Verify that the velocity potential & of the three-dimensional (axially symmetric) rectilinear flow and source (or sink) satisfy y₁ = 0.

For the velocity field in u = Ax , υ = By , and w = Cxy , the convectiveacceleration in the x-direction is( a ) Ax 2 , ( b ) A 2 x , ( c ) B 2 y , ( d ) By 2 , ( e ) Cx 2 y

An incompressible viscous flow is contained between two parallel plates separated from each other by distance b. as shown in Figure 1. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U =7 m/s and b= 1 cm, and there is no pressure gradient in the flow direction. A.) Start with Navier-Stokes equations and determine the velocity at the point x = 3 cm and y= 0.41 cm. The value of the velocity is.B.) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity. C.) Calculate the rate of angular deformation at the same point. The angular deformation value

The stream function o in a two-dimensional flow field is given as 9 = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. Find the potential flow function P(x, y) for this flow field with boundary condition 0 = 0 at x = 2, y = 1. (b)