Question

Determine the third velocity component such that continuity equation is satisfied if two components are u=x^2+y^2+z^2, v=xy^2 – yz^2 + xy

(a) -3xz-2xyz+z^2/3+f(y,z)

(b) -3xz+2xyz+z^3/3+f(y,z)

(c) -3xz-2xyz+z^3/3+f(x,z)

(d) -3xz-2xyz+z^3/3+f(y,z)

I got this question during a job interview.

The doubt is from Velocity and Acceleration in portion Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Right option is (d) -3xz-2xyz+z^3/3+f(y,z)

The explanation is: The continuity equation for incompressible is du/dx+dv/dy+dw/dz = 0.

Here du/dx=2x and v=2xy-z^2

On solving by integrating, we get w = -3xz-2xyz+z^3/3+f(y,z),