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For a two-dimensional potential flow, the velocity potential function is given by ϕ = 4x(3y − 4). The numerical value of stream function at the point (2, 3) is
- a)10 Units
- b)20 Units
- c)18 Units
- d)16 Units
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
For a two-dimensional potential flow, the velocity potential function...
Given ϕ = 12xy − 16x ∂ϕ /∂x = −u and ∂ϕ /∂y = −v
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∴ u = 16 − 12y & v = −12x
Also dψ = ∂ψ / ∂x dx + ∂ψ /∂y dy
and ∂ψ ∂x = −v and ∂ψ ∂y = u
∴ dψ = 12xdx + (16 − 12y)dy
ψ = 12x2 2 + 16y − 12y2 2
ψ = 6x2 + 16y − 6y2
Hence at point (2, 3) ψ = 6(2)2 + 16(3) − 6(3)2 ψ = 18 units
Most Upvoted Answer
For a two-dimensional potential flow, the velocity potential function...
To find the stream function at a given point, we need to use the relationship between the velocity potential and the stream function. In two-dimensional potential flow, the stream function (ψ) and the velocity potential (ϕ) are related by the following equation:
ψ = -∂ϕ/∂y
Given that the velocity potential function is ϕ = 4x(3y - 4), we can find the stream function by taking the partial derivative of ϕ with respect to y and negating it:
ψ = -∂(4x(3y - 4))/∂y
= -12x
To find the numerical value of the stream function at the point (2, 3), we substitute x = 2 into the equation:
ψ = -12(2)
= -24
The stream function at the point (2, 3) is -24 units. However, the question asks for the numerical value, which is the absolute value of the stream function. Therefore, the numerical value of the stream function at the point (2, 3) is 24 units.
However, none of the given options matches the calculated value. So, there might be an error in the options provided. If none of the given options is correct, we cannot determine the correct answer based on the information provided.
ψ = -∂ϕ/∂y
Given that the velocity potential function is ϕ = 4x(3y - 4), we can find the stream function by taking the partial derivative of ϕ with respect to y and negating it:
ψ = -∂(4x(3y - 4))/∂y
= -12x
To find the numerical value of the stream function at the point (2, 3), we substitute x = 2 into the equation:
ψ = -12(2)
= -24
The stream function at the point (2, 3) is -24 units. However, the question asks for the numerical value, which is the absolute value of the stream function. Therefore, the numerical value of the stream function at the point (2, 3) is 24 units.
However, none of the given options matches the calculated value. So, there might be an error in the options provided. If none of the given options is correct, we cannot determine the correct answer based on the information provided.
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For a two-dimensional potential flow, the velocity potential function is given by ϕ = 4x(3y − 4). The numerical value of stream function at the point (2, 3) isa) 10 Unitsb) 20 Unitsc) 18 Unitsd) 16 UnitsCorrect answer is option 'C'. Can you explain this answer?
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