Hydraulics. 2H

portional to the Square Root of the Pressureor Altitude os the Fluid [12LW)

From

rtiis Manner the Dimensions of a Conduct-Pipe maybe found for any other Number of Adjutages.

(LXXIV.) To represent these Propositions in Sym- PI. XV.ools may render them more perspicuous, and, perhaps, Fig. 6,more elegant. Therefore let Water spout from theSide of a Vessel at two different Depths B and E fromthe Surface of A ; the Momentum of the spouting Fluidwill be as the Force wh'ch protrudes it, and this Forceis everywhere proportional to the Altitude of the Fluid,therefore the Momentum of the Water at B and E willFe as AB and AE, which let be denoted by m and M.

Then letu and V be the Velocities with which the Wa-ter spouts ; and q and Qjthe Quantities of Water iffu-istg out in the fame Time from the Adjutages B and E,then we shall have m—vq, and M — V Q. And

therefore ^ —v, and V.

2 . Now the Quantity of Water spouting from anyHole in a oiven Time muss necessarily be as the Velo-city with which it flows for the greater the Velocity,the o-reater will be the Number of Particles which cometo tire fame Point in the fame Time, or the greater willbe the Quantity of Water which passes by the Orificeof the Adiutage, as is very easy to conceive ; therefore

™ M M M

? •• Q_:: n: V consequently ^ X y — —

X Qj or M a q — m Q_Q_i wherefore m\ M :: q q :

v v : V V, as is evident from the Proportiona-% of the Roots.) Therefore also q : Q.-- rJ • *

m v/aB : \/~KT. . , „

3- Hence if AB AE :: x ; 4» the Velocity, at hwill double the Velocity at B, and the Quantity otWater which flows from E will be twice as great asthat which flows from B in one Minute, or any gwen

- IfAE becq ua lM9 AB..h e V.l<.o,^

'V

hme.

3