GENERAL PRINCIPLES OF HYDRAULICS 447 
i “382, Influence of Velocity of Approach.—In the preceding Article 
th total energy per pound of the water at the free surface in the tank in 
g 127 was assumed to be h+h, Nel y the water being assumed to be 
ui ‘rest, But since the water is “iho at the orifice, the water in the 
tank above the orifice must have a downward velocity, called the velocity 
of oe. Let a denote the area of the cross section of the jet, and 
A the area of the free surface of the water in the tank, then if v is the 
velocity of the jet, and V the downward velocity at the free surface in 
re 2 
_ the tank, the energy per pound at the free surface is hehe ey, 
. 2 
‘and the energy of the jet per pound is byte also v=") hence 
ce eee res il fn Maat ——., 
; 29 * 997A? 2g 1 (4): 
Generally a/A is so smal] that a?/A? may be neglected. 
383. Flow through Sharp-edged Orifices.— When water issues 
h a sharp-edged orifice (Fig. 729) in the side or bottom of a tank 
‘it is found that the jet contracts to a minimum section, called the 
contracted section or vena contracta, which is a little distance in front of 
_ the orifice. This contraction of the jet is due to the fact 
that the water particles in approaching the orifice are not 
_ moving in parallel lines. For a circular orifice the 
_ distance of the contracted section in front of the sharp edge S===== 
of the orifice is about half the diameter of the orifice. The 
ratio of the area of the contracted section of the jet to the 
_ area of the orifice is called the coefficient of contraction. If ye, 799, 
_ A is the area of the orifice, @ the area of the contracted 
; __ Section, and & the coefficient of contraction, then a=kA. The value of 
_k for sharp-edged orifices may be taken as 0°63, but it varies slightly with 
_ the shape of the orifice and the head of water. The value of & in 
different cases may be determined from direct measurements of the jet. 
On account of friction the velocity of the water at the contracted 
_ section of the jet is less than ,/2gh, given by Torricelli’s theorem 
_ (Art. 381), and the ratio of the. actual 
velocity to the theoretical velocity is called ==={--7F 
the coefficient of velocity. If v is the actual 
_ velocity, and ¢ the coefficient of velocity, — 
then v=c,/2gh. An average value of ¢ is 
_ about 0°97. The value of ¢ may be found 
from observations on the path of the jet 
(Fig. 730). If the face of the orifice is 
vertical, then in ¢ seconds a particle of water Fia. 730. 
will travel a horizontal distance «=vt from 
the contracted section, and it will in the same time fall a distance 
y=4gt?. Hence oa act, and aE ot It will be seen from 
the equation #?=4c*hy that the path of the jet is a parabola whose 
> 
