Circulation in fluid dynamics: Circulation is defined as the line integral of velocity around a closed loop. It essentially measures the total "circulatory" effect or rotation of the fluid along a closed path.
Explanation: Within the context of fluid dynamics, circulation is best understood as the flux of vorticity. Vorticity, in turn, is a measure of local rotation within the fluid. Hence, the correct understanding connects circulation directly with the rotational aspects of the flow, thereby making it synonymous with the flux of vorticity through a given surface.
The options were:
Given this understanding, the correct answer is clearly Flux of vorticity.
Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m\(^{-3}\) while the density of water is 1000 kg m\(^{-3}\). For the manometer reading of \( h = 30 \) mm of mercury, the speed of air in the wind tunnel is _________ m s\(^{-1}\) (rounded off to 1 decimal place). 