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Q & A: Evaporation rate calculation

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Most recent answer: 10/22/2007
Q:
Is it possible to calculate the evaporation rate of a pool with the following variables, air 85F, water 85F, humidity 80%, wind speed 5 mph?
- John Martin
Bermuda
A:
Hi John,

The answer is "well, sorta." There are still some variables left off of your list which can affect the evaporation rate. A useful skill in approaching physics problems is to ask if the situation is fully specified before going about calculating the answer. And the question is, can you think of two pools, both with the parameters you have described, which may differ in some other way which can affect the rate of evaporation of the water?

One important thing that happens when water evaporates is that 540 calories per gram are absorbed by the water in the process, cooling it down. The surface of the water, then, will probably be below 85 F, and water will have to convect to replenish the heat. Depending on how deep the water is and if there are waves or currents, this can affect the temperature profile of the water.

Another important thing that happens when water evaporates is that the air in the boundary layer next to the water has a partial pressure of the water very close to the vapor pressure of the water at the temperature of the water at the surface. Normally, a lot of water is evaporating and immediately recondensing in equilibrium with this thin layer. Diffusion and convection of the water molecules away from this thin layer is what really drives the rate of evaporation. This is one reason why it is important to specify the wind speed, as you have nicely done. And also the humidity, because that is the far boundary condition on the diffusion equation -- the humidity of the air against the water surface will be much higher. Actually, the wind's effect probably is more important if there is turbulence near the surface of the water. The evaporation rate is enhanced if air currents move moist air away from the surface and dry air towards it. A smooth, horizontal flow of air won't do that except at the edges of the pool, and then it depends on how the pool is shaped and which way the wind is blowing. If there are waves and ripples on the water surface, this will help the airflow to be turbulent and take away more water vapor.

Air pressure affects how fast the water molecules will diffuse away -- higher air pressure will slow down the diffusion process. And if the air pressure is low enough (below the vapor pressure of water at that temperature), the water will even start to boil.

Good try!

Tom J.

(published on 10/22/2007)

Follow-Up #1: brewing lore

Q:
Once you have a boil, how does air preasure affect evaporation rate? (Im a brewer, and were trying to determine if our barometer will help us control our evaporation rate, as we can control our steam temperature and boil time.) Thank you.
- Stephen (age 38)
Verona, WI, USA
A:
If I understand right, you're trying to control the rate of boiling. Since there's a big latent heat of vaporization, that rate is mostly controlled by the rate at which heat flows into the liquid. (It's also reduced somewhat by other ways the heat can leak out.) The latent heat isn't particulalrly sensitive to pressure over the practical range of pressures. So probably what you want to do to control the boil rate is to have some rapid feedback from something measuring the boil rate (maybe a gas flow meter) to something controlling the heater (a valve or a switchable voltage control, depending on whether you've got gas or electric heat). Trying to control the boil rate via the pressure doesn't sound practical.

Mike W.

Lee H


(published on 10/22/2007)

Follow-up on this answer.