DISCHARGE. 
obferved, that though the water runs with the fame velocity 
through every fe&tion of the tube, yet it does not run with 
equal velocity through ee fies ie a aw feétion. Its 
motion is {wifter towards d flower towards 
the fides of the tube, ae ‘ti is ed by the friction 
againit the fides 
- Propofition IL When water, or other non-elaftic fluid, 
runs through a pipe or tube, which is kept continually full 
by means of a proper {uppiy; but which is not of an uniform 
fhape ; then the velocities of the fluid in aitereo fetions 
will be inverfely as the areas of the fectio 
Since the tube is always full, the ae quantity of water 
mutt pafs through every feétion of it in the fame time ; 3 but 
if the area of one feftion be half as great a of 
another fection, the fame quantity of w afs 
nau both fedtions at the fame time, am ie it pafles through 
the former feétion with double the velocity with which it paflcs 
through the latter. If the area of the former feGtion be one- 
third or one-fifth, of the area of the latter, the fame quantity 
_ Hence 
nding dire&tly above the aperture, 
an BD the loweft plate of the fluid immediately 
contiguous to the aperture. Alfo let v denote the velo- 
city which a heavy body would acquire in falling freely 
through BD, the height of the plate, and V the velocity 
scqniced byt the fame plate during its defcent throngh = 
fame fpace until it is a as by the preffure of the c 
Jumn CIKD. If w e fuppofe the Jowelt plate of uid 
ACBD to fail as a heavy body through a height B 
- moving force will be its own weight. geln, fuppofe it 
o be accelerated by its own ae = cae with the 
oe of the ambient fluid, about the eclni CIKD; 
Viz. 4 og Ww 
it is accelerated 
until it is oy. di charged: then (agreeably to the ef- 
tabl'fhed laws of dyna mics) the velocity in tbe former cafe 
will be to ta in ae ws ter, as mae moving forces an 
h they a& are inverfely as the velocities, the {pace 
through hk h the body is accelerated, being ii i“ the 
ee matter moved are equ val : therefore : 
aa Ve 
oe 3 whence vy? 
VBbD:” KD. wv is the velocity which a heavy 
body would actually aca in falling 
BD; piace el the velocity of the eff 
which a hea ould acquire in pe thro 
rifice 
the whcle altitude Jf the fluid above the or 
ane 
n the fame manne ie that if a pipe be 
soferted honaomlya in the a M N OP, fig. 7, the plate 
of fluid 
2 - CBD will be sicharged rg : ae meena 
as Ba reffur 
velocity, until a column had been difcharged whofe bafe is 
equal to the orifice, and height equal to the length of t 
tube: whereas we find b perience, that this full ay 
can be _— by the el plate which can be let efcape 
noe the aper 
ee and quantities difcharged at different 
cept are as the fquare roots of thede 
3. The quantity run out in any time is equal to a cylinder, 
or prifm, vuole bafe is the area of the orifice, and its alti- 
tude the {pace defcribed in that time by the velocity ac- 
quired by falling oe the height of the fluid. 
So that if 4 denote the height of the fluid, 
7, the time of cfllux 5 we fhall have for the quan« 
tity sapere ey Q=atv2gh; 
Or, when a and A are ene in feet, Q = 8.0208 at 
Wb, fee 
Wren aand 4 are expreffed in inches, Q = 27.7387 a; 
Vb, in 
If the orifice is a circle ha 
0.785395 d? mult be fabBitated for 
diameter is d, then 
And when 4 and / are ae ee in feet, Q = 6.29952 
d vob, f 
When d vad 4 are expreffed in inches, Q = 21.78592 
di? J}, 
And fon nee of thefe it will be eafy to find either a, 
water im inges 
ak any se body, is proportional . the altitude of 
e fluid above the orifice as the velocity 
pice by the quantity of matter; but fie quantity dif: 
charged in a given time is as the velocity; therefore the 
force is as the {quare of the velocity ; that is, by the al 
ftration of the propofition, as the height of the flui 
5. The water eee out with the fame velocity whether 
it be downwards, or upwards, or fideways; becaufe the 
preffure te han is the tne in all cH tee at the fame 
ept 
¢ ence, if the ee (viz. the laft appendage or 
e) be turned upwards, the 
circumftanc hich 
aaa aa configorstion of the ftream, which will be deleribed 
hereafte 
Propofition When a veffel is left to epee ie 
gradually through an artes in its bottom, if the area 
