Fluid Mechanics...

The velocity field for a 2 D, steady and incompressible flow is represented as V = (ax + by) i + (cx + dy) j, where a, b, c, d are constants. The condition for which it represents the fluid flow is:

The velocity field of an incompressible flow is given by V = 3y² i – 3x² j. The magnitude of the discharge occurring between the stream line passing through points (1, 2) and (3, 4) is:

For a 2-D potential flow, the velocity potential function is given as ϕ = 4x(3y - 4). The magnitude of stream function (ψ) at point (2, 3) is __________.

In a flow field at any point and at any time density is 2 kg/m³ and  density varies  with time as ρ =  1 + 0.5 t, where t is measured in sec and ρ is measured in kg/m³. Find the divergence of velocity (in sec^-1, up to two decimal places) at that point and that instant, if the mass of the flow is conserved.