Answered: 8. Now consider the steady velocity…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Transcribed Image Text:8. Now consider the steady velocity profile: - by bx u V = x + y? x + y which also has circular streamlines. (i) Calculate the vorticity vector for this flow. (ii) Calculate the circulation around the same path described in 7(iii), by performing a line integration. In light of Stokes' theorem, there may be an apparent contradiction between your results in parts (i) and (ii). Can you think of how this contradiction might be resolved?

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Vorticity - It is the rotational strength in the pair of fluid particles. (angular velocity between two particles).

Formula used -

$2 \vec{ω} = (\vec{\nabla} \times \vec{v}) ω_{z} = \frac{1}{2} (\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y})$

If vorticity is zero flow is considered to be irrotational.

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