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)
