Encyclopaedia Britannica > Volume 15, PLA-RAM

T*nmpf
79 .
rJ'he theory
denomina¬
ted lryifrO-
Jyfiamici,
8o
Jhough
imperteeft
is very
ufeful.
Sr
E-urdamen.
tal propofr
tion.
p U M
664 1
P U M
very elaborate treatifea on the fubjeil, urm : <* fhe very
appofite name of Hydrodynamics; in which, although
they have added little or nothing to the fundamental
proportions eftablifhed in fome fort by Newton, and
acquiefced in by them, yet they have greatly contribu¬
ted to our progrefs in it by the methods which they
have purfued in making application of thofe fundamen¬
tal propofitiens to the moil important cafes. It mud
be acknowledged, however, that both thefe propor¬
tions, and the exteniions given them by thefe authors,
are Supported by a train of argument that is by no
means unexceptionable; and that they proceed on af-
fumptions or poftulates which are but nearly true in
any cafe, and in many are inadmiflible : and it remains
to this hour a wonder or puzzle how thefe proportions
and their rebuts correfpond with the phenomena which
we obferve.
But fortunately this correfpondence docs obtain to
a certain extent. And it feems to be this correfpond¬
ence chiefly which has given thefe authors, with New¬
ton at their head, the confidence which they place in
their refpeftive principles and methods : for there are
conflderable differences among them in thofe refpedls ;
and each feems convinced that the others arc in a miffake.
Meffieurs d’Alembert and De la Grange have great¬
ly corre6ted the theories of their predeceffors, and have
proceeded on podulates which come much nearer to
the real date of the cafe. But their invedigations in¬
volve us in fuch an inextricable maze of analytical in-
vedigation, that even when we are again condudted to
the light of day by the clue which they have given us,
we can make no ufe of what we there difeovered.
But this theory, imperfeft as it is, is of great fer-
vice. It generalizes our obfervations and experiments,
and enables us to compofe a practical doRnne from a
heap of fails which otherwife mud have remained fo-
litary and unconneiled, and as cumberfome in their ap¬
plication as the charailers of the Chinefe writing.
The fundamental propofition of this practical hydro-
• dynamics is, that water or any fluid contained in an
open veflel of indefinite magnitude, and impelled by its
weight only, will flow through a fmall orifice with the
velocity which a heavy body would acquire by falling
from the horizontal furface of the fluid. Thus, if the
orifice is 16 feet under the furface of the water, it will
iiTue with the velocity of 32 feet in a fecond.
Its velocity correfponding to any other depth h of
the orifice under the furface, will be had by this eafy
proportion : “ As the fquare root of 16 is to the fquare
root of h ; fo is 32 feet to the velocity required : or,
alternately, //16 : 32 = y'A ; v, and v =
V 1 o
7 2
'V
8 \/ h : that is, multiply the fquare root of
the height in feet by eight, and the produdl is the re¬
quired velocity. f
On the other hand, it frequently occurs, that we
want to difeover the depth under the furface which will
produce a known velocity v
Therefore
y'i=s’
and h
64 : t^iat ‘s’ divide the fquare of the velo¬
city by 64* and the quotient is the depth wanted in
feet.
This propofiticn is fufficient for all our purpyftr. pump.
For fince water is nearly a perfe<£l fluid, and propagates
all impreflions undiminifhed, we can, in place of any lts 8-,.f
preflure of a pifton or other caufe, fubllitute a perpen- 5 ut“i y
dicular column of water whofe weight is equal to this
preflure, and will therefore produce the fame efflux.—-
Thus, if. the furface of a piffon is half a fquare foot,
and it be preffed down with the weight of 500 pounds,
and we would wlfti to know with what velocity it would
caufe the water to flow through a fmall hole, we know
that a column of water of this weight, and of half a
foot bafe, would be 16 feet high. And this propoii-
ti >n teaches us, that a veflel of this deptli will have a
velocity of efflux equal to 32 feet in a fecond.
If therefore our prefiing power be of fuch a kind
that it can continue to prefs forward the pillon with
the force of 50O pounds, the water will flow with this
velocity, whatever be the fize of the hole. All that re¬
mains is, to determine what change of afluul prejfure
on the pifton relults from the motion of the pillon it-
felf, and to change the velocity of efflux in the fubdu-
plicate ratio of the change of a£lual preffure. § .
But before we can apply this knowledge to the cir-Remirk
cumflances which take place in the motion of water in Previou*
pumps, we mult take notice of an important modxfica-\
tion of the fundamental propofition, which is but very
obfeurely pointed out by any good theory, but is efta¬
blifhed on the moll regular and unexceptionable obfer-
vation.
If the efflux is made through a hole in a thin plate-,
and the velocity is computed as above, we fflall difeover
the quantity of water which iffues in a fecond by obfer-
ving, that it is a prifm or cylinder of the length indica¬
ted by the velocity, and having its tranfverfe fedlion
equal to that of the orifice. Thus, in the example al¬
ready given, fuppofing the hole to be a fquare inch, the
folid contents of this prifm, or the quantity ol water if-
fuing in a fecond, is I X 32 X 12 cubic inches, or 384
cubic inches. This we can ealily meafure by recei¬
ving it in a veflel of known dimenfions. Taking this
method, we uniformly find a deficiency of nearly 38
parts in 100; that is, if we fliould obtain 100 gal¬
lons in any number of feconds, we (hall in fail get only
62. This is a moll regular fail, whether the velocities
are great or fmall, and whatever be the fize and form
of the orifice. The deficiency increafes indeed in a
very minute degree with the velocities. If, for in-
ftance, the depth of the orifice be one foot, the dil-
charge is rVoVs ; if it be 15 feet, the difeharge is
6 1 ? 1
t . . .
This deficiency is not owing to a diminution of
velocity ; for the velocity may be eaiily and accurately
meafured by the diftanee to which the jet will go, it
direiled horizontally. This is found to correfpond very
nearly with the propofition, making a very fmall allow¬
ance for friflion at the border of the hole, and for the s
reliftance of the air. Sir liaac Newton aferibed the de¬
ficiency with great jullice to this, that the lateral co¬
lumns of water, furrounding the column which is in¬
cumbent on the orifice, prefs towards the orifice, and
contribute to the expence equally with that column.
Thefe lateral filaments, therefore, ifliie obliquely, crofs-
ing the motion of the central ftream, and produce a
contraclion of the jet ; and the whole ftream does not
acquire a parallel motion and its ultimate velocity till it
7 • has