Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 4.4FEEP
Given the steady, incompressible velocity distribution u = Ax, v = By, and w = Cxy, where (A, B, C) are constants, This flow satisfies the equation of continuity if A equals (a) B, (b)B + C,(c)B- C, (d) -B, (e) -(B + C)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Given the steady, incompressible velocity distribution V =3 x i + Cy j + 0 k , where C is a constant, if conservation ofmass is satisfi ed, the value of C should be( a ) 3, ( b ) 3/2, ( c ) 0, ( d ) - 3/2, ( e ) - 3
3.3 Verify whether or not the following difference representation for the continuity equation for a
2-D steady incompressible flow has the conservation property:
(u;+1,j + U;+1.j-1 – U;,j – U;,j-1) , (Vi+1,j – Vi+1,j-1)
Ду
2Ax
where u and v are the x and y components of velocity, respectively.
3.3 Verify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (u, 1.j + u;41.j-1 - u.; – 4j.j-1) (1,j – 41,j-1) 2 Ax Ay where u and v are the x and y components of velocity, respectively. 3.4 Repeat Prob. 3.3, for the following difference representation for the continuity equation: (4i+ 1,5 - Uj-1,) (u, j+1 - V,j-1) + 2 Ax 2 Ay
Chapter 4 Solutions
Fluid Mechanics
Ch. 4 - Prob. 4.1PCh. 4 - Flow through the converging nozzle in Fig. P4.2...Ch. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - P4.8 When a valve is opened, fluid flows in...Ch. 4 - An idealized incompressible flow has the proposed...Ch. 4 - A two-dimensional, incompressible flow has the...
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - What is the most general form of a purely radial...Ch. 4 - Prob. 4.16PCh. 4 - An excellent approximation for the two-dimensional...Ch. 4 - Prob. 4.18PCh. 4 - A proposed incompressible plane flow in polar...Ch. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - An incompressible flow in polar coordinates is...Ch. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - P4.28 For the velocity distribution of Prob. 4.10,...Ch. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - Prob. 4.34PCh. 4 - P4.35 From the Navier-Stokes equations for...Ch. 4 - A constant-thickness film of viscous liquid flows...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Reconsider the angular momentum balance of Fig....Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Consider the following two-dimensional...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - P4.54 An incompressible stream function is...Ch. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - A two-dimensional incompressible flow field is...Ch. 4 - P4.58 Show that the incompressible velocity...Ch. 4 - Prob. 4.59PCh. 4 - Prob. 4.60PCh. 4 - An incompressible stream function is given by...Ch. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - A stream function for a plane, irrotational, polar...Ch. 4 - Prob. 4.68PCh. 4 - A steady, two-dimensional flow has the following...Ch. 4 - A CFD model of steady two-dimensional...Ch. 4 - Consider the following two-dimensional function...Ch. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.74PCh. 4 - Given the following steady axisymmetric stream...Ch. 4 - Prob. 4.76PCh. 4 - Prob. 4.77PCh. 4 - Prob. 4.78PCh. 4 - Prob. 4.79PCh. 4 - Oil, of density and viscosity , drains steadily...Ch. 4 - Prob. 4.81PCh. 4 - Prob. 4.82PCh. 4 - P4.83 The flow pattern in bearing Lubrication can...Ch. 4 - Consider a viscous film of liquid draining...Ch. 4 - Prob. 4.85PCh. 4 - Prob. 4.86PCh. 4 - Prob. 4.87PCh. 4 - The viscous oil in Fig. P4.88 is set into steady...Ch. 4 - Oil flows steadily between two fixed plates that...Ch. 4 - Prob. 4.90PCh. 4 - Prob. 4.91PCh. 4 - Prob. 4.92PCh. 4 - Prob. 4.93PCh. 4 - Prob. 4.94PCh. 4 - Two immiscible liquids of equal thickness h are...Ch. 4 - Prob. 4.96PCh. 4 - Prob. 4.97PCh. 4 - Prob. 4.98PCh. 4 - For the pressure-gradient flow in a circular tube...Ch. 4 - W4.1 The total acceleration of a fluid particle is...Ch. 4 - Is it true that the continuity relation, Eq....Ch. 4 - Prob. 4.3WPCh. 4 - Prob. 4.4WPCh. 4 - W4.5 State the conditions (there are more than...Ch. 4 - Prob. 4.6WPCh. 4 - W4.7 What is the difference between the stream...Ch. 4 - Under what conditions do both the stream function...Ch. 4 - Prob. 4.9WPCh. 4 - Consider an irrotational, incompressible,...Ch. 4 - Prob. 4.1FEEPCh. 4 - Prob. 4.2FEEPCh. 4 - Prob. 4.3FEEPCh. 4 - Given the steady, incompressible velocity...Ch. 4 - Prob. 4.5FEEPCh. 4 - Prob. 4.6FEEPCh. 4 - C4.1 In a certain medical application, water at...Ch. 4 - Prob. 4.2CP
