Velocity potential/stream function—M (C). In a certain two-dimensional irrotational flow,...

Velocity potential/stream function—M (C). In a certain two-dimensional irrotational flow, the velocity potential is given by:

,

where a = 0.1 s‒1.

Evaluate the constant b, and derive an expression for the corresponding stream function. Considering only the region x > 0, y > 0, sketch a few typical streamlines and hence determine the flow pattern that ϕ represents.

If at time t = 0 an element of fluid is at the point P (x = 10 cm, y = 20 cm), find its position Q at a time t = 2 s, and illustrate its path on your diagram.