Question

The velocity components for a flow of an incompressible fluid are given by the following equations. Determine the value of k in order to have a physically possible flow.

a) k = 1
b) k = -1
c) k = 2
d) k = -2

Answer 1

The value of k that would result in a physically possible flow is k = 1.

Step-by-step explanation:

Flow rate and velocity are related by the equation Q = AU, where A is the cross-sectional area of the flow and U is its average velocity. For incompressible fluids, the flow rate at various points must be constant to ensure continuity of flow. In this case, since the cross-sectional area of the pipe decreases, the velocity must necessarily increase. In order to have a physically possible flow, the value of k should be positive. So the correct value of k in this case would be k = 1 (option a).