Question

In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + by + cy2 and v = cxy. What should be the condition for the flow field to be incompressible

Answer 1

The condition for the flow field to be incompressible is independent of a and c

Step-by-step explanation:

We are given the component of the velocity along the X-axis and the Y-axis as;

u = ax² + by + cy²

v = cxy

Now, the condition for the flow to be incompressible is;

du/dx + dv/dy = 0

Now,

du/dx = 2ax

dv/dy = cx

Thus;

2ax + cx = 0

(2a + c)x = 0

Thus,the condition for the flow field to be incompressible is independent of a and c