448 APPLIED MECHANICS 
vertex is at the contracted section, and whose directrix is horizontal and 
at a distance c?h above the vertex. ; 
If Q is the actual volume of water flowing through the orifice per 
second, then Q=av=kAc ,/2gh=CA ,/2gh, where C (which is equal to 
ck) is called the coefficient of discharge, and is the ratio of the actual dis- 
charge to the theoretical discharge. By the theoretical discharge is 
meant the discharge neglecting friction and the contraction of the jet. ~ 
The coefficients *, c, and C are called the hydraulic coefficients for 
an orifice. The coefficient C is the one which is of most importance in 
practice, and it is the one which is most easily determined by direct — 
measurements. Taking k = 0°63, and c= 0:97, then C = 0°63 x 0:97 = 0-61, 
which agrees with the mean value of C, as determined directly from ~ 
numerous experiments with sharp-edged orifices. 
384. Miner’s Inch.—In selling water in mining districts the water 
is frequently measured by delivering it through rectangular orifices 
under a small but constant head. The miner’s inch is the quantity of 
water delivered per minute through an orifice 1 inch square, in a vertical 
plane, under a head which varies in different localities from 6 to 9 
inches, measured to the centre of the orifice. With a head of 6} inches, 
measured to the centre of the orifice, the miner’s inch is equivalent to 
about 14 cubic feet of water per minute. 
385. Entire and Partial Suppression of Contraction of Jet.— 
Fig. 731 shows the form of the jet issuing through a sharp-edged orifice 
in a plate, the thickness of which is such 
that its outside face is in the plane of 
the smallest section of the jet. The NG _ NJ ; 
space shown in black is the empty space Sa — 
between the surface of the orifice and = 
that of the jet. It is obvious that if 
EE ———— 
eae a i 
the space shown in black be filled up, SSZZ== SS ; 
or if the orifice be shaped to the natural ia 
form of the jet within the plate, the ; 
smallest diameter of the jet will then be Fra. "731. FIG. 32, 
the same as the smallest diameter of the orifice, and the coefficient of con- 
traction will become unity. 
Rounding the inside edge of the orifice to a greater or less extent, as 
shown in Fig. 732, will evidently have the effect of diminishing the con- 
traction of the jet, and therefore of increasing the coefficient of contraction. 
An orifice which is to be used for the measurement of the water 
delivered by it should be sharp edged and of the form shown in Fig. 729, 
because the coefficient of contraction for an orifice with a rounded edge is 
uncertain, varying with the amount of rounding. 
386. Loss of Energy or Head.—When water is discharged through 
an orifice under a head h, it has been shown that the actual velocity at 
the vena contracta is equal to c ,/2gh, where c is the coefficient of velocity. 
The energy in 1 lb. of water at the vena contracta is therefore equal to ch. 
If the water lost no energy in reaching and passing through the orifice, its 
. energy at the vena contracta would be h. The loss of energy per Ib. 
of water is therefore h —c?h=h(1-—c?). This is also the expression for 
the loss of head, that is to say, the head which would produce the actual 4 
