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The velocity potential function in a two dimensional flow field is given by ∅=x2-y2. The magnitude of velocity at point (1, 1) is
- a)zero
- b)2
- c)2√2
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Calculation of Velocity Potential Function
Given:
The velocity potential function in a two-dimensional flow field is given by ∅=x2-y2.
To Find:
The magnitude of velocity at point (1, 1).
Solution:
Step 1: Calculation of Velocity Components
The velocity components can be calculated as follows:
Vx = ∂∅/∂x = 2x
Vy = -∂∅/∂y = 2y
Step 2: Calculation of Velocity Magnitude
The magnitude of the velocity can be calculated as follows:
V = √(Vx^2 + Vy^2)
Substituting the values of Vx and Vy, we get:
V = √(4x^2 + 4y^2)
At point (1,1), the magnitude of velocity can be calculated as follows:
V = √(4(1)^2 + 4(1)^2)
V = 2√2
Therefore, the magnitude of velocity at point (1, 1) is 2√2, which is option C.
Given:
The velocity potential function in a two-dimensional flow field is given by ∅=x2-y2.
To Find:
The magnitude of velocity at point (1, 1).
Solution:
Step 1: Calculation of Velocity Components
The velocity components can be calculated as follows:
Vx = ∂∅/∂x = 2x
Vy = -∂∅/∂y = 2y
Step 2: Calculation of Velocity Magnitude
The magnitude of the velocity can be calculated as follows:
V = √(Vx^2 + Vy^2)
Substituting the values of Vx and Vy, we get:
V = √(4x^2 + 4y^2)
At point (1,1), the magnitude of velocity can be calculated as follows:
V = √(4(1)^2 + 4(1)^2)
V = 2√2
Therefore, the magnitude of velocity at point (1, 1) is 2√2, which is option C.
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The velocity potential function in a two dimensional flow field is given by ∅=x2-y2. The magnitude of velocity at point (1, 1) isa)zerob)2c)2√2d)8Correct answer is option 'C'. Can you explain this answer?
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