Concept explainers
Consider the same two concentric cylinders of Prob. 4-44. This time, however, the inner cylinder is rotating. but the outer cylinder is stationary. In the limit, as the outer cylinder is very large compared to the inner cylinder (imagine the inner cylinder spinning very fast while its radius gets very small), what kind of flow does this approximate? Explain. After a long time has passed, generate an expression for the tangential velocity profile, namely
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Fluid Mechanics: Fundamentals and Applications
- 1. 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_forwardThe velocity potential function (0) is given by an expression xy' x'y x* + 3 3 (i) Find the velocity components in x and y direction. (ii) Show that o represents a possible case of flow.arrow_forward4s-1, Given the velocity field V = Axî – Ayĵ, where A %3D (a) Sketch the velocity field. (you can do this by hand or use software of your choice)arrow_forward
- The velocity field for a line vortex in the r?-plane is given byur = 0 u? = K / rwhere K is the line vortex strength. For the case with K = 1.5 m/s2, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.arrow_forwardConsider fully developed Couette flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary, as illustrated in the figure below. The flow is steady, incompressible, and two-dimensional in the XY plane. The velocity field is given by V }i = (u, v) = (v² )i +0j = V (a) Find out the acceleration field of this flow. (b) Is this flow steady? What are the u and v components of velocity? u= V² harrow_forwardA 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_forward
- Consider the configuration shown below with w1 = 2.5 rad/s, w2 = 1.0 rad/s, and wz = 5.4 rad/s. Find the magnitude of velocity at point P of the disk B3. 0.2 m 0.4 m Bz- @, rad/s 0.3 m 0, rad/s 0.1 m @z rad/s Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.arrow_forwardA source and sink of equal strength, m = 25 m²ls, are near a wall, as in Fig. induced by this pair at point A on the wall. 5- 4. . Find the resultant velocity 4 m 3 m 4 m 3 marrow_forwardAy j. Is this a possible case of incompres- 3.9 A velocity field is given by V= Axyi -- %3D sible flow? If yes, obtain the stream function and find the value of constant A for which the flow rate between the streamlines passing through the points (3, 3) and (3, 4) is 18 units. Axy Ans: V = 12 + C, A 7 2arrow_forward
- Consider 3D flow with velocity components below. u=x²+2xy v=2x-y²+z² w=-2xz+y² Is this flow incompressible? Show your work. b. Is this flow irrotational? Show your work.arrow_forwardDerive an equation for volumetric strain rate and use it to verify that the following velocity field is incompressible: V=(uo+bx)i-byjarrow_forwardPerform the convective on velocity vectors u in cylindrical coordinates : Du/Dtarrow_forward
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