458 APPLIED MECHANICS — i q 
compared with a, the value of m is about 0°45, which makes k=0°6. 7 f 
a = 10a, the value of m is about 0°36, which makes £= 0-625, a8 
397. Loss of Energy or Head due to Obstructions in Pipes.—An 
Z| 
UASTLPS 17 
‘ 
4 
=v =U 
Fig. 751. Fie. 752. Fig. 753. 
expression for the loss of energy or head obtained in the preceding 
2 2 2 
Article, namely, 5 pies 1) me ma may be used, where a is the area of 
J\% ; y. 
the section of the pipe, v the velocity of the water through it, and a, the ~ 
area of the section of the contracted stream as it passes through the 
hole in the diaphragm. If a, is the area of the hole in the diaphragm, 
the ratio a,/a,= will depend’ on the ratio of a, to a. Values of m ~ 
corresponding to various values of a,/a are given in the following table 
on the authority of Weisbach :— 
: 
aja | O01 | O2 | O8 | O4 | OF | O6 | OF | O8 | OD 
i lo 
m 226 47°8 30°8 7°80 3°75 1°80 | 0°80 | 0°29 | 0°06 | — 
_ The above values of m are also approximately true for a sluice partly — 
open (Fig. 752). i. 
For a cock in a cylindrical pipe (Fig. 753), the loss of energy or head — 
2 
is also given by the expression me Weisbach gives the following q 
values of a,/a and m for various values of 6, a being the area of the — 
pipe, and a, the effective area through the cock when turned through the 
angle @ :— | 
6 5° 10° | 20° | 30° | 40°. | 45° | 60° | ‘60° | Go" 
aja | 0:93 | 0°85 | 0°69 | 0:54 | 0:39 | 0:32 | 0:25 | 0-14 | 0-09 | ~ 
m 0:05 | 0-29 | 1:56 | 5:47 |17°3. | 31:2 |526 | 206 | 486 
398. Flow through a Cylindrical Mouthpiece.—A short pipe or — 
mouthpiece AF (Fig. 754), having a length of from two to three times — 
its diameter, projects from the side of a tank, as shown. The water on — 
entering the pipe converges, as in sharp-edged orifices, to a jet of sectional 
area a, at AB within the mouthpiece, and then expands until it has a 
sectional area a equal to that of the mouthpiece. 
Let P and a be the pressure and velocity of the jet at EF, and let P, 
a 
