Question

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

(a) a + b = 0

(b) a – b = 0

(c) x + y = 0

(d) x – y = 0

This question was posed to me in an international level competition.

Enquiry is from Continuity Equation in portion Kinematics of Flow and Ideal Flow of Fluid Mechanics

Answer 1

Correct option is (c) x + y = 0

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

by + bx = 0

x + y = 0.