Concept explainers
Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely lons round pipe annulus of inner radius
FIGURE P9-98
the x-axis, and
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
- Consider a velocity field where the radial and tangential components ofvelocity are Vr = 0 and Vθ = cr, respectively, where c is a constant. Is the flow field given is irrotational? Prove your answer.arrow_forwardIn which segments of this stream tube Bernoulli’s equation would be valid and which segments would not be valid. Explain the reasoning each of them in a sentence or two.arrow_forwardConsider the steady, two-dimensional velocity field given by V-› = (u, ?) = (1.6 + 2.8x) i-› + (1.5 − 2.8y) j-›. Verify that this flow field is incompressible.arrow_forward
- For each statement, choose whether the statement is true or false, and discuss your answer briefly. (a) The velocity potential function can be defined for threedimensional flows. (b) The vorticity must be zero in order for the stream function to be defined. (c) The vorticity must be zero in order for the velocity potential function to be defined. (d) The stream function can be defined only for two-dimensional flow fields.arrow_forwardIn your own words, c. Explain why the stream function ψ is restricted to 2-D flows and you have to use the velocity potential ζ to define 3-D flows.arrow_forwardConsider a flow field in polar coordinates, where the stream function isgiven as ψ = ψ(r, θ). Starting with the concept of mass flow betweentwo streamlines, derive your answer.arrow_forward
- Show that the axisymmetric potential flow formed by the superpositionof a point source +m at (x, y) = (-a, 0), a pointsink -m at (+a, 0), and a stream U∞ in the x-direction formsa Rankine body of revolution as in Fig. P8.95. Find analyticexpressions for determining the length 2L and maximumdiameter 2R of the body in terms of m, U∞, and a.arrow_forwardQ#1: What is stream wise acceleration? How does it differ from normal acceleration? Can a fluid particle accelerate in steady flow? Express the Bernoulli equation in three different ways using (a) energies, (b) pressures, and (c) heads.arrow_forwardThe velocity components in a two-dimensional flow are u = y^3 /3 + 2x-x²y and v= xy²-2y-x^3 /3. Show that it is an irrotational flow.arrow_forward
- Under what conditions do both the stream function ψ andthe velocity potential ϕ exist for a fl ow fi eld? When doesone exist but not the other?arrow_forwardBy analogy with laminar shear, τ = μ du/dy, T. V.Boussinesq in 1877 postulated that turbulent shear couldalso be related to the mean velocity gradient τturb = ε du/dy,where ε is called the eddy viscosity and is much larger thanμ. If the logarithmic overlap law, is valid withτturb ≈τw, show that ε ≈ κρu*y.arrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Given that the density of the fluid does not vary spatially and changes only with time, what differential equa9on for the density, ⍴(t), must be satisfied for this scenario to represent a physical, compressible flow field?arrow_forward
- 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