THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. 103 
In every case the effect of the projection is to increase the loss, the effect being 
greater the greater the length of the projection and also the less the angle of divergence 
of the conical sides. The loss is, in fact, greater in every case than would be experienced 
if the pipe walls were tapered off from the extremity of the projecting pipe, as shown 
by the dotted lines in fig. 2. 
§ 4. RecrancuLaR PIPES WITH UntiroRMLy Divercinc BouNDARIES. 
Three sets of rectangular pipes were examined, these having one pair of sides 
parallel and 1°329 inch apart in every case. The areas of the small and of the large 
ends of these pipes were, in the case of the pipes having area-ratios of 4:1 and 9:1, 
identical with those of the circular taper pipes having the same ratios of enlargement. 
The details of the pipes are as follows :— 
Dimensions of Pipes (inches). 
Area-Ratio. Values of 6. 
Small End. Large End. 
590 x 1°329 5°315 x 1°329 Oral 10°, 15°, 20°, 26°, 40°, 60°, 90° 
1°329 x 1°329 5'315 x 1°329 : ae | Bi LOny Lor22" 42-30". 40; 
1°329 x 1:329 2°990 x 1°329 2°25: 1 10°, 15°, 20° 30° 
The results of the means of the experiments on these pipes are plotted in fig. 3. 
From these it appears that the percentage loss in such pipes is very approximately the 
same for all ratios of enlargement between 2°25 to 1 and 9 to 1 for values of 6 between 
10° and 40°, and that it varies but little with the dimensions of the pipe. The minimum 
loss is obtained when 4 is approximately 11°, the percentage loss under these circum- 
stances being about 17°5 per cent. As 0 is increased the loss increases rapidly, and 
attains a value of 100 per cent. when 4 is between 31° and 40°, the value of this critical 
angle being less with the smaller ratios of enlargement and with the pipes having the 
smaller mean sectional areas. For values of 6 between 10° and 35”, the only values of 
any use in practice, the loss can be expressed with a fair degree of accuracy by the 
relationships— 
A V2 
loss = ‘0072 61° Oa feet, where @ is in degrees. 
1°40 
= 5°30 (tan 5) (Crete feet. 
2 2g 
The following table shows a comparison between experimental results and values 
calculated from these relationships :— 
