpose of the Reynolds...Ch. 4 - Prob. 88CPCh. 4 - True or false: For each statement, choose whether...Ch. 4 - Consider the integral ddtt2tx2. Solve it two ways:...Ch. 4 - Prob. 91PCh. 4 - Consider the general form of the Reynolds...Ch. 4 - Consider the general form of the Reynolds...Ch. 4 - Prob. 94PCh. 4 - Prob. 95PCh. 4 - Prob. 96PCh. 4 - Prob. 97PCh. 4 - The velocity field for an incompressible flow is...Ch. 4 - Consider fully developed two-dimensional...Ch. 4 - For the two-dimensional Poiseuille flow of Prob....Ch. 4 - Combine your results from Prob. 4—100 to form the...Ch. 4 - Prob. 103PCh. 4 - Prob. 107PCh. 4 - Prob. 108PCh. 4 - Prob. 109PCh. 4 - Prob. 110PCh. 4 - Prob. 112PCh. 4 - Prob. 113PCh. 4 - Prob. 114PCh. 4 - Prob. 116PCh. 4 - Based on your results of Prob. 4—116, discuss the...Ch. 4 - Prob. 118PCh. 4 - In a steady, two-dimensional flow field in the...Ch. 4 - A steady, two-dimensional velocity field in the...Ch. 4 - A velocity field is given by u=5y2,v=3x,w=0 . (Do...Ch. 4 - The actual path traveled by an individual fluid...Ch. 4 - Prob. 123PCh. 4 - Prob. 124PCh. 4 - Prob. 125PCh. 4 - Water is flowing in a 3-cm-diameter garden hose at...Ch. 4 - Prob. 127PCh. 4 - Prob. 128PCh. 4 - Prob. 129PCh. 4 - Prob. 130PCh. 4 - Prob. 131PCh. 4 - An array of arrows indicating the magnitude and...Ch. 4 - Prob. 133PCh. 4 - Prob. 134PCh. 4 - Prob. 135PCh. 4 - A steady, two-dimensional velocity field is given...Ch. 4 - Prob. 137PCh. 4 - Prob. 138PCh. 4 - Prob. 139PCh. 4 - Prob. 140PCh. 4 - Prob. 141P
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
- 1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2jarrow_forward4. Consider the steady, two-dimensional velocity field given by: u = 2xy-y²; v=x-y². Show that it is a possible 2d incompressible flow. Find the component of acceleration in x direction of a fluid particle at point (x, y) = (1,2)arrow_forwarda. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.arrow_forward
- An unsteady flow has velocity field v = t2 (x2y, xy2) in cartesian plane. 1. is the flow compresible or incompresible? 2. Find a streamfunction of the flow. 3. Find the pattern of instantaneous streamline for the flow.arrow_forwardThe velocity components of a flow field are given by: = 2x² – xy + z², v = x² – 4xy + y², w = 2xy – yz + y² (i) Prove that it is a case of possible steady incompressible fluid flow (ii) Calculate the velocity and acceleration at the point (2,1,3)arrow_forwardUse Eq. dx/u =dy/v=dz/w=dr/V to find and sketch the streamlines of the followingfl ow field:u = Kx; v = -Ky; w = 0, where K is a constant.arrow_forward
- Need correctly.arrow_forwardConsider the incompressible, irrotational, 2D flow. where the stream function is given by: 4 = 424 1) determine the Velocity field and prove the flow is Physically Possible and irrotutional ₂) Calculate and graph (do not sketch) the streamline pattern. 3) find the velocity potential for this flow and graph the lines of constant potential on the same graph as the streamlines.arrow_forwardA steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: u = 1.85 + 2.05x + 0.656y ? = 0.754 − 2.18x − 2.05yCalculate the acceleration field (find expressions for acceleration components ax and ay), and calculate the acceleration at the point (x, y) = (−1, 3).arrow_forward
- 1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].arrow_forwardPlease answer botharrow_forwardA steady, incompressible, two-dimensional velocity field is given by the following components in the xy-plane: u = 0.205 + 0.97x + 0.851y ? = −0.509 + 0.953x − 0.97y Calculate the acceleration field (find expressions for acceleration components ax and ay) and calculate the acceleration at the point (x, y) = (2, 1.5).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