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Suppose I pass water through a pressure reducing valve, which can lower the pressure enough for the water to boil, will the water fully boil? If so, what would happen if that vapour passed to a tube, for instance, with atmospheric pressure? Will the water return to the liquid state? If it returns back to liquid, how do I sustain the vapour state?

Thanks in advance!

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The water might boil if pressure is reduced below the vapor pressure of the water. That means the outlet of the PRV must be at a low pressure.

Boiling water at normal temps requires a very low pressure. Just a reducing valve won't be enough, you will need to induce vacuum at the exit. At room temp, this is around 1/20 of an atmosphere. Doing this through a valve will likely result in freezing; you still have to remove the heat from the liquid, and the most likely mechanism for this is through freezing.

If you mean a momentary flashing to vapor going through a throttle or such, this will likely only be some of the water, and it will immediately condense back to liquid when the high velocity-low pressure condition is no longer there.

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Water will boil when the pressure is reduced below its vapor pressure. It is in vapor-liquid equilibrium at that temperature, it is unlikely to be completely vaporized.

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