Question

Determine the third velocity component such that continuity equation is satisfied if two components are u=2y^2, w=2xyz.

(a) -2xy+x^2y+f(y,z)

(b) 4xy-x^2y+f(y,z)

(c) -4xy-x^2y+f(y,z)

(d) -2xy-x^2y+f(y,z)

I had been asked this question in an internship interview.

This question is from Velocity and Acceleration topic in section Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Right answer is (c) -4xy-x^2y+f(y,z)

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

Here du/dx=0 and w=2xy.

On solving by integrating, we get v = -4xy-x^2y+f(y,z).