Determine the acceleration field for a three-dimensional flow with velocity components

General guidance

Concepts and Reason

Velocity of a fluid particle is a function of location and time. Velocity is a vector which has both magnitude and direction.
The acceleration of a fluid particle is the time rate of change of velocity.

Fundamentals

The velocity vector for a fluid particle,

The acceleration vector for a fluid particle in three dimensional flow,

The scalar components of acceleration vector,

Step-by-step

Step 1 of 2

The x-component of acceleration,

The y-component of acceleration,

The z-component of acceleration,

Find the components of acceleration along the three Cartesian coordinate axes using the spatial and time derivatives of velocity components.

Find the acceleration field.

Step 2 of 2

Find the acceleration field using the relation,

The acceleration field is .

Write the acceleration field vector using the components of acceleration of the fluid particle.

Answer

The acceleration field is .

Answer only

The acceleration field is .

V=ui + vj+wk
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-(-) 4(4)4xy2) (-2) =(0) + (-x) (-1)+4xy² (0)+(x-y)(0) =X
– (ar v)+(-7) (ap ya) ar yn olaf y) = (x ->)>(axy) ду =(0)+(-x)(8xy?) + 4x’y? (8x’y)+(x- y)(0) = -8x’y+32x*y?
-+ Ow – @x +- w Oy = (x+y)+(+)0(4,7″+ 4x?p: 0(8+3)+(-»)O(x-») = (0)+(-x)(1-0) + 4x’y?(0-1)+(x-y)(0) =-x-4x²y2
a =q i+a, j+ak = xi +(+8x”y? +32x*y’);+(-x-4x’y?)k
xi +(-8x’y? +32x*y);+(-x-4x’y?)k
xi +(-8x’y? +32x*y);+(-x-4x’y?)k
Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y Determine the acceleration field for a three-dimensional flow with velocity components u= -x, v = 4x^2y^2, and w = x-y

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