.... 5 vs 3 100' pipes only raised the effectiveness from 68 to 77%.
A 200' version makes 82%... 200' of 4" drainpipe would wrap around
the lower 3' of an 86" diam x 48" tall STSS heat storage tank.

15 DIM TF(20),TG(20)
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 CSERIES=CFRESH*CGREY/(CFRESH+CGREY)'caps in series (Btu/F)
70 RC=CSERIES/UPIPE'combined time constant (hours)
80 EXPF=EXP(-1/60/RC)'exponential factor
90 FOR SHOWER = 1 TO 100'simulate showers
100 FOR M=0 TO 59'simulate 10 min shower + 50 min rest
110 IF M9 GOTO 270'rest vs shower
120 IF SHOWER 100 GOTO 160
130 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy
140 GLOSS=GLOSS+CFRESH*(TG(19)-55)'greywater heat loss
150 PRINT 400+M;"'";M,TF(0),RHEAT,TG(19),GLOSS
160 TF(0)=TF(1)'move fresh water up
170 TGT=TG(0)'save original Tg(0) for later Tg(1) calc
180 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top
190 FOR S=1 TO 18'pipe section (19-fresh water in and greywater out)
200 TF(S)=TF(S+1)'move fresh water up
210 TGP=TG(S)'save original Tg(s) for later Tg(s+1) calc
220 TG(S)=(TGT*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down
230 TGT=TGP'prepare for Tg(s+1) calc
240 NEXT S
250 TF(19)=55'move cold water in at the bottom
260 TG(19)=(TGT*CFRESH+TG(19)*(CGREY-CFRESH))/CGREY'move greywater down
270 FOR S=0 TO 19'rest
280 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)
290 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F)
300 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F)
310 NEXT S
320 NEXT M
330 NEXT SHOWER
340 SHOWERGY=10*CFRESH*(100-55)'if no GWHX (Btu)
350 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY

0 96.58958 35.51103 62.44146 77.4842
1 95.26726 84.79071 62.58688 156.4826
2 93.96446 147.6357 62.76867 237.3738
3 92.78384 222.7741 62.93455 319.9923
4 91.76805 308.4892 63.09611 404.293
5 90.9036 403.2055 63.25129 490.2096
6 90.16348 505.6282 63.40093 577.6842
7 89.52875 614.6602 63.54522 666.6613
8 88.98529 729.3508 63.68448 757.0885
9 88.52072 848.8789 63.81895 848.9157

848.8789 4685.625 .8188334

Nick