THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. 1138 
Value of Loss of Head expressed 
6 in as a Percentage of 
Value of 6 | Length ; Percent- 2 
Be Straight the Loss in 
Ratio of Areas. Mees Fine Taper Sa 
: Pipe 
Loss. (inches). Here e|ecelends Straight @ansed 
Length. Pipe. Pipe. 
1 Sau ot Ae ea { 
( ai 10° 20’ | 17-95 15° 16-2 54:9 | 81:0 
Sections 59 in. x 1°329 in. } _ eel ou De 1) | el 
pad si5 im x1320um, | 4. ue -| o2 |) 20 Le — Hs 
- ieee Beery £08 | “60° ») 20:8 | 
Ay 10° 20’ 15°15 15° 15°6 53°8 aes 
ins 4:1 11° 00’ 11°30 20° 15:3 32°6 60:5 
= { 1:329 in. square to ; 12° 00’ 7°45 30° 18:2 22:0 53°6 
=| 1:°329 in. x 5°315 in, 12° 45) 5°48 40° 22:0 21-1 53-0 
3 15S 530; 3°45 60° 29°4 a 
jem ———————— = ~ 
Yay & A 10° 40’ 6°30 15° 15:2 51:5 aie 
1:329 in. square to | 13° 20° 3°10 30° 22°8 26'8 43:0 
' 1*329 in. x 2:99 in. { 15° 40’ 2°29 40° 28-2 25:2 
a | de 10! 3°80 ee 13°6 52°3 58-2 
oi ‘59 in. diam, to 1°50 in. diam. | 11° 00’ 1:870 30° 18:2 27°2 48:0 
[oF = 
on Areal tT 100" 8575 10° 12°7 73°5 ae 
3 1:50 in. diam. to 3:0 in. diam, iB a0 2°802 30° 20°8 22°2 58°5 
5 
3 22D i Oo 5715 10° 13°4 725 
2:0 in. diam. to 3-0 in. diam. 15° 00’ 1:870 30° 24-3 35-2 
The loss may be still further reduced by replacing the straight taper portion of 
these pipes by curved pipes having the same initial and final areas and having 
boundaries calculated as already described. With pipes so designed the percentage 
losses become approximately as shown in the table on p. 114:— 
From these results it appears that the effect of replacing the straight taper by a 
curve is proportionately greater in the pipes having the greater length, owing to the 
fact that as the pipe is lengthened the proportion of the total loss which takes place 
during the gradual enlargement is increased, while that taking place at the subsequent 
sudden enlargement is reduced. 
Expressed as a percentage of the loss at a sudden enlargement, the effect of intro- 
ducing the curve is approximately the same for all the pipes, being to reduce this loss 
by about 2°5 per cent. in the rectangular and 1°9 per cent. in the circular pipes. 
§ 7. Summary anp ConcLusIons. 
The following are the chief conclusions to be drawn from the experiments :— 
(a) In a circular pipe with uniformly diverging boundaries the loss of head ex- 
pressed as a percentage of (v,—v,)’/2g varies somewhat with the mean diameter of 
TRANS. ROY. SOC. EDIN., VOL. XLVIII. PART I. (NO. 5). 18 
