MECHANICS. 
Table V. Comparifott of the Theoretical with the Real Dif- 
c barges from a Cylindrical Tube one Inch in Diameter and 
two Inches long. 
Con (tanl al¬ 
titude of the 
Water in the 
Refervoir 
above ths 
Cenlre of the 
Orifice. 
Theoretical 
Difcharges 
through a cir¬ 
cular Orifice 
one Inch in 
Diameter. 
Real Dllcharges 
in the fame Time 
by a Cylindrical 
Tube one Inch 
in Diameter and 
two Inches 
long. 
Ratio of the 
Theoretical to 
the Real Dif¬ 
charges. 
Paris Feet. 
Cubic Inches. 
Cubic Inches. 
z 
438 r 
3539 
1 to o'8i78i 
% 
6196 
5002 
1 to o - 8o729 
3 
7589 
6126 
1 to 0-80724 
4 
8763 
7070 
1 to 0 80681 
5 
9797 
79OO 
1 to 0-80638 
6 
1073 ^ ' 
8654 
1 to 0-80638 
7 
II 592 
9340 
1 to 0-80573 
8 
I 239 Z 
9975 
I to 0-80496 
1 9 
13144 
10579 
I to 0-80485 
i 10 
1385S 
11151 
I to 0 80483 
1 11 
14530 
11693 
I to 0-80477 
1 IZ 
15180 
12205 
I to 0-80403 
i 13 
15797 
12699 
I to 0-80390 
I 
16393 
1 3 'i 77 
I to 080382 
| is 
16968 
13620 
1 to 0-80270 
i 1 
2 
3 
4 
By comparing the preceding Table with Table II. we 
From thefe experiments we are authorifed to conclude, 
c. That the real difcharges are lefs than thole deduced 
from theory, which in the prefent cafe is 2742.5 cubic 
inches in a minute, a. That when the interior orifice 
of the tube is enlarged to a certain degree, the quantity 
difcharged is increased 5 but that, when this enlargement 
is too great, a contraflion takes place without the exte¬ 
rior orifice, and ths quantity difcharged fuffers a diminu¬ 
tion. If the fmallelt bafe of the conical tube be inferted 
in the fide of the refervoir, it will furnilh more water 
than a cylindrical tube whofe diameter is equal to the 
fmalleft diameter of the conical tube: for the divergency 
of its fides changes the oblique motion which the parti¬ 
cles would otherwife have had, when palling from the 
refervoir into the tube. 
Dr. Matthew Young, late bilhop of Clonfort, paid par¬ 
ticular attention to the various circumliances connected 
with the difcharge of fluids from orifices of different 
kinds, but he appears to have been molt f'uccefsful in his 
enquiries into the caufe of the increafed velocity of efflux 
through additional tubes. This fedlion will, therefore, be 
terminated by an extraft from his paper in vol. vii. of 
the Tranfaffions of the Royal liilh Academy, which 
contains feme judicious remarks relative to his own ex¬ 
periments, and applicable at the lame time to feme expe¬ 
riments made by Mr. Profe(Tor Vince. 
“ When a tube mnrs (fig. 24.) is inferted into the 
veffel AB CD, it is found that the velocity is increafed 
nearly in the fubduplicate ratio of the length of the pipe 5 
and that it approaches nearer to that fubduplicate ratio 
according as the length of the pipe is increafed. To ac¬ 
count for this increafe of velocity has appeared a matter 
Vol. XIV. No. 1007. 
717 
Ihall find that cylindrical tubes difcharge 3 much greater 
quantity of water than fimple orifices of the fame dia¬ 
meter, and that the quantities difcharged are as 81 to 62 
nearly. This is a curious phenomenon, and will be after¬ 
wards explained. 
