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In most cases the path used for pressure determination is obliged to cross (at least one) fluid interface. On one side of an interface there is say "Fluid A" while on the other side exists "Fluid B." How does pressure change as a consequence of passing through an interface, as from "Fluid A" to "Fluids B?"
It will not be proved here, but if the interface is flat, there is no pressure change. However, for spherical droplets in air and for the very small diameter jets of water (as with of cutting machines) in air, the pressure of water inside its substantially greater than atmospheric. Consider water that issues downward from a faucet.
Derive an equation for the pressure within a slow-moving fluid stream.
♦ The sketch shows our system taken as half of a horizontal slice of the falling water, viewed from above. Newton's Second Law is applied to the element to determine the pressure within a jet of diameter, D.
The surface tension of water (σ) is very small. Thus, the pressure change across the air to water interface of a jet equals zero except for jets of very small diameter as with water jet cutting tools.
Our calculation presumes the water jet to remain a jet. If that is the case, the calculations are valid. More commonly however is that the jet is turbulent and breaks into fragments of flow. For energy analysis such "sprayed of fragmented flows" has the pressure, one atmosphere.