Which of the following velocity fields satisfies the continuity equation for a steady, three-dimensional flow of an incompressible fluid?

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Physics · Fluid Mechanics

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

u = 4 − 5xy2 + 7x3y; v = 5 + 6y2z − 7yz3; w = 2 − 3x2z + 6xz3

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Answer 1

u = 7 + 3x2y − 4xy2; v = 1 + 8yz2 − 4y2z; w = 6 + 7xz3 − 5x2z

Answer 2

u = 3 − 2y2z + 4yz2; v = 2 + 6x3z2 − 7x2z; w = 5 − 8x2y3 + 9xy

Answer 3

u = 4 − 5xy2 + 7x3y; v = 5 + 6y2z − 7yz3; w = 2 − 3x2z + 6xz3

Answer 4

u = 9 + 3x3y − 5x2y3; v = 10 − 4y2z + 7y3z2; w = 7 + 5x2z3 − 2xz2

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