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- Example 10.4-2 Stream Function and Velocities from potential Function The potential function for 2D, irrotational, incompressible flow filed is given as: Ø = x² – 2y – y² %3D Find the stream function y and the velocity components and y?arrow_forward3.14. Find the vorticity in polar coordinates for the following velocity com- ponents (c) vr Ve= 0arrow_forwardProblem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.arrow_forward
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- a) A Newtonian fluid flows with external force in the y-direction in space between two stationary parallel plates that are separated by a distance 2D as shown in Figure 1. The length and the width of each plate are L and W, respectively. 2D Center Line Figure 1 Flow between parallel plates Derive the velocity profile for system using shell momentum balance. State all your postulate and assumptions.arrow_forwardA turbine (see the figure of Example IIIa.3.21) is located at an elevation H1 from the surface of a lake with the discharge pipe located at an elevation H2 from the turbine centerline. Find flow velocity, V4 in terms of H1, H2, P1, P4, h,, and p where subscript 4 refers to the discharge piping. [Ans.: V, = (2/p)[(R – P.) + pg (Z, – Z, –h,)]. Lake H, h. D2 4 D4 H4 Turbinearrow_forward3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian coordinates by u == AxBt. Show that x = f(x, t) in the Lagrange coordinates can be obtained from the Eulerian system. The in- itial position of the fluid particle is designated by x) and the initial time to = 0 may be assumed.arrow_forward
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