daestrom wrote:

While I agree that 'batch' flows that do not fully purge your apparatus will
give you some improvements, we haven't seenn any of your 'numbers' for that.

Here are some numbers for that. If 100' of 3 1" pipes (polyethylene, with
a 0.07" wall thickness) has 78.5 ft^2 of surface with U = 10 Btu/h-F-ft^2,
10' has 78.5 Btu/h-F...

20 UPIPE=78.5'U-value of 10' section of pipe (Btu/h-F)
30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F)
40 VGREY=10*3.14159*(2/12)^2'volume of 10' of greywater (ft^3)
50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F)
60 FOR SHOWER = 1 TO 1000'simulate showers
70 FOR M=0 TO 359'simulate 10 min shower + 350 min rest
80 IF M10 GOTO 170'rest vs shower
90 TF(0)=TF(1)'move fresh water up from below
100 TG(0)=(100*CFRESH+TG(0)*CGREY)/(CFRESH+CGREY)'move greywater in at the top
110 FOR S=1 TO 8'pipe section (9-fresh water in and greywater out)
120 TF(S)=TF(S+1)'move fresh water up
130 TG(S)=(TG(S-1)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)'move greywater down
140 NEXT S
150 TF(9)=55'move cold water in at the bottom
160 TG(9)=(TG(8)*CFRESH+TG(9)*CGREY)/(CFRESH+CGREY)'move greywater down
170 FOR S=0 TO 9'rest
180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)
190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)
200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)
210 NEXT S
220 NEXT M
230 NEXT SHOWER
240 FOR S=0 TO 9'results
250 PRINT S,TF(S),TG(S)
260 NEXT S
270 E=(TF(0)-55)/(100-55)'effectiveness
280 PRINT E

pipe fresh water greywater
section temp (F) temp (F)

0 93.32178 93.3218
1 90.556 90.55602
2 87.60851 87.60853
3 84.60492 84.60494
4 81.62819 81.62821
5 78.71178 78.71181
6 75.86447 75.8645
7 73.08838 73.0884
8 70.3852 70.38522
9 67.75679 67.75681

effectiveness

..8515951

The fresh and greywater temps are very close, about 6 hours after
a shower, since the pipe time constant is much shorter (less than
8 minutes.) These results wouldn't change much with only a half-hour
between showers. The effectiveness would be higher for shorter bursts.

Maybe it's worth adding 2 more $20 100' pieces of 1" pipe (altho that
would be a tight squeeze), or a handheld showerhead that only runs
when a button is pushed. Who sells them?

Nick