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A stream function is given by ψ = 4x − 3y. The magnitude of resultant velocity at any point is
- a)7.81 units
- b)7 units
- c)3.5 units
- d)5 units
Correct answer is option 'D'. Can you explain this answer?
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A stream function is given by ψ = 4x − 3y. The magnitude of resultant...
Given, ψ = 4x − 3y
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As per definition of stream function
u = ∂ψ / ∂y and v = −∂ψ / ∂x
∴ u = −3 & v = −4 So V- = −3î − 4ĵ
and magnitude of resultant velocity is given |⃗V⃗ | = √u2 + v2 = 5
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A stream function is given by ψ = 4x − 3y. The magnitude of resultant...
Given stream function: ψ = 4x - 3y
To find the magnitude of the resultant velocity at any point, we need to determine the velocity components in terms of the stream function.
The velocity components can be found using the following equations:
Vx = ∂ψ/∂y
Vy = -∂ψ/∂x
where Vx and Vy are the x and y components of the velocity vector, respectively.
Let's calculate the velocity components:
Vx = ∂ψ/∂y = -3
Vy = -∂ψ/∂x = 4
The magnitude of the resultant velocity (V) can be calculated using the Pythagorean theorem:
V = √(Vx^2 + Vy^2)
Substituting the velocity components:
V = √((-3)^2 + 4^2)
V = √(9 + 16)
V = √25
V = 5 units
Therefore, the correct answer is option 'D' - 5 units.
To find the magnitude of the resultant velocity at any point, we need to determine the velocity components in terms of the stream function.
The velocity components can be found using the following equations:
Vx = ∂ψ/∂y
Vy = -∂ψ/∂x
where Vx and Vy are the x and y components of the velocity vector, respectively.
Let's calculate the velocity components:
Vx = ∂ψ/∂y = -3
Vy = -∂ψ/∂x = 4
The magnitude of the resultant velocity (V) can be calculated using the Pythagorean theorem:
V = √(Vx^2 + Vy^2)
Substituting the velocity components:
V = √((-3)^2 + 4^2)
V = √(9 + 16)
V = √25
V = 5 units
Therefore, the correct answer is option 'D' - 5 units.
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A stream function is given by ψ = 4x − 3y. The magnitude of resultant velocity at any point isa) 7.81 unitsb) 7 unitsc) 3.5 unitsd) 5 unitsCorrect answer is option 'D'. Can you explain this answer?
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