298 Proceedings of the .Royal Society of Edinburgh. [Sess. 
calculated from these figures ; if D is measured in inches the results are in 
gallons per minute. The figures entered in the third column of Table I are 
the discharges calculated for an orifice 2^ inches in diameter. 
Table I. 
Head = H. 
Theoretical Discharge. 
Height of 
Layer of 
Maximum 
Discharge. 
Orifice of any 
Diameter. 
Gallons per minute. 
Orifice of 2^ inches 
Diameter. 
Gallons per minute. 
OTD 
0'0434D 5 / 2 
0-428 
•053D 
0-2 
0T711 
1-689 
•102 
0-3 
0-3808 
3-758 
•145 
0-4 
0-6652 
6-563 
•183 
0-5 
1-004 
9-904 
•217 
0-6 
1-398 
13-79 
•247 
0-7 
1-831 
18-07 
•274 
0-8 
2-290 
22-59 
•298 
0-9 
2-747 
27-11 
•319 
1-0 
3-169 
31-27 
•337 
IT 
3-519 
34-72 
•353 
1-2 
3-820 
37-69 
•366 
1-3 
4-109 
40-55 
•377 
1-4 
4-362 
43-04 
•386 
1-5 
4-615 
45-54 
•395 
1*6 
4-832 
47-68 
•403 
1*7 
5-061 
49-94 
•409 
1*8 
5-278 
52-08 
•414 
T9 
5-471 
53-98 
•418 
2-0 
5-675 
56-00 
•422 
If the areas under the curves of fig. 2 are taken as abscissae, and the 
corresponding values of the head as ordinates, a curve is obtained which 
shows the total discharge of the weir for any head ; this curve is given in 
fig. 3. The discharge for the orifice, under a head of water equal to some 
fraction of the diameter of the hole, can be obtained by multiplying the 
abscissa of fig. 3, measured at the corresponding head, by D 5i2 , D being 
taken in inches. The curves, of course, are applicable to any circular orifice, 
since all circles are similar. 
The results obtained until now refer to what is generally known as 
“ theoretical discharge ” — that is, the quantity of water which would escape 
from the orifice if there were no friction, and no contraction of the jet. The 
actual discharge is considerably less than the theoretical, chiefly on account 
of the fact that the free jet is smaller than the area through which it has 
emerged. The ratio of the actual to the theoretical discharge is usually 
called the “ coefficient of discharge.” 
