Vorticity and its Dimension

- Vorticity is a fundamental concept in fluid dynamics that describes the local rotation of a fluid element.
- It is defined as the curl of the velocity vector field of the fluid.
- Vorticity is a vector quantity, with both magnitude and direction.

Dimensional Analysis

- Dimensional analysis is a method used in physics to determine the dimensions of a physical quantity by examining the units of its associated variables.
- It helps in understanding the relationships between different physical quantities and their dimensions.

Dimension of Vorticity

- To determine the dimension of vorticity, we can analyze its definition in terms of other physical quantities.
- Vorticity is defined as the curl of the velocity vector field.
- The dimension of velocity is [LT^-1] (length per time).
- Taking the curl of the velocity vector involves taking the derivative with respect to position, which introduces an additional length term.
- Therefore, the dimension of vorticity can be determined by taking the derivative of the dimension of velocity, which gives [L^2T^-2] (length squared per time squared).

Answer Explanation

- Among the given options, option 'B' (T^-1) is the correct answer for the dimension of vorticity.
- This is because the dimension of vorticity is [L^2T^-2], which can be rearranged as [T^-1] (time to the power of -1) when considering only the time component.
- The other options, option 'A' (T^2), option 'C' (T), and option 'D' (T^-2), do not correspond to the correct dimension of vorticity.
- Option 'A' (T^2) would correspond to the dimension of acceleration, not vorticity.
- Option 'C' (T) would correspond to the dimension of time, which is only a component of the dimension of vorticity.
- Option 'D' (T^-2) would correspond to the dimension of the rate of change of vorticity, not vorticity itself.

Conclusion

- The dimension of vorticity is T^-1 (time to the power of -1).