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
- Q.5 A stream function is given by Y = (x² – y2). The Velocity potential function (b) of the flow will be A 2xy + f(x) B -2xy + constant © 2(x2 -y2) D 2xy + f(y)arrow_forward.3 2. 1. If u = 3x*yt and v = -6x°y´t“ answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1).arrow_forwardGiven the steady, incompressible velocity distributionu = Ax , υ = By , and w = Cxy , where ( A , B , C ) are constants.This fl ow satisfi es the equation of continuity ifA equals( a ) B , ( b ) B + C , ( c ) B - C , ( d ) - B , ( e ) - ( B + C )arrow_forward
- 1. If u = 3x*yt and v = -6x°y*t´ answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1).arrow_forward1. If u- 3x'yr and v = -6x'y'r answer the following questions giving reasons, Is this flow or fluid: (a) Real (Satisfies Continuity Principle). (b) Steady or unsteady. (c) Uniform or non-uniform. (d) One, two, or three dimensional. (e) Compressible or incompressible. Also, Find the acceleration at point (1,1). %3Darrow_forwardQ.2 A flow is described by the stream function v = 25xv, The coordinates of the point at which velocity vector has a magnitude of 4 units and makes an angle 150 ° with the X-axis is A x=1.0, y=0.5774 B X=0.5774, Y=1.0 WRONG C X=1, Y=-0.5774 D X=-1, Y=0.5774arrow_forward
- (1) (a) What is the physical meaning of the equation of continuity? (b) Is the continuity equation for steady incompressible flow satisfied if the following velocity components are invelved? V = 2.x2 - xy + z2 V, = x2 - 4xy + y, V2 = -2xy-yz + y² %3D (c) A gas flows through a square conduit. At one point along the conduit, the conduit sides are 0.100 m, the velocity is 7.55 m/s, and the gas's mass density is (for its particular pressure and temperature) 1.09 kg/m'. At a second point, the conduit sides are 0.250 m and the velocity is 2.02 m/s. Find the mass flow rate of the gas and the gas's mass density at the second point. (2) equation for turbulent flow in a fully-filled tube. (a) Write out and define all the terms of the overall Mechanical Energy per unit mass (b) Determine the energy loss in 300 m of new, uncoated 30.5 cm inside diameter cast iron pipe when water at 15°C flows at 1.5 m/s. Assume that the pipe has a roughness of 0.244 mm. Viscosity and density of water are 1 x 10 Pa…arrow_forwardVelocity field of an inviscid, steady state and incompressible flow is given by the equation, V = (3xy? – 2zx)i – y³j+z°k Density of the fluid is Ps. Neglecting gravity, what is pressure gradient in x direction? 2prx²(-y* + 4zy² – z²) –2p;xGy* – 6zy² + 2z²) C ApxGy* – 4zy² + z²) d. -2p;xGy* – 6zy² + z³) e4ppxGy* – 4zy² + z²)arrow_forwardProblem (5.9): In a three-dimensional incompressible fluid flow, the velocity components are: u = x? +z? + 5, v = y² + z? – 3 () Determine the third component of velocity. (ii) Is the fluid flow irrotational? )w = -2(x+ y)z +f(x, y, t)(ii) No. ]arrow_forward
- An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.arrow_forwardVerify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (Ui+1,j + U₁+1, j-1 — Ui, j — Ui,j-1) (Vi+¹, j — Vi+1,j-1). Ay + 2Ax where u and v are the x and y components of velocity, respectively.arrow_forward1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VXS, S(r, z, t) = Uz = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 Ꭷ r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin 0 S(R, 0, t) UR uo Y(r, z, t) r = = -eq, and Up = = 1 ay R2 sin Ꮎ ᎧᎾ 1 ƏY R sin Ꮎ ᎧR -eq 2 (1) (2) (3)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 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