446 APPLIED MECHANICS 
the total force transmitted to each end of the tube will be 
| "wadxw*x  waw* | ; wan 7? 
0 g J Jo 
ww 
and the intensity of the pressure will be 5} . 
381. Torricelli’s Theorem.—Fig. 727 shows a tank containing 
liquid with jets issuing at a depth h below the 
free surface of the liquid and at a height h, above 
a datum line AB. 
Let P) be the pressure of the atmosphere, and 
v the velocity of the liquid as it leaves the orifice {i 
and issues into the atmosphere. At the free sur- -( 
face of the liquid in the tank the potential energy 
is h+h,, the pressure energy is Po/w, and the h . 
kinetic energy is zero, per pound of "liquid. The a H Be 
pressure of the liquid in the jet is P,, and its _ 
pressure energy is therefore P,/w, the potential FIG. Tats 
energy is h,, and the kinetic energy is v*/29g, per pound. If the loss © 
of energy due to friction be neglected, then 4 
h+h +t, 0=h eis % and thoselies leas 
Peg eke Oe ~ 2° 
That is, the velocity of the issuing liquid is that which a body would 
acquire in falling freely from rest under the action of gravity through a 
height equal to the depth of the orifice below the free surface of the 
liquid. If the jet be directed vertically upwards, as shown to the left in 
Fig. 727, the liquid will rise to nearly the level of the free surface of 
the liquid i in the tank. It will not quite reach the level of the free 
surface of the liquid, on account of the air resistance and the friction of 
the liquid on the sides of the orifice or nozzle. 
If the jet enters into a second tank (Fig. 728) in which the hq 
stands at a height h, above the jet, then the pres- _ 
sure of the liquid in ' the jet is P) + whe, and if v 
is its velocity, the total energy of the jet per 
2 
pound of liquid is h, pone ae a and as be- 
~ 
fore, neglecting friction, 
ee rh os 
+ 99? 
yw ‘ A 
and therefore h—h, 22g , which shows that the 
velocity is that due to a head equal to the 
difference of level of the liquid in the two tanks, and is independent of . 
the depth of the jet below the free surface of the liquid in the second 
tank. a 
In like manner it follows that if the jet enters a. vessel in which 
there is a partial vacuum, such as a steam-engine condenser, the head - 
due to the pressure in this vessel will be negative and easel to, say, — hg, 
2 
then h +h, == 
2g" 
hth +2240 = hy + 
