114 PROFESSOR A. H. GIBSON ON THE RESISTANCE TO FLOW OF WATER 
Value of 6 in 
| Area on : Percentage 
Ratio. Soe ee ne Loss of Head. 
of same Length. 
15° 13:1 
oie 30° 13°0 
40° 13°9 
4:1 15° 12°6 
Rectangular 30° 16-0 
Pipes. 40° 20-0 
15° 12-6 
22D 1 30° 20°9 
40° 25°9 
Wheat 15° 12°2 
30° 158 
eat on 10° 11 
ee 0 irs 
22252 ol 10° 12°2 
30° 22°1 
the pipe, and with the ratio of final to initial area, as well as with 6 An increase 
in the mean diameter slightly reduces the percentage loss, as does an increase in the 
ratio of enlargement. For values of 6 between 6° and 35°, however, the differences 
are comparatively small and the loss of head can be expressed by the relationship 
— 4).\2 
loss = 0110 '0%1=2) feet 
24 
where 6 is in degrees. The minimum loss of head is attained with a value of 0 in the 
neighbourhood of 5° 30’. The loss of head at a sudden enlargement of section also 
varies slightly with the smaller diameter d and with the ratio of enlargement m, and 
is given very nearly by the relationship 
l 
OSS 100 
_ 102° + °25m — 2-0d { (v, — »,)* ; Fook 
29 
As @ is increased from 5° 30’ the loss rapidly increases to attain a maximum, greater 
in every case than 100 per cent., for a value of 6 in the neighbourhood of 65°. The 
value of 6, which makes the loss equal 100 per cent., varies from 40° to 60°, and in 
practice a sudden enlargement of section is more efficient in the transformation of 
kinetic into pressure energy than is a gradual enlargement in which @ exceeds this 
critical value. 
(b) By projecting the parallel portion of the pipe into the space bounded by the 
