Question

In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax^2 + bxy and v = bxy + ay^2. The condition for the flow field to be continuous is

(a) independent of the constants (a; b) but dependent on the variables (x; y)

(b) independent of the variables (x; y) but dependent on the constants (a; b)

(c) independent of both the constants (a; b) and the variables (x; y)

(d) dependent on both the constants (a; b) and the variables (x; y)

I got this question in quiz.

This question is from Continuity Equation in chapter Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Correct choice is (a) independent of the constants (a; b) but dependent on the variables (x; y)

The best explanation: The condition for the flow field to be continuous is:

2ax + by + 2ay + bx = 0

x + y = 0

Hence, the condition for the flow field to be continuous is independent of the constants (a; b) and dependent only on the variables (x; y).