Page 379 - Civil Engineering Formulas

308 CHAPTER TWELVE

FLOW THROUGH ORIFICES

An orifice is an opening with a closed perimeter through which water flows. Ori-
fices may have any shape, although they are usually round, square, or rectangular.

Orifice Discharge into Free Air
Discharge through a sharp-edged orifice may be calculated from

Q Ca 2gh (12.50)
3
3
where Q discharge, ft /s (m /s)
C coefficient of discharge
2
2
a area of orifice, ft (m )
2
2
g acceleration due to gravity, ft/s (m/s )
h head on horizontal center line of orifice, ft (m)
Coefficients of discharge C are given in engineering handbooks for low
velocity of approach. If this velocity is significant, its effect should be taken
into account. The preceding formula is applicable for any head for which the
coefficient of discharge is known. For low heads, measuring the head from the
center line of the orifice is not theoretically correct; however, this error is cor-
rected by the C values.
The coefficient of discharge C is the product of the coefficient of velocity C v
and the coefficient of contraction C . The coefficient of velocity is the ratio
c
obtained by dividing the actual velocity at the vena contracta (contraction of
the jet discharged) by the theoretical velocity. The theoretical velocity may be
calculated by writing Bernoulli’s equation for points 1 and 2 in Fig. 12.8.
2 2
V 1 p 1 V 2 p 2
Z 1 Z 2 (12.51)
2g w 2g w
With the reference plane through point 2, Z h, V 0, p /w p /w 0, and
1 1 1 2
Z 0, the preceding formula becomes
2
V 2 2gh (12.52)
The coefficient of contraction C is the ratio of the smallest area of the jet,
c
the vena contracta, to the area of the orifice. Contraction of a fluid jet occurs if
the orifice is square edged and so located that some of the fluid approaches the
orifice at an angle to the direction of flow through the orifice.

Submerged Orifices
Flow through a submerged orifice may be computed by applying Bernoulli’s
equation to points 1 and 2 in Fig. 12.9: