Example 3. Find the continuously differentiable streamfunction (r) of a singularity-free incompressible plane rotational flow with the vorticity field w = = @(r) ez, where r is the polar (cylindrical) radius, and a + a w(r) = 290 × r≤a r> a where and a are constant. Use the found streamfunction to determine the velocity field. Write the last result in the form which emphasises the role of the parameter a as a length scale.
Example 3. Find the continuously differentiable streamfunction (r) of a singularity-free incompressible plane rotational flow with the vorticity field w = = @(r) ez, where r is the polar (cylindrical) radius, and a + a w(r) = 290 × r≤a r> a where and a are constant. Use the found streamfunction to determine the velocity field. Write the last result in the form which emphasises the role of the parameter a as a length scale.
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Transcribed Image Text:Example 3. Find the continuously differentiable streamfunction (r) of a singularity-free incompressible plane
rotational flow with the vorticity field = w(r) ez, where r is the polar (cylindrical) radius, and
w(r) = 290 ×
r
a
a
r
2
r≤a
r> a
where and a are constant.
Use the found streamfunction to determine the velocity field. Write the last result in the form which emphasises
the role of the parameter a as a length scale.
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