1. The potential function of fluid flow motion is given by, [(x+c)?+y² p = log zá+z(2¬x)] a) Prove that, fluid is incompressible, b) Find the velocity field, c) Find the geometric location of the providing IV? = constant.
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- As a mechanical engineer, you can predict the performance of a new centrifugal pump using two methods which are One Dimensional Analysis (Velocity Triangle) and Hydraulic Scaling. Describe the limitation of each method.An incompressible fluid flows in a linear porous medium with the following properties: Lenth = 3000 ft k = 100 md p1 = 2000 psig p2 = 1980 psig height = 25 ft porosity = 20% width = 300 ft viscosity = 2 cP Assume the dimension is slanted, i.e., a dip angle of 5 degrees (downward from p1 location to p2 location), what is the apparent fluid velocity under this new boundary condition?1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].
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