THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. 115 
diverging walls (fig. 2) the loss is in every case increased, the difference increasing 
with the length of the projection. 
(c) The percentage loss of head in rectangular pipes having one pair of sides parallel 
and the second pair uniformly diverging, varies little with the size of pipe and with 
the ratio of enlargement. 
It can be expressed with fair accuracy for values of 6 between 10° and 35° by the 
relationship 
loss = 0072 gr(%1= 2) feet 
2g 
where @ is in degrees. This loss is in general greater than in a circular pipe having the 
same value of 0, except where @ is between 10° and 15°. The minimum loss is obtained 
when @ is approximately 11°. The maximum loss is apparently obtained with values 
of 8 in the neighbourhood of 70°. 
(d) In pipes of square section the minimum loss of head is obtained with a value of 
6 in the neighbourhood of 6°, and has a value of about 14°5 per cent. As @ increases 
the loss becomes much greater-—up to 85 per cent. greater—than in the corresponding 
circular pipe. 
(ce) By making the pipes trumpet-shaped, with curves designed so as to make 
ae’) =constant, the loss of head in a pipe of given length may be considerably reduced. 
The proportional saving is greater as the length of pipe is less, and, in the pipes 
examined, varied from 20 per cent. to 60 per cent. 
(f) A still greater saving, combined with great simplicity, may be effected by a 
desion giving a gradual uniform enlargement in section from the initial section A, to 
one having an area A;, and a sudden enlargement from A, to the final section Ag, as 
shown in fig. 5. The value of 4 in the taper portion of the pipe, which gives a minimum 
loss of head, may be obtained from formule (3) or (4), p. 112, when the length of this 
pipe is settled. This value varies from 10° to 16° in the rectangular pipes and from 7° 
to 16° in the circular pipes, increasing, for a given length of pipe, as the ratio of 
enlargement is reduced, and, for a given ratio, increasing as the length is reduced. In 
any cases likely to occur in practice its value may be taken as follows, without any very 
| great variation from conditions of maximum efliciency :— 
Ratio of enlargement : : Cea 4:1 2°25: 1 
Value of @ (rectangular pipe) . ale 12° 30’ 13° 30’ 
Value of @ (circular pipe). : OF 10° 30’ 11° 30 
By this method of construction the loss may be reduced in favourable circumstances 
to about 90 per cent. (in rectangular pipes) and to about 96 per cent. (in circular pipes) 
