This little test measures how much shower water cools down from the time it leaves the shower head until it goes down the shower drain. This question comes up in grey water heat exchanger design, since the heat lost from shower head to drain cannot be recovered in a grey water heat exchanger.
The answer appears to be that the temperature drops about 10F to 11F from the shower head to the shower drain, as the plot below shows.
The head temperature sensor was mounted in the shower flow just below the shower head, and the drain sensor was mounted in the drain grating.
The triangles from left to right mark:
Water on (between 1 and 2 shower water is running with no one in shower)
Person enters shower
End of shower -- water off.
The shower flow rate was 2 qts in 18 seconds, or 1.67 gpm.
How Much Heat Did the Shower Use?
How Much Heat Could Be Recovered By A Greywater Heat Exchanger?
How much heat is transferred to the room?
If you only count the part between 2 and 3 plus 30 seconds warm up time, then the energy used for this shower is:
Q = (weight flow rate)(Shower length)(T shower - T groundwater) (Specific Heat of Water)
Qin = (1.67 gal/min)(8.3 lb/gal)(4.6 min)(104F - 45F) (1 BTU/lb-f) = 3762 BTU
(With a 60% efficient water heater this would be (3762/0.6) = 6270 BTU )
A 100% efficient grey water heat exchanger could recover:
Max Recovery = (94F - 45F)/(104F - 45F) = 83%
Given that flow might be on the order
of 1.7 gpm and temperature loss from shower to drain was 10-11 F, with a
five-minute shower we can estimate the sensible internal gains to the space from
Eg. 1.7gpm * 8.3lbs/gal * 10dt * 5min = 705 Btu
This added heat to the room would be
helpful during the heating season, as it would help heat the room. But,
would be bad during the cooling season as it would be additional heat that the
AC would have to take care of.
This shower design might reduce this: