Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 9, Problem 13P
Yy13
To determine
The cylindrical velocity components
The nature of the flow.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A velocity field is given by u = 5y2, v = 3x, w = 0. (a) Is this flow steady or unsteady? Is it two- or three- dimensional? (b) At (x,y,z) = (3,2,–3), compute the velocity vector. (c) At (x,y,z) = (3,2,–3), compute the local (i.e., unsteady part) of the acceleration vector. (d ) At (x,y,z) = (3,2,–3), compute the convective (or advective) part of the acceleration vector. (e) At (x,y,z) = (3,2,–3), compute the (total) acceleration vector.
[2] Consider the following stedy, incompressible, two-dimensional velocity field:
V=(u,v)=(0.5+1.2x) 7+ (-2.0-1.2y)
Generate an analytical expression for the flow streamlines and draw several streamlines in
the upper-right quadrant from x=0 to 5 and y=0 to 6. (Here use the relation: dy/dx=v/u in
the streamlines.)
Converging duct flow is modeled by the steady, two-
dimensional velocity field
V = (u, v) = (U₁ + bx) i-by. For the case
in which Ug = 3.56 ft/s and b = 7.66 s¯¹, plot several
streamlines from x = 0 ft to 5 ft and y=-2 ft to 2 ft. Be
sure to show the direction of the streamlines. (Please
upload you response/solution using the controls provided
below.)
Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dACh. 9 - Prob. 4CPCh. 9 - Prob. 5CPCh. 9 - Prob. 6CPCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P
Ch. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Alex is measuring the time-averaged velocity...Ch. 9 - Let vector c be given G=4xziy2i+yzkand let V be...Ch. 9 - The product rule can be applied to the divergence...Ch. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20CPCh. 9 - In this chapter we derive the continuity equation...Ch. 9 - Repeat Example 9-1(gas compressed in a cylinder by...Ch. 9 - Consider the steady, two-dimensional velocity...Ch. 9 - The compressible from of the continuity equation...Ch. 9 - In Example 9-6 we derive the equation for...Ch. 9 - Consider a spiraling line vortex/sink flow in the...Ch. 9 - Verify that the steady; two-dimensional,...Ch. 9 - Consider steady flow of water through an...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Two velocity components of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - What is significant about curves of constant...Ch. 9 - In CFD lingo, the stream function is often called...Ch. 9 - Prob. 39CPCh. 9 - Prob. 40CPCh. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - As a follow-up to Prob. 9-45, calculate the volume...Ch. 9 - Consider the Couette flow of Fig.9-45. For the...Ch. 9 - Prob. 48PCh. 9 - AS a follow-up to Prob. 9-48, calculate the volume...Ch. 9 - Consider the channel flow of Fig. 9-45. The fluid...Ch. 9 - In the field of air pollution control, one often...Ch. 9 - Suppose the suction applied to the sampling...Ch. 9 - Prob. 53PCh. 9 - Flow separates at a shap corner along a wall and...Ch. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 58PCh. 9 - Prob. 59PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63EPCh. 9 - Prob. 64PCh. 9 - Prob. 65EPCh. 9 - Prob. 66PCh. 9 - Prob. 68EPCh. 9 - Prob. 69PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Wht in the main distionction between Newtormine...Ch. 9 - Prob. 77CPCh. 9 - What are constitutive equations, and to the fluid...Ch. 9 - An airplane flies at constant velocity Vairplane...Ch. 9 - Define or describe each type of fluid: (a)...Ch. 9 - The general cool volume from of linearmomentum...Ch. 9 - Consider the steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider liquid in a cylindrical tank. Both the...Ch. 9 - Engine oil at T=60C is forced to flow between two...Ch. 9 - Consider steady, two-dimensional, incompressible...Ch. 9 - Consider steady, incompressible, parallel, laminar...Ch. 9 - Prob. 89PCh. 9 - Prob. 90PCh. 9 - Prob. 91PCh. 9 - The first viscous terms in -comonent of the...Ch. 9 - An incompressible Newtonian liquid is confined...Ch. 9 - Prob. 94PCh. 9 - Prob. 95PCh. 9 - Prob. 96PCh. 9 - Prob. 97PCh. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Consider again the pipe annulus sketched in Fig...Ch. 9 - Repeat Prob. 9-99 except swap the stationary and...Ch. 9 - Consider a modified form of Couette flow in which...Ch. 9 - Consider dimensionless velocity distribution in...Ch. