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If the velocity components of flow are u = 3xy3 and v = x3 - y3 , then the flow is
- a)continuous
- b)discontinuous
- c)tangential
- d)radial
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the velocity components of flow are u = 3xy3 and v = x3 - y3 , then...
Understanding the given flow velocity components
The given flow velocity components are u = 3xy^3 and v = x^3 - y^3.
Here, u represents the velocity component in the x-direction, and v represents the velocity component in the y-direction.
Checking for continuity
To determine if the flow is continuous, we need to check if the flow satisfies the continuity equation. The continuity equation states that the divergence of the velocity field should be zero.
Mathematically, the continuity equation can be written as:
∂u/∂x + ∂v/∂y = 0
Calculating the divergence
Let's calculate the divergence of the given velocity components:
∂u/∂x = ∂(3xy^3)/∂x
= 3y^3
∂v/∂y = ∂(x^3 - y^3)/∂y
= -3y^2
∂u/∂x + ∂v/∂y = 3y^3 - 3y^2
Checking the continuity equation
Since the divergence of the velocity field is given by 3y^3 - 3y^2, we can see that it is not equal to zero.
Therefore, the flow does not satisfy the continuity equation, and it is not continuous.
Conclusion
Based on the above calculations, we can conclude that the correct answer is option 'B' - discontinuous.
The given flow velocity components are u = 3xy^3 and v = x^3 - y^3.
Here, u represents the velocity component in the x-direction, and v represents the velocity component in the y-direction.
Checking for continuity
To determine if the flow is continuous, we need to check if the flow satisfies the continuity equation. The continuity equation states that the divergence of the velocity field should be zero.
Mathematically, the continuity equation can be written as:
∂u/∂x + ∂v/∂y = 0
Calculating the divergence
Let's calculate the divergence of the given velocity components:
∂u/∂x = ∂(3xy^3)/∂x
= 3y^3
∂v/∂y = ∂(x^3 - y^3)/∂y
= -3y^2
∂u/∂x + ∂v/∂y = 3y^3 - 3y^2
Checking the continuity equation
Since the divergence of the velocity field is given by 3y^3 - 3y^2, we can see that it is not equal to zero.
Therefore, the flow does not satisfy the continuity equation, and it is not continuous.
Conclusion
Based on the above calculations, we can conclude that the correct answer is option 'B' - discontinuous.
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Community Answer
If the velocity components of flow are u = 3xy3 and v = x3 - y3 , then...
differentiating , we get
Substituting the values in equation of continuity, we get
= 0
Hence, flow is continuous.
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If the velocity components of flow are u = 3xy3 and v = x3 - y3 , then the flow isa)continuousb)discontinuousc)tangentiald)radialCorrect answer is option 'A'. Can you explain this answer?
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