Question

For a flow in the xy plane, the x component of velocity is given by u = Ax2y2, where A = 0.4 m-3 · s-1, and x and y are measured in meters. (a) Find a possible y component for steady, incompressible flow. (b) Is it also valid for unsteady, incompressible flow? (c) How many possible y components are there? (d) Determine the equation of the streamline for the simplest y component of velocity (use C as constant).

Answer 1

Answer: v=(-2/3)*(A*x*y³)

              The equation is not valid for the unsteady flow, as there is no dependence upon time neither on x or y component of the velocity,

The corresponding stream function:-

                                             v(x,y)=  (1/3)(A*x²*y³)

Coordinates through the streamline:- (1,4) and (2,4)

                                             y(x) = Cx^(-2/3)

Explanation:

Use continuity equation:-

                                             $\frac{du}{dx} +\frac{dv}{dy} = 0\\\\\frac{dv}{dy}=-\frac{du}{dx}=-2Axy^2$

Integrate V to obtain to obtain:-

v= -2/3*A*x*y^3