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Prob. 104PCh. 9 - Prob. 105PCh. 9 - Prob. 106PCh. 9 - Prob. 107CPCh. 9 - Prob. 108CPCh. 9 - Discuss the relationship between volumetric strain...Ch. 9 - Prob. 110CPCh. 9 - Prob. 111CPCh. 9 - Prob. 112PCh. 9 - Prob. 113PCh. 9 - Look up the definition of Poisson’s equation in...Ch. 9 - Prob. 115PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - For each of the listed equation, write down the...Ch. 9 - Prob. 119PCh. 9 - Prob. 120PCh. 9 - A block slides down along, straight inclined wall...Ch. 9 - Water flows down a long, straight, inclined pipe...Ch. 9 - Prob. 124PCh. 9 - Prob. 125PCh. 9 - Prob. 126PCh. 9 - Prob. 128PCh. 9 - The Navier-Stokes equation is also known as (a)...Ch. 9 - Which choice is not correct regarding the...Ch. 9 - In thud flow analyses, which boundary condition...Ch. 9 - Which choice is the genera1 differential equation...Ch. 9 - Which choice is the differential , incompressible,...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady velocity field is given by...Ch. 9 - Prob. 137P
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 steady, two-dimensional, incompressible velocity field has Cartesian velocity components u = Cy/(x2 + y2) and ? = −Cx/(x2 + y2), where C is a constant. Transform these Cartesian velocity components into cylindrical velocity components ur and u?, simplifying as much as possible. You should recognize this flow. What kind of flow is this?arrow_forward1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics? 2. Is the flow field V = xi and ρ = x physically realizable? 3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt: (a) Is the flow one-, two-, or three-dimensional? (b) What is the x-component of the acceleration following a fluid particle? (c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?arrow_forward1. 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_forward
- A incompressible, steady, velocity field is given by the following components in the x-y plane: u = 0.205 + 0.97x + 0.851y ; v = v0 + 0.5953x - 0.97y How would I calculated the acceleration field (ax and ay), and the acceleration at the point, v0= -1.050 ? Any help would be greatly appreciated :)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(a) Given the following steady, two-dimensional velocity field. [Diberi medan halaju yang mantap dan dua dimensi.] V = (u, v) = (8x + 6)ï + (-8y – 4)j (i) Is this flow field an incompressible flow? Prove your answer. (ii) Is this flow field irrotational? Prove your answer. (iii) Generate an expression for the velocity potential function if applicable.arrow_forward
- Velocity Field Assignment 4 2 -5 -4 2 -1 N -4 W- E Consider the steady, two-dimensional velocity field of wind as: V= (u, v)= (8 – 0.5x)i + (0.5 - 5y)j where x- an y- coordinates are in m, time in s, and the magnitude of the velocity is in m/s. Determine: (a) A stagnation point, if existed. (b) Sketch the velocity vector for the given coordinate on the map. (c) Sketch the relevant streamlines on a different graph. (d) Verify if the flow is rotational or irrotational flow. (e) Looking at the velocity vector, which section of the country will receive the most rain if the wind brings rainy season from the south-china sea?arrow_forward1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.arrow_forward3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.arrow_forward
- For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.arrow_forward2. Consider the two-dimensional time-dependent velocity field u(x, t) = (sint, cost, 0), in the basis of Cartesian coordinates. a) Determine the streamlines passing through the point x = 0 at the times t = 0, π/2, π and 3π/2. b) Determine the paths of fluid particles passing through the point x = 0 at the same times, to = 0, π/2, 7 and 37/2. Hence, describe their motion. ㅠ c) Find the streakline produced by tracer particles continuously released at the point xo = 0 and find its position at t = 0, π/2, π and 37/2. Hence describe its motion.arrow_forward4. Consider a velocity field V = K(yi + ak) where K is a constant. The vorticity, z , is (A) -K (B) K (C) -K/2 (D) K/2arrow_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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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