EW. Blake on the flow of Elastic Fluids through Orifices. 79 
If the velocity with which a fluid flows through an orifice 
from one vessel into another be represented by V, the density 
under which it passes the orifice by D, and the area of the orifice 
by 8, then the product VDS is the measure of the quantity of 
fluid discharged in a given time. It is an established law in the 
dynamics of fluids, that the velocity of the flow is directly as the 
square root of the pressure and inversely as the square root of the 
density. If then the efficient pressure which produces this flow 
be represented by P, the general law expressed by symbols 
ill be, 
DSV e 
VDS a sy i 
The above expression is in accordance with the received theory, 
and properly understood it is correct, and applicable to all fluids, 
elastic as well as inelastic. But it must be observed that D in 
this expression must in all cases represent the density under which 
the fluid passes the orifice. 
In all the treatises on the dynamics of fluids that I have ex- 
amined, the quantity D in the foregoing expression represents 
the density of the fluid in the discharging vessel: it being as- 
sumed that the fluid passes the orifice without change of density. 
This assumption is correct so far as respects inelastic fiuids, but 
as respects elastic fluids it is far otherwise. A. particle cannot 
even begin to approach the orifice without a change of density. 
Surrounded by other particles, it will not begin to move until the 
pressure before it becomes less than the pressure behind it. If 
the pressure before it is less than the pressure behind it, then the 
density there is less also, and consequently the density of the 
particle itself is diminished, for that must be intermediate be- 
tween the density before and behind it; and as it cannot begin 
to move without a change of density, so for the same reasons its 
motion cannot be accelerated without a further change of den- 
the efficient pressure which causes the discharge, (represented 
by P in the above expression,) as equal in all cases to the differ- 
ence of pressure in the two vessels. The true amount which is 
to be deducted from the pressure in the discharging vessel, in 
er to find the efficient pressure that produces the discharge, is 
the elastic foree that is due to the density which the fluid has in 
its passage through the orifice; for it is obvious that that alone 
reacts against the pressure in the discharging vessel. From this 
sideration also we may arrive at the same conclusion as was 
deduced in the last paragraph, viz. that the fluid must pass the 