The application of this Table to other additional tubes 
under different altitudes of the fluid, not contained in the 
firft column, is very fimple. Let it be required, for ex¬ 
ample, to find the quantity of water difcharged by a cy¬ 
lindrical tube, 4 inches in diameter, and 8 inches long, 
the altitude of the fluid in the refervoir being 25 feet. In 
order to refolve this queftion, find (by Table II.) the theo¬ 
retical quantity difcharged, w hich in the prefent inftance 
will be 350490 cubic inches, and this number diminilhed 
in the ratio of 1 to 0 81 will give 284773 for the quantity 
required. The length of the tube in this example was 
made 8 inches ; becaufe, when the length of the tube is 
lefs than twice its diameter, the water does not eafily follow 
its interior circumference. If the tube were longer than 
8 inches, the quantity of fluid difcharged would have been 
greater, becaufe it uniformly increases with the length 
of the tube 5 the greateft length of the tube being always 
fmall, in companion with the altitude of the fluid in the 
refervoir. 
Hitherto we have fuppofed the tube to be exaflly cy¬ 
lindrical. When its interior fur face, however, is conical, 
the quantities difcharged undergo a confiderable variation, 
which may be eftimated from the following experiments 
of the marquis Poleni, publifhed in his work De Cajlellis 
per qua derivantur Fluviorum Aqua, &c. which appeared at 
Padua in 1718. 
of fome difficulty, fince the water cannot iflue at rs witjh 
a greater velocity than it enters at m n ; and it does not 
appear how the velocity at mn can be increafed by inferr¬ 
ing a tube beneath it. In order to explain the caufe of 
this effedf, we are to confider that the whole force with 
which the plate mn is prefled down is the weight of a co¬ 
lumn of water equal to emnf, together with the weight 
of a column of air, of the.fame bafe, reaching to the top 
of the atmofphere; and the whole force with which it is 
preffed up is the weight of an equal column of air, dimi¬ 
nilhed by the weight of a column of water equal to mnrs j 
therefore the aftual force with which the plate mn is 
preffed down is the weight of a column of water equal 
to ef rs-, the velocity therefore with which the plate mn 
will iflue through the orifice mn will be the fame as 
through the orifice rs in the veffel AbcD-, that is, equal 
to the velocity which a heavy body would acquire in 
falling through the altitude er ; and all the plates of wa¬ 
ter in the tube mnrs will delcend with the fame velocity 5 
for they cannot defeend fafter, becaufe otherwife there 
would be a vacuum left in the tube, which is prevented 
by the upward preffure of the atmofphere. And the ve¬ 
locity of the effluent water will be the fame, whatever be 
the preffure of the atmofphere, provided the weight of a 
column of air of the fame bafe with r s, and whofe height 
is equal to that of the atmofphere, be either greater than of 
equal to the weight pillar of water -mnrs. This might be 
proved experimentally by a veffel of water with a pipe 
inferted in the bottom placed under an exhaufted receive! - . 
But, as the operation of exhaultion is obftruCfed more by 
the evaporation of water than of mercury, it will be bet¬ 
ter to uie mercury in thefe experiments. Now, if D be 
8 U the 
Table VI. Quantities of Water difcharged by Conical Tubes of different Diameters. 
Apertures employed. 
Interior 
Diameter. 
Exterior 
Diameter. 
Quantity difcharged 
in a Min. in Cubic Feet. 
l ime in which 
Inches were 
73031 Cub. 
difcharged. 
Conftant alti- 
Length of 
Orifice in a thin plate. 
26 lines 
26 lines 
15877 
4 ' 
36" 
tude of the water 
each tube 
Cylindrical tube. 
26 
26 
23434 
5 ' 
7 ,f 
in the refervoir, 
92 lines. 
ill Conical tube, 
33 
26 
24758 
z' 
57" 
256 lines, or 1 
or 7 
ad Conical tube. 
42 
26 
24619 
z' 
58" 
foot 9 inches and 
inches 
3d Conical tube, 
6O 
26 
24345 
3' 
o" 
4 lines. 
8 lines. 
4th Conical tube. 
118 
26 
23687 
3 ' 
5" 
