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A large container of heated water is floating in space. How can I calculate leak rate if a small puncture is opened?

I'm assuming the water is kept at 298K and in the liquid state inside the chamber.

I guess that upon depressurization the water will immediately vaporize and then take some time to freeze and cool. I'm not sure if the phase change is important for estimating the leak flow rate.

I also expect that the flow rate will be proportional to the pressure difference, viscosity of water, and the size of the hole. Just not sure how to put this all together.

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1 Answer 1

Some more information would be needed to answer this question.

You say that the water is kept at 298K - fair enough, you get to pose the conditions, but you might want to think if that's a reasonable or realistic condition to give, for the situation you are interested in. (I would think a more realistic condition would be to say that the water starts at 298K, and from that point on no heat is added or removed from the system, so the water temperature drops as steam is produced)

Other conditions that would be helpful:

  1. Is the tank full of water only, or is there water in there plus an air space too?
  2. What is the initial pressure of the water? Is this maintained, or is it allowed to freely evolve?

Let's say for the sake of discussion that the water tank was initially 100% full of water (no airspace), at atmospheric pressure (say 100,000Pa). When a hole is opened, water will start to squirt out. The pressure throughout the bulk of the water will drop very rapidly, but before it reaches zero the water will start to boil (when the pressure reaches the point where steam/water are in equilibrium at 298K). This won't be an equilibrium boiling, the actual temperature local temp and press will depend on various kinetic factors (e.g. nuclei to promote the formation of steam bubbles etc).

It might not be 100% realistic but it might be useful to assume that the steam generation takes place away from the orifice - i.e. the orifice is ejecting water only, rather than a water/steam mix (much more complicated!)

As a first approximation you might want to just look up the vapour pressure of water at 298K, assume that is uniformly applied to liquid water, and look up the appropriate equations for the flow of a liquid through an orifice with a modest pressure drop (assume from the vapour pressure of the water on the inside, to p=0 on the outside). Depending on whether the hole is sharp-edged or if it has rounded corners, you'll find different applicable formulas. A standard book of engineering tables could well have what you need (I might start looking in the Chemical Engineers Handbook). If the hole isn't very small, the viscosity of the water might have little to no influence; if the hole is quite small then the viscosity will matter but this will be an easily known quantity (from the temp of the water; the only potentially unrealistic assumption we're making is that it is pure liquid water and not a water-steam-ice mixture).

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