THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. 109 
would be made to diverge uniformly at this best angle up to a point where its straight 
sides would intersect the calculated curved sides. 
If, on the other hand, the length of pipe is small or the ratio of areas large, the 
calculated curves may, towards the larger end of the pipe, diverge at an angle greater than 
that (about 35° in a rectangular pipe) giving a loss equal to that at a sudden enlargement. 
In such a case—as was confirmed by experiment—a more efficient pipe is obtained 
by enlarging the pipe to its final section by a sudden enlargement at the point at which 
the angle of divergence becomes equal to this critical value. 
A still more efficient pipe is obtained if, from the point at which the angle of 
divergence becomes 35”, the section is enlarged gradually, the best angle of divergence 
being found to vary but slightly in such circumstances and in any cases likely to be 
found in practice, being approximately 20°. 
All the pipes were first constructed with a continuous curve from inlet to outlet, 
and those pipes in which the angle at outlet exceeded the critical value were, after 
being used, modified as shown by the dotted lines in fig. 4, A. After further examination 
they were again modified as shown in fig. 4, B, with the results indicated in the following 
table :— 
Percentage Loss in Trumpet-shaped Pipes. 
Value of 6 : 
in CG Curved Pipe. 
| Ratio of Pipe of Straight 
| Enl g ipe. ; ; 
mateqment. po es th ene Continuous Modified Modified 
Pipe. Curve. as in “A.” as in * B.” 
Ort 20° 48:0 24:1 21:3 19°5 
9:1 26° 795 37°6 34:2 30°3 
a 
Rectangular | 4:1 22° 42’ 50°5 44-4 + 
Pipes. 1 26°4 
4:1] 30° 85:1 38:0 35:9 33°9 
Al) I 40° 100:0 48-9 AT 41:5 
2°25: I 20° 47-4 28:1 
2°25: 1 30° 94:0 53°0 
O)e il 15s 28-0 23°4 im 
9:1 30° 67:0 39:4 38:0 
Circular 4:1 10° 17-5 13-9 a 
Pipes. 4:1 30° 82:5 38:8 35-5 
2:25:1 10° 18:5 14°5 
| PED 21 30° 69:0 40°9 
| 
* & = constant. if “t= constant, 
