Recuperate some of the heat from a group of showers

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A garden hose connection might backflush the outer tubing and upper drum automatically, with a solenoid valve from a dead washing machine and a $3 hose bibb vacuum breaker that closes the tubing outlet and opens the hose connection behind it for 10 minutes when the upper drum is full too often, eg when an upper-drum float switch has been open a long time.
If the basement is 70 F and the switch heats a 1-quart water bottle with 12V 82 and 91 ohm 1 W resistors glued to the bottom, inside a 6"x6"x1' R20 box with conductance G = 2.5ft^2/R20 = 0.125 Btu/h-F, the final temp will be 161 F. With the upper drum always full and RC = 2/0.125 = 16 hours, the bottle will reach 140 F in -16ln((140-161)/(70-161)) = 23 hours.
An $8 Grainger 2E248 snap disk thermostat on the other side of a 6"x6" R5 wall between the thermostat and the bottle could open the backflush solenoid when it reaches 140 F and close it when it the thermostat reaches 120 F. A 33K 1/2 W hysteresis resistor could keep the thermostat closed with 3.412x120^2/33K = 1.49 Btu/h of heat until the bottle temp drops to 120-1.49R5/0.25ft^2 = 90 F.
A rubber stopper with 2 tubes in the bottleneck might move P pounds of 60 F backflush water into the 140 F water, so the bottle temp reachs 90 F when (60P+(140(2-P)/2 = 90, ie P = 0.8. If this takes 10 minutes, 0.8/(10x8.33) = 0.0096 gpm would flow through the tubes.
Nick
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We could use a float switch and a metering pump like the $185 Mec-O-Matic D75 to move 64.3 gpd at C = 22 Btu/h-F (0.044 gpm) with NTU = 30x27/22 = 36 and E = 0.97. Preheated water might thermosyphon into the lower part of a water heater from the fresh water heat exchanger outlet 3' above the floor into a T 3' above the floor, connecting the upper and lower parts of the tank, with a common cold water connection at floor level, with the lower tank heating element disconnected.
This looks promising, with Poiseuille's equation for thermosyphoning:
20 PI=4*ATN(1) 30 TC=(50-32)/1.8'cold temp (C) 40 TW=(75-32)/1.8'warm temp (C) 50 RSLOPE=(998.2-988)/(20-50)'density slope 60 RHOC8.2+(TC-20)*RSLOPE'cold density (kg/m^3) 70 RHOW8.2+(TW-20)*RSLOPE'warm density (kg/m^3) 80 H=3*.3048'height diff (meters) 90 DP=(RHOC-RHOW)*H*9.8'pressure difference (N/m^2) 100 VSLOPE=(.001002-.000547)/(20-50)'viscosity slope 110 VC=.001002+(TC-20)*VSLOPE'cold viscosity (Ns/m^2) 120 VW=.001002+(TW-20)*VSLOPE'warm viscosity (Ns/m^2) 130 RC$/2/12*.3048'cold pipe radius (meters) 140 RW=1.049/2/12*.3048'warm pipe radius (meters) 150 LC=3*.3048'cold pipe length (meters) 160 LW0*.3048'warm pipe length (meters) 180 NE=6'number of elbows 190 LC=LC+50*RC'equivalent cold pipe length (meters) 200 RESC=8*VC*LC/(PI*RC^4)'cold flow resistance 210 RESW=8*VW*LW/(PI*RW^4)'warm flow resistance 220 V=DP/(RESC+RESW)'flow (m^3/s) 230 GPM=V*15850!'flow (gpm) 240 PRINT GPM
.2886552 gpm
Nick
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