Theory of the Orifice Meter
5
and the intrinsic energy may be assumed constant, and the velocity through the orifice may be expressed theoretically by the equation
v = V2ghl, where hi is the head producing the velocity change, expressed in feet, of a column of the fluid at the density existing in the orifice, and g is the acceleration due to gravity. In cases where the ratio of the diameter of the orifice to that of the pipe is not small. and the fluid in the pipe has an appreciable velocity (v1) as it approaches
the orifice, a part of the actual velocity through the orifice is due to this velocity of approach, and the effective total head producing the vis velocity v through the orifice, instead of being hi is H = 114รท2,g From this expression the general equations of flow of liquids are
derived, and are as follows: in units of volume per unit of time (1)
V = K,Ed2
in units of weight per unit
kG
W =K
of time
ji:2 d4
(2)
D4
For most liquids, E may be taken equal to 0.606, and combined with the constants K. and K. in order to form simplified equations as follows:
V = MRd2 W = NRd2Nlica
volume units
(3)
weight units
(4)
In the above equations, d = Diameter of orifice, inches. D = Diameter of pipe, inches. E = Efficiency, or coefficient of discharge. h = Differential pressure, inches of water head. G = Specific gravity of flowing liquid at temperature of flow, re-
ferred to water at Sr F. IC and .if arc constants for volume units. K. and A' are constants for weight units. 1-14
iP
1 D4
mod`
Correction factor for velocit y of approach, from Table 2.
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