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In a two dimensional flow, the component of the velocity along the X-axis and the Y-axis are u = ax2 + bxy + cy2 and v = cxy. What should be the condition for the flow field to be continuous?
  • a)
    a + c = 0
  • b)
    b + c = 0
  • c)
    2a + c = 0
  • d)
    2b + c = 0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a two dimensional flow, the component of the velocity along the X-a...
Solution:

To ensure continuity in a two-dimensional flow field, the following condition should be satisfied:

∂u/∂x + ∂v/∂y = 0

Given, u = ax2 + bxy + cy2 and v = cxy

∂u/∂x = 2ax + by

∂v/∂y = cx

Substituting these in the continuity equation, we get:

2ax + by + cx = 0

This equation can be written in the form:

2a + c = 0

Therefore, the condition for the flow field to be continuous is 2a + c = 0.

Hence, option C is the correct answer.
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Community Answer
In a two dimensional flow, the component of the velocity along the X-a...
According to the condition for continuity,

2ax + cx = 0
2a + c = 0.
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