Bernoulli’s principle is a derivation of the conservation of energy – a fluid contains a given amount of energy, in this case we are looking at the trade-off between potential and kinetic energy.
The kinetic component is related to how fast the fluid is moving
The potential component is a combination of gravitational potential and pressure energy. In Bernoulli’s principle, he limits the application to horizontal flow, so the gravitational component is constant, and can be discarded.
Pressure potential energy is a measure of how much force each fluid molecule is applying to its neighbours. The more pressure applied to a fluid, the closer the molecules get together, and the force they apply on each other increases (sort of like compressing a spring).
As energy can’t be created out of nothing, as the flow velocity (and hence kinetic energy) increases, it must be accompanied by a proportional decrease in pressure (i.e. potential energy) and vice-versa – otherwise we are creating energy out of nothing
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