The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is ________.
Show Hint
- 2
- 3
- \( \frac{1}{2} \)
- 1
The Correct Option is A
Solution and Explanation
Step 1: Definition of Vorticity.
Vorticity is a measure of the local rotation of the fluid at a point, and it is defined as the curl of the velocity field: \[ \boldsymbol{\omega} = \nabla \times \mathbf{v}. \] Step 2: Definition of Rate of Rotation.
The rate of rotation in a fluid flow is the angular velocity of the fluid elements, which is proportional to the vorticity.
Step 3: Theoretical Relationship.
In some types of flows, the ratio of the magnitudes of vorticity to the rate of rotation is twice the rate of rotation, which is consistent with the behavior in certain types of fluid dynamics.
Step 4: Conclusion.
Thus, the ratio of the magnitudes of vorticity to rate of rotation is 2 in this case.
Correct Answer: (A) 2.
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