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In this chapter, we discuss the line vortex (Fig. 10-109) as an example of an irrotational flow field. The velocity components are
FIGURE P10-109
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Fluid Mechanics: Fundamentals and Applications
- 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_forwardIn a steady, two-dimensional flow field in the xyplane, the x-component of velocity is u = ax + by + cx2 where a, b, and c are constants with appropriate dimensions. Generate a general expression for velocity component ? such that the flow field is incompressible.arrow_forwardShow the step by step solution and explanation on how we arrive in the answerarrow_forward
- Can you solve the questionarrow_forwardA 2-D flow field has velocity components along X-axis and y-axis given by u = x't and v = -2 xyt respectively, here, t is time. The equation of streamline for the given velocity field is : (а) ху — сonstant (с) ху' — сonstant (b) x´y = constant (d) x + y constantarrow_forwardA common flow encountered in practice is the crossflow of a fluid approaching a long cylinder of radius R at a free stream speed of U∞. For incompressible inviscid flow, the velocity field of the flow is given as in fig. Show that the velocity field satisfies the continuity equation, and determine the stream function corresponding to this velocity field.arrow_forward
- provide explanation and free body diagram for each part also commentarrow_forwardPlease answer botharrow_forwardWrite down the continuity equation and the Navier-Stokes equations in the x-, y-, and z-directions for an incompressible, three-dimensional flow. There should be a total of fourequations. If we make the assumptions that the flow is steady and inviscid, what do thesefour equations simplify to? Note: this is notvan assignment question and not a grade questionarrow_forward
- need urgent help, thanks the question is related to advanced fluid mechanicsarrow_forwardConsider irrotational flow past a stationary sphere of radius R located at the origin. In the limit r→∞, the velocity field v = U2, as in Fig. 8-6 in the book. (a) Calculate the velocity field v assuming potential flow given by v = Vo(r, 0, 0), where the potential can be assumed to be independent of the azimuthal coordinate and vo= 0. Here, since ə rde Ə Ər for large r/R, look for solutions of the form = f(r) cos 0. Assume a no-penetration boundary condition at the surface of the sphere. (b) Calculate the pressure P and the drag force due to pressure. Vr = U cos 0 and Vo = -U sin 0arrow_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_forward
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