For each of the velocity and density distributions of Problem 2.20, (a) Show that the equation of mass conservation is satisfied. (b) Develop the expression for the stream function of the mass flux....

For each of the velocity and density distributions of Problem 2.20,

(a) Show that the equation of mass conservation is satisfied.

(b) Develop the expression for the stream function of the mass flux.

Problem 2.20

Velocity components of the flow and density of a fluid are given by

where ˛ and 0 are constants.

(a) Calculate the components of the acceleration.

(b) Calculate the rate of change of density of the fluid particles, assuming that ˛ is small and has negligible effect on u and v.