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If the stream function for a 2D flow is given as ψ = 3xy, then the velocity at the point (2, 3) will be
- a)7.21 units
- b)18 units
- c)10.82 units
- d)54 units
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the stream function for a 2D flow is given as ψ = 3xy, then the ve...
Given, ψ = 3xy By definition of ψ
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u = ∂ψ / ∂y and v = −∂ψ / ∂x
So u = 3x, v = −3y
at point (2, 3)
⃗V = 6î − 9ĵ and |⃗V⃗ | = √62 + 92 = 10.816
≈ 10.82 Units
Most Upvoted Answer
If the stream function for a 2D flow is given as ψ = 3xy, then the ve...
To determine the velocity at a given point (2, 3) in a 2D flow, we can use the relationship between the stream function (ψ) and the velocity components (u, v) given by:
u = ∂ψ/∂y
v = -∂ψ/∂x
Given that the stream function ψ = 3xy, we can calculate the velocity components at the point (2, 3) as follows:
1. Calculating ∂ψ/∂y:
∂ψ/∂y = 3x
Substituting x = 2:
∂ψ/∂y = 3(2) = 6
2. Calculating ∂ψ/∂x:
∂ψ/∂x = -3y
Substituting y = 3:
∂ψ/∂x = -3(3) = -9
3. Calculating the velocity components:
u = ∂ψ/∂y = 6
v = -∂ψ/∂x = -(-9) = 9
Therefore, the velocity components at the point (2, 3) are u = 6 and v = 9.
To find the magnitude of the velocity, we can use the following formula:
Velocity magnitude = √(u^2 + v^2)
Substituting the values of u and v:
Velocity magnitude = √(6^2 + 9^2)
Velocity magnitude = √(36 + 81)
Velocity magnitude = √117
Velocity magnitude ≈ 10.82 units
So, the correct answer is option C) 10.82 units.
u = ∂ψ/∂y
v = -∂ψ/∂x
Given that the stream function ψ = 3xy, we can calculate the velocity components at the point (2, 3) as follows:
1. Calculating ∂ψ/∂y:
∂ψ/∂y = 3x
Substituting x = 2:
∂ψ/∂y = 3(2) = 6
2. Calculating ∂ψ/∂x:
∂ψ/∂x = -3y
Substituting y = 3:
∂ψ/∂x = -3(3) = -9
3. Calculating the velocity components:
u = ∂ψ/∂y = 6
v = -∂ψ/∂x = -(-9) = 9
Therefore, the velocity components at the point (2, 3) are u = 6 and v = 9.
To find the magnitude of the velocity, we can use the following formula:
Velocity magnitude = √(u^2 + v^2)
Substituting the values of u and v:
Velocity magnitude = √(6^2 + 9^2)
Velocity magnitude = √(36 + 81)
Velocity magnitude = √117
Velocity magnitude ≈ 10.82 units
So, the correct answer is option C) 10.82 units.
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If the stream function for a 2D flow is given as ψ = 3xy, then the velocity at the point (2, 3) will bea) 7.21 unitsb) 18 unitsc) 10.82 unitsd) 54 unitsCorrect answer is option 'C'. Can you explain this answer?
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