*>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.*

OTOH, with full mixing vs stratification, if dp pounds of 60 F water

flows into the 2-pound bottle and dp pounds of T (F) water flows out and

Tnew = (60dp+T(2-dp)/2 = T+dp(30-T/2), Tnew-T = dt, and dt/dp + T/2 = 30

(an equation of form dx/dt+cx = d with solution x = -d/c+(x0-d/c)e^(-ct)),

T = 60+(140-60)e^(-P/2) = 90 when P = -2ln((90-60)/(140-60)) = 1.96 pounds.

Nick

*>>A counterflow exchanger with equal heat capacity flow rates Cmin = Cmax*

*>>= 536/6h = 89 Btu/h-F and effectiveness E = 0.9 = NTU/(NTU+1) needs NTU*

*>>= 9 = AU/Cmin. With wall conductivity U = 30 Btu/h-F-ft^2, heat exchange*

*>>area A = 27 ft^2, eg 100' of 1" black PE plastic water pipe inside 100'*

*>>of 1.5" pipe, coiled around the the drum, surrounded by insulation.*

We could use a float switch and a metering pump like the $85 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

>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.