For a certain incompressible, two-dimensional flow field the velocity component

smellmovinglz

smellmovinglz

Answered question

2021-11-12

For a certain incompressible, two-dimensional flow field the velocity component in the y direction is given by the equation
v=3xy+x2y
Determine the velocity component in the x direction so that the volumetric dilatation rate is zero.

Answer & Explanation

Susan Yang

Susan Yang

Beginner2021-11-13Added 20 answers

Given:
v=3xy+x2y
Solution:
In order to satisfy the continuity equation, the following equation must be writtem:
Equation one:
dudx+dudx+dvdy=0
We can see that we only have given the v component of velocity, so now we can derive it:
Equation two:
dvdy=3x+x2
We can now rewrite equation one:
dudx=dvdy
dudx=(3x+x2)
dudx=3xx2
Final step is to integrate the upper equation:
du=3xx2
u=32x2x33+f(y)

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