# Empirical data regarding shower heads and water

Hello everyone,

I was wondering if anyone can direct me to references or techniques in calculating the convective heat transfer coefficient for steam from a hot shower. It’s a standard showerhead emitting 2.5gpm with an average temperature of about 107.5 F.

Also how much of the water coming out of the showerhead vaporizes?

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jim hardy
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no takers yet?

i too have been curious and think of this every time i fog up the bathroom.
My Dad was a meteorologist and I remember him saying that evaporation rates were a complex calculation.

So, being as i'm real simple minded i would have to look at end points and approximate.

i guess the upper limit would be when volume of bathroom is filled with saturated steam at temperature of shower...

from steam tables that'd be .0035 lb/ft^3 of water vapor in a 300 cubic foot bathroom, lets see , .0035 X 300 would be about a pound of water
partial pressure of steam would be close to 1 psia the other 13.7 psi is air of course.

thereafter water from showerhead could only evaporate further at same rate as it condenses out on mirror and walls.

the heat of vaporization of water at that temperature is near 1032 BTU/lb

so if it takes ten minutes to get the bathroom completely warmed and saturated
that's 1032 BTU in 1/6 hour; rate of heat addition = 6192 BTU/hr = 1.81 kilowatts.
Afterward it would slow down to some value set by heat flow out of room, if through the drywall maybe 0.9 BTU/ft^2/hour per degree across drywall??

For me that'd be a sanity check on a more exact algorithm.

maybe somebody with better thermo background knows of an equation..

old jim

Thank you for the response Jim.

I was wondering if there is a way to calculate which fraction of that water is in vapor form. I was thinking about using a y-x table, since its saturated at that point. Perhaps I can find a y-x table at that specific temp and pressure...

now that I think about it the temperature 107.5 F is below the boiling point for water. Is that because the water coming out of the shower head is at a low pressure?

jim hardy
Gold Member
2019 Award
Dearly Missed
Thank you for the response Jim.

I was wondering if there is a way to calculate which fraction of that water is in vapor form. I was thinking about using a y-x table, since its saturated at that point. Perhaps I can find a y-x table at that specific temp and pressure...
I usually use the steam table at boilerroomservices.com, but a google returns plenty of them. You want the saturated table.

[ QUOTE]now that I think about it the temperature 107.5 F is below the boiling point for water. Is that because the water coming out of the shower head is at a low pressure?[/QUOTE]

remember that water evaporates at any temperature if its partial pressure is below boiling pressure(aka saturation) for that temperature. 212 is just the point at which water's partial pressure is one whole atmosphere. Ice will evaporate in a good enough vacuum.

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That helps a lot! Thank you!