440 APPLIED MECHANICS — , "a 
also if the liquid may be considered as incompressible, so that there is no 
internal work due to change of volume, then, if the mass of liquid ¢ 
sidered moves without doing external work or without having exten 
P 2 5 mn 
work done upon it, not only is H=h+—+4 5 at any instant, but H isa_ 
Ww J G 
constant quantity, although the quantities h, v, and P may vary. This 
is known as Bernoulli’s theorem. 3 
374. Flow through a Smooth Pipe of Varying Section.—Fig. 7 
shows a pipe of varying cross section 4 
conveying water from a tank to a 
datum level, say the level of the ; 
sea. The free surface of the water 
in the tank is at a height H above 
datum. Neglecting friction, and 
assuming that the motion of the ss 
water is steady, the total energy of \ 
a 1 lb. mass of the water will be é isi 
the same in every position. The — hy 
table below shows the amounts of es his 
the various forms of energy in a a 
1 lb. mass of the water in four 
different positions. Where P, and 
P, are the pressures of the pe $k at A, and A, respectively, w is the 
Ace T1153 
= Potential | Pressure | Kinetic 
Position. | “per gy. .| Energy. | Energy. Total Energy. 
A H nil nil H : 
? Py 
A P ee H=A 1 
hy Pe % | Haass Ps4%s 
w 29 aS a ag 
B nil nil if hy 
2y 29 
specific weight of the water, v,, v,, and v are the velocities of the water — 
at A,, A,, and B respectively. | 
If a,, 4, and a@ are the areas of the cross sections of the pipe at 
A,, A,, and B respectively, then, if the pipe is running full, the quanti 
of water passing through each cross section in a given time must be the | 
same, hence a0) = dav) = av. | 
375. Venturi Water Meter.—Bernoulli’s theorem has an importauill 
and interesting application in the Venturi water meter, by means of 
which the rate of flow of water through a water main may be deter-— 
mined without interposing any moving part in the flowing wat fe 
Figs. 716-719 * show the main parts of a Venturi meter. There are 
conical pipes AB and CD (Figs. 716 and 717), whose smaller ends are 
connected by a short pipe BC, forming the throat of the meter. This 
combination is introduced so as to form a part of the water main, : 
"* Figs. 716-719 have been prepared from working arene kindly supplied 
by Mr. George Kent, High Holborn, London, 
