60 
joint product ugA is constant all along the stream so that 
W 
A = 
W . 
gpu 
where — is the mass of fluid which passes any section per 
second. 
In the case of a liquid p is constant so that the area of the 
section of the stream is inversely proportional to the velocity, 
and therefore the stream will continuously contract in sec- 
tion in the direction in which the velocity increases and the 
pressure falls, as in fig. 1, also fig 2a. 
In the case of a gas, however, p diminishes as the velocity 
increases and the pressure falls ; so that the area of the sec- 
tion will not be inversely proportional to u, but to nxg and 
will contract or increase according to whether u increases 
faster or slower than p diminishes. 
As already described the value of gu may he expressed in 
terms of the pressure. Making this substitution it appears 
that gib increases from zero as p diminishes from a definite 
value p-i until p = -527^i ; after this gu diminishes to zero as 
p diminishes to zero. A varies inversely as pu and there- 
fore diminishes from infinity as p diminishes from p^ till 
p = •5272:>i ; then A has a minimum value and increases to 
infinity as p diminishes to zero, as in fig. 2. 
The equations contain the definite law of this variation, 
which, for a particular fall of pressure is shown in fig 2 A. 
