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The stream function for a two dimensional flow is given by Y = 2xy. The velocity at (2,2) is
- a)4√ 2
- b)4
- c)2 √2
- d)√2
Correct answer is option 'A'. Can you explain this answer?
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The stream function for a two dimensional flow is given by Y = 2xy. Th...
**Given information:**
- The stream function for a two-dimensional flow is given by Y = 2xy.
**To find:**
- The velocity at (2,2).
**Solution:**
The stream function (Y) for a two-dimensional flow is defined as the function that satisfies the following equation:
∂Y/∂x = -V_y
∂Y/∂y = V_x
where V_x and V_y are the x and y components of velocity, respectively.
In this case, the stream function is given by Y = 2xy.
Taking the partial derivatives of Y with respect to x and y, we get:
∂Y/∂x = 2y
∂Y/∂y = 2x
From the above equations, we can determine the x and y components of velocity (V_x and V_y) at any point in the flow field.
To find the velocity at the point (2,2), we substitute x = 2 and y = 2 into the equations:
V_x = ∂Y/∂y = 2(2) = 4
V_y = -∂Y/∂x = -2(2) = -4
Therefore, the velocity at the point (2,2) is V = (V_x, V_y) = (4, -4).
However, none of the given options match the calculated velocity.
Hence, the given answer is incorrect and none of the options provided are correct.
- The stream function for a two-dimensional flow is given by Y = 2xy.
**To find:**
- The velocity at (2,2).
**Solution:**
The stream function (Y) for a two-dimensional flow is defined as the function that satisfies the following equation:
∂Y/∂x = -V_y
∂Y/∂y = V_x
where V_x and V_y are the x and y components of velocity, respectively.
In this case, the stream function is given by Y = 2xy.
Taking the partial derivatives of Y with respect to x and y, we get:
∂Y/∂x = 2y
∂Y/∂y = 2x
From the above equations, we can determine the x and y components of velocity (V_x and V_y) at any point in the flow field.
To find the velocity at the point (2,2), we substitute x = 2 and y = 2 into the equations:
V_x = ∂Y/∂y = 2(2) = 4
V_y = -∂Y/∂x = -2(2) = -4
Therefore, the velocity at the point (2,2) is V = (V_x, V_y) = (4, -4).
However, none of the given options match the calculated velocity.
Hence, the given answer is incorrect and none of the options provided are correct.
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The stream function for a two dimensional flow is given by Y = 2xy. The velocity at (2,2) isa)4√2b)4c)2 √2d)√2Correct answer is option 'A'. Can you explain this answer?
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