98 PROFESSOR A. H. GIBSON ON THE RESISTANCE TO FLOW OF WATER 
varnished. The circular pipes were of brass bored out to the correct taper, or, in the 
case of the pipes with varying curvature, carefully bored out to template. Calling @ 
the angle of conicity of a pipe (the angle contained between its opposite faces), 
the following table shows the range of uniformly tapering circular pipes experi- 
mented upon :— 
Initial Diameter. Final Diameter. Ratio of Final to Value of 0. 
Initial Area. 
Inches. Inches. 
65 2°15 10°96 180° (sudden enlargement) 
910) 1°50 9:0 10°, 20°, 40°, 60°, 90°, 180° 
1:00 3°00 9:0 20°, 40°, 60°, 90°, 180° 
oe 155%0) 3°00 4:0 3°) 45.0, (ey 10 Wee, Deli 
20°, 30°, 40°, 50°, 60", 90°, 1805 
2°00 3°00 D5) 10°, 20°, 40°, 60°, 90°, 180° 
The mean velocities of flow in these experiments ranged from 1°83 feet per second 
to slightly over 21 feet per second. The results show that in any given pipe the loss 
me 2 
of head, expressed as a percentage of the loss, ee theoretically obtained at a 
sudden enlargement between the same areas, does not vary in any definite manner with 
the velocity, and is, in fact, sensibly constant for all velocities above the critical; and 
in giving the results the losses have, in every case, been expressed as a percentage 
of this quantity. 
§ 2. EXPERIMENTS ON CIRCULAR Pipes witH UNirorMLy DivereGine BounpaRIEs. 
The following table gives the mean of all experiments carried out on each pipe, 
while the results are shown graphically and are compared with those of the former 
experiments, in fig. 1 :— 
a Ne 
S V1 —v : 
Loss of Energy expressed as a Percentage of Gee , the Theoretical Loss at a 
4 
Sudden Change of Velocity from v, to v,. 
| Value of 6 . 2 ; : 180°. 90°. | 60°. 40°. 20°. KO 
65 to 2°15 103°5 aac | a sn ane ke 
Pipe mean D0 ,, 1°50 102°8 1026 | 102°8 82:0 45:0 16°6 
BET ae: LO) yy 20) 102-1 104°1 | 101°3 80°8 44:0 abc 
we Is) ax) LOM, Ley 120°5 101°7 42°5 17°5 
| 2:0 30 99°2 112°1 ade 88°7 41°9 186 
* These experiments are described in the former paper. 
