Question

For each velocity field given below, determine whether the flow is incompressible or not incompressible. Justify your answer/show all work.

(a) = (2+4)^−3(+)^
V = (2x + 4y)xt i^ - 3(x + y)yt j^

Answer 1

The given velocity field is not incompressible because its divergence is not equal to zero.

Step-by-step explanation:

The velocity field given is V = (2x + 4y)xt i^ - 3(x + y)yt j^. To determine if the flow is incompressible or not, we need to check if the divergence of the velocity field is zero. In this case, the divergence is given by:

∇ · V = ∂(2x + 4y)xt/∂x - ∂(3(x + y)yt)/∂y

Simplifying further, we get:
∇ · V = 2t + 4xt + (3t - 3yt)

The divergence is not equal to zero, which means the flow is not incompressible.