Question

For fluid flows obeying conservation of mass, what is the value of k if v=4x+ky denotes the velocity at any point in the flow?

(a) -4

(b) 4

(c) -2

(d) 2

I got this question in an internship interview.

This is a very interesting question from Governing Equations in portion Flows of Viscous Incompressible Fluids of Finite Element Method

Answer 1

Correct answer is (a) -4

Best explanation: A flow obeys conservation of mass if \(\frac{\partial v_x}{\partial x}+\frac{\partial v_y}{\partial y}\)=0. Comparing v=4x+ky with v=vx+vy, we get vx=4x and vy=ky.

Using the conservation of mass, we get  \(\frac{\partial (4x)}{\partial x}+\frac{\partial (ky)}{\partial y}\)=0

4+k=0

K=-4.