Consider a two-dimensional fluid flow whose velocity field in Cartesian form is u = -yi + x - atj, where a is a positive constant. Is the flow:
i) incompressible?
ii) irrotational?
iii) steady?
Give a reason for each of your answers.
b) Write down the equations describing the stream function for this flow, and hence find the stream function.
ii) Find the equation of the streamline that passes through the point (1,0) at time t=0.
c) Suppose that the fluid is inviscid and of constant density, and that it is acted upon by a body force (per unit mass F = ati - yj). Find the pressure distribution in the fluid (up to an arbitrary function of time), and hence show that the pressure along a streamline at t=0 is independent of position.