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A stream function is given by ψ = 3x2 - y3. What is the magnitude of velocity components at the point (2, 1)?
- a)8.52
- b)9.17
- c)10.81
- d)12.37
Correct answer is option 'D'. Can you explain this answer?
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A stream function is given by ψ = 3x2 - y3. What is the magnitude ...
Given Stream Function
The stream function is given as ψ = 3x^2 - y^3.
Calculate Velocity Components
To find the velocity components, we can use the relation:
u = ∂ψ/∂y and v = -∂ψ/∂x.
Calculate Velocity Components at Point (2, 1)
At the point (2, 1), we can calculate the velocity components as follows:
u = -3y = -3(1) = -3
v = -6x = -6(2) = -12
Calculate Magnitude of Velocity Components
To find the magnitude of the velocity components, we use the formula:
|V| = sqrt(u^2 + v^2).
Substitute the calculated values:
|V| = sqrt((-3)^2 + (-12)^2)
|V| = sqrt(9 + 144)
|V| = sqrt(153)
|V| ≈ 12.37
Therefore, the magnitude of the velocity components at the point (2, 1) is approximately 12.37. Hence, the correct answer is option 'D'.
The stream function is given as ψ = 3x^2 - y^3.
Calculate Velocity Components
To find the velocity components, we can use the relation:
u = ∂ψ/∂y and v = -∂ψ/∂x.
Calculate Velocity Components at Point (2, 1)
At the point (2, 1), we can calculate the velocity components as follows:
u = -3y = -3(1) = -3
v = -6x = -6(2) = -12
Calculate Magnitude of Velocity Components
To find the magnitude of the velocity components, we use the formula:
|V| = sqrt(u^2 + v^2).
Substitute the calculated values:
|V| = sqrt((-3)^2 + (-12)^2)
|V| = sqrt(9 + 144)
|V| = sqrt(153)
|V| ≈ 12.37
Therefore, the magnitude of the velocity components at the point (2, 1) is approximately 12.37. Hence, the correct answer is option 'D'.
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Community Answer
A stream function is given by ψ = 3x2 - y3. What is the magnitude ...
Given:
Stream function is ψ = 3x2 – y3
Now the velocity components will be
At P(2,1),
→ U = 3 × (1)2 m/s ⇒ U = 3 m/s
→ V = 6 × (2) m/s = 12 m/s
Now the magnitude of velocity at point P (2, 1) will be
∴ Magnitude of velocity components at the point (2, 1) is 12.37 m/s
Stream function is ψ = 3x2 – y3
Now the velocity components will be
At P(2,1),
→ U = 3 × (1)2 m/s ⇒ U = 3 m/s
→ V = 6 × (2) m/s = 12 m/s
Now the magnitude of velocity at point P (2, 1) will be
∴ Magnitude of velocity components at the point (2, 1) is 12.37 m/s
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A stream function is given by ψ = 3x2 - y3. What is the magnitude of velocity components at the point (2, 1)?a)8.52b)9.17c)10.81d)12.37Correct answer is option 'D'. Can you explain this answer?
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