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A steady incompressible 2D flow field is given by u = 2x2 + y2 and v = −4xy. The convective acceleration along x-direction at point (1, 2) is
- a)6 units
- b)24 units
- c)− 8 units
- d)− 24 units
Correct answer is option 'C'. Can you explain this answer?
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A steady incompressible 2D flow field is given by u = 2x2 + y2 and v ...
U = 2x2 + y2, v = −4xy
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ax = (2x2 + y2)(4x) + (−4xy)(2y) + 0 + 0
∴ at point (1, 2) ax
= (2 + 4)(4) − (8)(4) ax
= 24 − 32 ax
= −8 units
Most Upvoted Answer
A steady incompressible 2D flow field is given by u = 2x2 + y2 and v ...
Convective acceleration is the rate of change of velocity with respect to time as observed by an observer moving with the fluid. It is given by the convective derivative, which is the sum of the local acceleration and the convective acceleration.
The convective acceleration along the x-direction can be calculated using the convective derivative formula:
a_convective_x = ∂u/∂t + u(∂u/∂x) + v(∂u/∂y)
Given that the flow field is steady, there is no change in velocity with respect to time (∂u/∂t = 0). Therefore, the convective acceleration along the x-direction simplifies to:
a_convective_x = u(∂u/∂x) + v(∂u/∂y)
Substituting the given expressions for u and v:
u = 2x^2 + y^2
v = -4xy
∂u/∂x = 4x
∂u/∂y = 2y
a_convective_x = (2x^2 + y^2)(4x) + (-4xy)(2y)
= 8x^3 + 4xy^2 - 8xy^2
= 8x^3 - 4xy^2
To find the convective acceleration along the x-direction at point (1, 2), substitute x = 1 and y = 2 into the equation:
a_convective_x = 8(1)^3 - 4(1)(2)^2
= 8 - 16
= -8
Therefore, the convective acceleration along the x-direction at point (1, 2) is -8 units. Hence, the correct answer is option 'C'.
The convective acceleration along the x-direction can be calculated using the convective derivative formula:
a_convective_x = ∂u/∂t + u(∂u/∂x) + v(∂u/∂y)
Given that the flow field is steady, there is no change in velocity with respect to time (∂u/∂t = 0). Therefore, the convective acceleration along the x-direction simplifies to:
a_convective_x = u(∂u/∂x) + v(∂u/∂y)
Substituting the given expressions for u and v:
u = 2x^2 + y^2
v = -4xy
∂u/∂x = 4x
∂u/∂y = 2y
a_convective_x = (2x^2 + y^2)(4x) + (-4xy)(2y)
= 8x^3 + 4xy^2 - 8xy^2
= 8x^3 - 4xy^2
To find the convective acceleration along the x-direction at point (1, 2), substitute x = 1 and y = 2 into the equation:
a_convective_x = 8(1)^3 - 4(1)(2)^2
= 8 - 16
= -8
Therefore, the convective acceleration along the x-direction at point (1, 2) is -8 units. Hence, the correct answer is option 'C'.
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A steady incompressible 2D flow field is given by u = 2x2 + y2 and v = −4xy. The convective acceleration along x-direction at point (1, 2) isa) 6 unitsb) 24 unitsc) − 8 unitsd) − 24 unitsCorrect answer is option 'C'. Can you explain this answer?
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