Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:

Where h is the height of the liquid above the opening. This relationship assumes atmospheric pressure at both the reservoir surface and the jet exit. The fluid column's height governs the fluid's velocity at the nozzle in a reservoir, where the fluid's potential energy converts into kinetic energy during flow.

The phenomenon of vena contracta occurs when the liquid exits through a sharp-edged orifice, causing the jet diameter d_j to be smaller than the nozzle diameter d_o. This occurs because the fluid streamlines cannot follow the abrupt edges, creating a contracted flow region. The contraction coefficient is the ratio of the jet's cross-sectional area at the vena contracta to the nozzle's cross-sectional area, quantifying the degree of jet contraction. This parameter is influenced by the nozzle's geometry, with various designs such as knife-edge, sharp-edge, well-rounded, and re-entrant nozzles producing distinct flow patterns and contraction characteristics. For a well-rounded nozzle, C_c = 1.0, while sharp or knife-edged orifices reduce C_c to approximately 0.61. Re-entrant nozzles exhibit even lower values.

These flow characteristics and contraction effects are critical in engineering applications involving liquid discharge, from reservoirs to industrial nozzles.