MECHANIC S. 
•the bottom ef the veffeJ, it is called a horizontal orifice, 
v and, when it is in the fide of it, it is called a lateral orifice. 
715 
By attending to the preceding obfervations, the refults 
of theory may be fo corrected, that the quantities of water 
difcharged in a given time may be determined with the 
greatelt accuracy poffible. 
The abbe Boffut has given the following Table, con¬ 
taining a companion of the theoretical with the real dif- 
charges, for an orifice one inch diameter, and for different 
altitudes of the fluid jn the refervoir. The real difcharges 
were not found immediately by experiment, but were de¬ 
termined by the precautions pointed out in the preceding 
articles, and may be regarded to be as accurate as if direft 
experiments had been employed. The fourth column 
was computed by M. Prony. 
Table II. Comparifon of the Theoretic with the Real Dif¬ 
charges from an Orifice one Inch in Diameter. 
8s.onltiii‘t Altitude 
l')f the Water in the 
Refervoir above the 
Centre of the Oii- 
Ike. 
theoretical Uii- 
charges through 
a Circular Orifice 
one Inch in Dia¬ 
meter. 
Keal Oil- 
charges in the 
fame Time 
through the 
fame Orifice. 
Ratio of tlu 
Theoretical to 
the Real Dif¬ 
charges. 
Paris Feet. 
Cubic Inches. 
Cubic Inches 
I 
438i 
2 722 
1 to o - 62I33 
2 
6196 
3S46 
I tO 0 ' 620 J\ 
3 
7589 
4710 
t to o'62o641 
4 - 
8763 
5436 
1 to o' 6203 i| 
5 
9797 
6075 
I tO O 62OJCB 
6 
10732 
6654 
I tO 0 ' 6200 o 5 
7 
11592 
7183 
1 to C6196J 
8 
12392 
7672 
1 to o - 6 1 9 1 j 1 
9 
13144 
8i35 
i to 0’6 s89c| 
IO 
13255 
8574 
t to o'6x88d 
I I 
14530 
8990 
1 to o'6i87 ; ',3 
I 2 
15180 
9384 
1 to o' 61 S1 c | 
13 
15797 
9764 
1 to o 6i8ic| 
14 
16393 
IOI 30 
1 to o - 6i79c! 
‘ 15 
16968 
10472 
x to 0*6171 £ J 
1 ' 
2 
3 
4 1 
It is evident from the preceding Table, that tlie theo¬ 
retical as well as the real difcharges are nearly proportional 
to the fquare-roots of the altitudes of the fluid in the re¬ 
fervoir. Thus, if we take the altitudes i and 4, whofe 
fquare-roots are as 1 to 2, the real difcharges taken from 
the Table are 2722 and 54.36, which are to one another 
very nearly as 1 to 2, their real ratio being as 1 to i'997. 
The fourth column of the preceding Table alfo (hows us 
that the theoretical are to the real difcharges nearly in the 
ratio of 1 to o - 62i or more accurately, as 1 to o , 6i93S ; 
therefore 0-62 is the number by which we mult multiply 
the difcharges as found by the formulae in the preceding 
fefrion, in order to have the quantities of water actually 
difcharged, 
In order to find the quantities of fluid difcharged by 
orifices of different fizes, and under different altitudes of 
water in the refervoir, we muft ufe the Table in the fol¬ 
lowing manner. Let it be required, for example, to find 
the quantity of water furnifhed by an orifice three inches 
in diameter, the altitude of the water in the refervoir 
being 30 feet. As the real difcharges are in the com¬ 
pound ratio of the area of the orifices and the fquare- 
roats of the altitudes of the fluid, and as the theoretical 
quantity of water difcharged by an orifice one inch in dia¬ 
meter, is,by the fecond column of the Table, 169x8 cubic 
inches in a minute, we lhall have this analogy, 14/15 : 
94/30=16968 : 215961 cubic inches, the quantity re¬ 
quired. Tliis quantity being diminifhed in the ratio of 
1 to '62, being the ratio of the theoretical to the afhial 
difcharges, gives 133896 for the real quantity of water 
difcharged by the given orifice. But the quantity dif- 
charged ought to be a little greater than 133896, becaufe 
greater orifices difeharge more than frnall ones ; and alfo, 
the quantity ought to be lefs than 133896, becaufe the al- 
3 tintde 
Table. I. Quantity of Water difeketrged in one Minute, by 
Orifices differing in Form and fofition. 
