CHAPTER XXVIII 
GENERAL PRINCIPLES OF HYDRA ULICS 
373. Energy of Water—Bernoulli’s Theorem.—In connection with 
hydraulics, the total energy in a given quantity of water consists of three 
_ parts: (1) The potential energy, or the energy due to the height through 
_ which it may fall, or the energy due to its position ; (2) the pressure 
energy, or the energy due to the pressure which the water exerts on the 
- sides of the containing vessel or pipe; (3) the ‘inetic energy, or the 
_ energy due to its motion. 
In what follows, the energy of one pound weight of the water will be 
considered. 
(1) The potential energy of 1 lb. of water which is capable of falling 
through a height of / feet is h foot-pounds. ER 
(2) The pressure energy of 1 Ib. of water which exerts a pressure of 
_ P lbs. per square foot is P/w, where w is the weight of a cubie foot of 
the water. For if 1 cubic foot of water be admitted into a cylinder 
which is fitted with a piston having an area of 1 square foot, then the 
piston will move through a distance of 1 foot ; and if the water exerts all 
the time a pressure of P Ibs. per square foot, the work done by the cubic 
foot of water will be P foot-pounds. Therefore the work done by 1 |b. 
_ of water is P/w foot-pounds. It is important to notice that in proving 
that the pressure energy of 1 Ib. of water is P/w, it is assumed that the 
_ full pressure P is kept up during the time that the 1 Ib. of water is being 
used to do the work P/w. 
(3) The kinetic energy of 1 lb. of water which is moving ;with a 
velocity of v feet per second is v?/2q. ! 
A portion of water may have all three of the above forms of energy, 
but one, two, or all of them, may be zero. Also, the energy in one form 
may be so small compared with the energy in another form, that it may 
be neglected. For example, in the transmission of power ‘by water 
pressure amounting to, say, 1000 Ibs. per square inch, the water will have 
a velocity seldom exceeding 5 feet per second. Here the pressure 
energy is a ft.-Ibs., and the kinetic energy when the 
velocity is 5 feet per second is 5 eA Oe = 0°39 ft.-Ib., a quantity so small 
compared with 2311 that it may be neglected. : 
If H is the total energy in one pound weight of liquid, then 
wonety S 
w 22g 
Tf all the particles of a 1 lb. mass of water are moving with the same 
velocity at any instant, and there is no frictional resistance to the motion, 
439 
