The stream function ?? in a two-dimensional flow field is given as ?? = 4?? −...

The stream function ?? in a two-dimensional flow field is given as ?? = 4?? − 3?? + 7???? (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function Ф(??, ??) for this flow field with boundary condition Ф = 0 at x = 2, y = 1.

Expert Solution

The stream function ? in a two-dimensional flow field is given as ? = 4? − 3? + 7?² (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (10 marks)

(b) Find the potential flow function Ф(?, ?) for this flow field with boundary condition Ф = 0 at x = 2, y = 1.

we know with boundary condition Ф = 0 at x = 2, y = 1, which is used to find constant C

0 = -3(2) - 4(1) + C

C = 10

thus Ф = -3x -4y + 10 is potential flow function

samet mamat answered 1 year ago

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