F Altitude 
of the Fluid 
above the 
Centre of 
the Orifice. 
Form and Pofition of 
the Orifice. 
Diameter of 
the Orifice 
is* ot | 
Cub. In.t 
difehar-j 
ged in a; 
Minute- 
[Ft. In. Lin. 
Circular and Horizontal 
6 lines 
23 I I 
811 8 10 
Circular and Horizontal 
1 inch 
9281! 
i 
Circular and Horizontal 
2 inches 
372031 
1 
Rectangular and Horizontal 
xin.by3lin. 
2 933 i 
Horizontal and Square 
1 inch, fide 
11817 
Horizontal and Square 
2 inch, fide 
4736 x 1 
900 
Lateral and Circular 
6 lines 
20181 
Lateral and Circular 
1 inch 
8135! 
0 
0 
* 
Lateral and Circular 
6 lines 
I 353 1 
i 
Lateral and Circular 
1 inch 
543 6 3 
? 507 
Lateral and Circular 
1 inch 
628; 
From the relulrs contained in the preceding Table, we 
may draw the following conclufions : 
1. That the quantities of water difcharged in equal 
times by different apertures, the altitudes of the fluid 
being the fame, are very nearly as the areas of the orifices. 
That is, if A or a reprefent the areas of the orifices, and 
W, tv, the quantities of water difcharged, W : w=zA : a. 
2. The quantities difcharged in equal times by the fame 
aperture, the altitude of the fluid - being different, are to 
one another very nearly as the fquare-roots of the altitudes 
of the water in the refervoir, reckoning from the centres 
of the orifices. That is, if H, k, be the different alti¬ 
tudes of the fluid, we thall have W : zo= 4/ H : fk. 
3. Hence we may conclude in general, that the quan¬ 
tities difcharged in the fame time by different apertures, 
and under different altitudes in the refervoir, are in the 
compound ratio of the areas of the orifices, and the fquare 
roots of the altitudes. Thus, if W, to, be the quantities 
difcharged in the fame time from the orifices A, a,.under 
the fame altitude of water; and, if W', w, be the quan¬ 
tities difcharged in the fame time by the fame aperture a 
under different altitudes H, h ; then by the firft of the two 
preceding articles, 
W : w— A : a\ and by the fecond 
w : W=4/H : 4 /h. Multiplying thefe analo¬ 
gies together, gives us, 
VV w : W'ai^zAt/H : a 4 /h \ and, dividing by to, 
W : W' =A\/U : a fh. 
This rule is fulficiently correct in p raff ice ; but, when 
great accuracy is required, the following remarks muff be 
attended to. 
4. Small orifices difeharge lefs water in proportion than 
great ones, the altitude of the fluid being the fame. The 
circumference of the finall orifices being greater in pro¬ 
portion to the iffuing column of fluid than the circumfer¬ 
ences of greater ones, the friffion, which increafes with the 
area of the rubbing furfaces, will alio be greater, and will 
therefore diminifh the velocity, and confequently the quan¬ 
tity difcharged. 
5. Hence, of feveral orifices whofe areas are equal, that 
which has the fmalleff circumference will difeharge more 
water than the reff under the lame altitude of fluid in the 
refervoir, becaufe in this cafe the fnffion will be leaft. 
Circular orifices, therefore, are the tnoff advantageous of 
all ; for the circumference of a circle is the Ihortelt of all 
lines that can be employed to indole:: given fpace. 
6. In confequence of a fmail increafe which the con¬ 
traction of the vein of fluid undergoes, in proportion as 
the altitude of the water in the refervoir augments, the 
quantity difcharged ought alfo to diminilh a little as that 
altitude increafes. 
