For a certain incompressible flow field it is suggested tl 2- velocity components are given by the equations u = 2xy v = -xy w= 0 Is this a physically possible flow field? Explain.

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Homework What is the third velocity component such that continuity equation is satisfied if two components are u = 1. 2y2, w = 2хyz ? 2. Consider the following steady, two-dimensional, incompressible velocity field V = (Ax? + B)i + (-Ay + Cx²)j where A, B, and C are constants. Calculate the pressure as a function of x and y.

Consider 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 0