THROUGH PIPES OR PASSAGES HAVING DIVERGENT BOUNDARIES. Dab 
angle of divergence still further without altering the length, thus introducing a sudden 
enlargement from A, to A, and a corresponding loss of head, but at the same time 
reducing the change of velocity, and therefore the loss, in spite of the increasing 
percentage coefficient, in the taper portion of the pipe. As will be seen from the 
experimental results, given at a later stage in the paper, these conclusions are justified, 
and it becomes possible to design a pipe—often with a considerable reduction in length 
—in which the boundaries are straight, and in which the loss is still appreciably less 
than in a straight taper pipe giving the full enlargement of section with the best 
possible value of 9. 
The total loss of head in such a pipe as shown in fig. 5, and consisting of a straight 
taper pipe terminating in a sudden enlargement of section, is theoretically equal to 
K%—%) , a—%)” foot 
29 2g 
where K is obtained from the curves of figs. 2 and 3. As 2= Ay ; while ce = where 
A represents the corresponding area this becomes 
ix -G- 8) 
a7 i + cane eet 
i A, ) ( DeoNe e my tls 
oe eae \K 1 =] + gs eet. 
In a rectangular pipe whose breadth increases uniformly from 6, to b; in a length L, 
or 
b,=b, + 2D tan § 
= 6, + L@ (approximately) where 0 is in angular measure, 
so that 
A,=A,+L48, 
