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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 and v = bxy + ay2. The condition for the flow field to be continuous is
- a)independent of a and b
- b)independent of a and c
- c)independent of b and c
- d)independent of a, b and c
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a two dimensional flow, the component of the velocity along the X-a...
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 a, b and c.
2ax + by + 2ay + bx = 0
x + y = 0
Hence, the condition for the flow field to be continuous is independent of a, b and c.
Most Upvoted Answer
In a two dimensional flow, the component of the velocity along the X-a...
Continuity Equation:
The continuity equation is the principle of mass conservation, which states that the mass of a fluid that enters a control volume must equal the mass that leaves it.
In two-dimensional flow, continuity equation can be written as:
∂ρ/∂t + ∂(ρu)/∂x + ∂(ρv)/∂y = 0
Where,
ρ is the density of fluid
u is the velocity along X-axis
v is the velocity along Y-axis
Condition for Continuous Flow:
For the flow field to be continuous, the mass of fluid entering and leaving the control volume must be equal. This means that the density of the fluid must be the same at all points within the control volume.
The condition for the flow field to be continuous can be expressed as:
∂ρ/∂t + ∂(ρu)/∂x + ∂(ρv)/∂y = 0
Solving for this equation, we get:
∂ρ/∂t + ρ(∂u/∂x + ∂v/∂y) + u(∂ρ/∂x) + v(∂ρ/∂y) = 0
For the flow to be continuous, the last two terms in the above equation must be equal to zero.
∂ρ/∂x = 0 and ∂ρ/∂y = 0
Substituting the given values of u and v, we get:
∂ρ/∂x = a(2x)bxy and ∂ρ/∂y = b(xy)ay2
For the flow to be continuous, the above equations must be equal to zero. This is possible only when a = 0 and b = 0.
Therefore, the condition for the flow field to be continuous is independent of a, b, and c. The correct answer is option D.
The continuity equation is the principle of mass conservation, which states that the mass of a fluid that enters a control volume must equal the mass that leaves it.
In two-dimensional flow, continuity equation can be written as:
∂ρ/∂t + ∂(ρu)/∂x + ∂(ρv)/∂y = 0
Where,
ρ is the density of fluid
u is the velocity along X-axis
v is the velocity along Y-axis
Condition for Continuous Flow:
For the flow field to be continuous, the mass of fluid entering and leaving the control volume must be equal. This means that the density of the fluid must be the same at all points within the control volume.
The condition for the flow field to be continuous can be expressed as:
∂ρ/∂t + ∂(ρu)/∂x + ∂(ρv)/∂y = 0
Solving for this equation, we get:
∂ρ/∂t + ρ(∂u/∂x + ∂v/∂y) + u(∂ρ/∂x) + v(∂ρ/∂y) = 0
For the flow to be continuous, the last two terms in the above equation must be equal to zero.
∂ρ/∂x = 0 and ∂ρ/∂y = 0
Substituting the given values of u and v, we get:
∂ρ/∂x = a(2x)bxy and ∂ρ/∂y = b(xy)ay2
For the flow to be continuous, the above equations must be equal to zero. This is possible only when a = 0 and b = 0.
Therefore, the condition for the flow field to be continuous is independent of a, b, and c. The correct answer is option D.
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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 and v = bxy + ay2. The condition for the flow field to be continuous isa)independent of a and bb)independent of a and cc)independent of b and cd)independent of a, b and cCorrect answer is option 'D'. Can you explain this answer?
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