Malcolm Shealy discusses this at http://www.leaningpinesoftware.com/hot_water_pipes_pipe_cooling.shtml
The SRCC OG-300 solar water heater test procedure uses 6 hourly 3 gpm 10.7 gallon 135 F bursts in a 67.5 F environment...
With no insulation, 1' of 135 F 1/2" horizontal bare copper pipe with a 0.625" OD in 67.5 F still air would have a 0.27((135-67.5)/0.625"/12))^0.25 = 1.62 Btu/h-F-ft^2 convective thermal conductance, using equation 2.20US for laminar free convection from a horizontal pipe in Kreider and Rabl's 1994 Heating and Cooling of Buildings book. With pipe conductance Gb = Pi0.625"/12x1'x1.62 = 0.265 Btu/h-F-ft, it would lose (135-67.5)0.265 = 17.9 Btu/h per linear foot. A 2 gpm (1000 Btu/h-F) water stream would lose 2 F with a 2000 Btu/h pipe loss after flowing through 2000/17.9 = 112 feet of bare pipe.
How much will a $1.18 piece of R2.3 6' pipe insulation save in 1 year, if we heat water with electricity at $0.10/kWh and use it in 6 10.7 gallon 3 gpm hourly bursts each day? http://www.homedepot.com/p/Armacell-Tubolit-3-4-in-x-6-ft-Polyethylene-Pipe-Wrap-Insulation-OEP07838/100539941#specifications
With "R2.3 insulation" (ie a system R-value after installation, including the outer air film), Gi = Pi0.625"/12x1'/R2.3 = 0.071 Btu/h-F-ft, so the pipe would lose (135-67.5)0.071 = 4.8 Btu/h per linear foot. A 2 gpm insulated water stream would be 2 F warmer than a bare pipe stream after flowing through 2000/(17.9-4.8) = 153 feet of insulated pipe.
Type M 1/2" copper pipe http://www.homedepot.com/h_d1/N-5yc1v/R-203540899/h_d2/ProductDisplay?catalogId=10053&langId=-1&keyword=1%2F2%22+copper+pipe&storeId=10051 weighs 0.933lb/5' = 0.1866 lb/foot, with a 0.0915x0.1866 = 0.0171 Btu/F thermal capacitance. Its 0.5" ID holds 62.33Pi(0.25/12)^2x1'= 0.085 lb of water, making the total (tiny) capacitance C = 6x0.1021 = 0.6126 Btu/F.
If hot water uses are 3.6 minutes long, with (60-3.6)/60 = 0.94 hours between uses, bare pipe with a C/Gb = 0.39 hour time constant would cool from 135 to 67.5+(135-67.5)e^(-0.94/0.39) = 73.4 F before the next use during the day, and 67.5 F overnight. Reheating 6' of water to 135 F would take (5((135-73.4)+(135-67.5)0.6126 = 169 Btu/day, or 61644 Btu/year, worth about $0.10x61644/3412 = $1.81/year.
Insulated pipe with a C/Gi = 1.44 hour time constant would cool to 67.5+(135-67.5)e^(-0.94/1.44) = 102.6 F during the day, and 67.5 F overnight. Reheating it takes (5((135-102.6)+(135-67.5)0.6126 = 141 Btu/day, or 51341 Btu/year, worth about $0.10x51341/3412 = $1.50/year.The reheating difference is 31 cents per year.
So this $1.18 investment has a 100x$0.31/$1.18 = 26% tax free return and a $1.18/$0.31 = 3.8 year simple payback, if the pipe is in an unheated space and labor is free, with hourly hot water uses.
Pipe insulation within a few feet of a water heater makes even more sense, but plumbing heat traps don't seem to make sense, given pipe insulation, since they only slow convection inside a single pipe, unless there's a hot-cold connection above. And a 4 watt mechanical timer that turns off a well-insulated water heater at night would use more electrical power than it saves.
How about a simple greywater heat exchanger? Home Depot sells 300' of 1" HDPE 100 psi NSF plastic pipe for $96.64... http://www.homedepot.com/p/Advanced-Drainage-Systems-1-in-x-300-ft-IPS-100-PSI-NSF-Poly-Pipe-2-1100300/202282480#.Ue-zaDbD_IU
With a 1.049" ID and a 1.119" OD, and a 0.035" wall thickness and still clean water on the inside and some crud on the outside, 1' of pipe could have a 1'xPi1.049/12x20 = 5.50 Btu/h-F conductance and a Pi(1.049/24)^2x62.33 = 0.374 Btu/F conductance and an RC = C/G = 0.374/5.50 = 0.068 hour (4.1 minute) time constant, so a 300' pressurized pipe coil near the top of a tall unpressurized stratified tank with a much larger volume and non-conductive walls and a drain from the bottom (eg a 4' diameter x 8' tall culvert or ferrocement or thin bent plywood tank in a basement with an insulated lining and a greywater dip tube to the bottom) could heat Pi(1.049/24)^2x7.48x200 = 13.5 gallons of 60 F water to 105-(105-60)e^(-0.94/0.068) = 104.9999554 F between hourly uses, with a 105 F shower drain temp.
Every piece of NSF pipe is tested to 5 times the nominal pressure rating at 73 F, and it loses about 10% of its strength for each 10 F temperature increase above 73 F.
"Scott L" <shiva@...> wrote from Fairbanks:
>... we insulate our cold and hot water pipes is to keep them from freezing as fast if the heat quits.
NREL says the average temp is -10.1 F in January in Fairbanks, with a -18.5 min and a -61.0 30-year record low and a 0.0006 humidity ratio. The deep ground temp is 26.9 F.
Insulation doesn't help much with small pipes. At -10.1, a 1/2" pipe with R2.3 insulation and a 1.43 hour time constant would cool from 70 to 32 F in -1.43ln((32-(-10))/(70-(-10)) = 0.92 hours and freeze solid after another 0.085x144/((32-(-10))0.071) = 4.1 hours. A battery or generator could run (32-(-10))0.071/3.412 = 0.87 watts/foot of heat tape under pipe insulation when the heat quits. A 12V 200 Ah battery could keep 200' of R2.3 pipe from freezing for 13.7 hours.
>The cold water pipes sweat and drip if left uninsulated and exposed to a heated area with our cold water.
The air would need significant moisture for that to happen. Air with a w = 0.0006 humidity ratio has vapor pressure P = 29.921/(0.62198/w+1) = 0.0288 "Hg and dew point Tdp = 9621/(17.863-ln(P))-460 = -10.6 F.
> Lots of us haul or have our water delivered. $80 for 800 gallons in the town area and easily twice that if you live outside the city area by much. You can not afford to run the water until it gets hot over a long distance.
We could insulate both hot and cold pipes and use a motion detector and pump to circulate water back through the heater before hot water uses. That could also help avoid frozen pipes when the heat quits. Cooling a 50 gallon 135 F tank to 32 F with 200' of R2.3 pipe in -10 F air would take (135-32)50x8.33Btu/(200x(32-(-10))0.071) = 72 hours.