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<p>Reference: Richard W. Miller's <u>Flow Measurement Engineering Handbook</u> - Third Edition<br />\
<img src='images/orifice.png' ALT='Reference' border='0'><br />\
d = F<sub>ad</sub>d<sub>measure</sub> = [1 + &alpha;<sub>pe</sub>(T<sub>F</sub> - 68)]d<sub>measure</sub> (Eq. 9.51)<br />\
D = F<sub>aD</sub>D<sub>measure</sub> = [1 + &alpha;<sub>pe</sub>(T<sub>F</sub> - 68)]D<sub>measure</sub> (Eq. 9.50)<br />\
S<sub>M</sub> = (G<sub>b</sub>q<sub>v</sub>)/(N<sub>vG</sub>D<sup>2</sup>sqrt(F<sub>p</sub>)sqrt(G<sub>f</sub>)sqrt(h<sub>w</sub>)) (Table 9.23)<br />\
R<sub>D</sub> = [17,902.78(F<sub>p</sub>G<sub>f</sub>)/(&mu;<sub>cP</sub>DN<sub>vG</sub>)]q<sub>v</sub> (Table 9.20)<br />\
 &beta;<sub>0</sub> = [1 + (0.6/S<sub>M</sub> + 0.06)<sup>2</sup>]<sup>-1/4</sup> for R<sub>D</sub> &lt; 200,000 (Table 9.28)<br />\
&beta;<sub>0</sub> = [1 + (0.6/S<sub>M</sub>)<sup>2</sup>]<sup>-1/4</sup> for R<sub>D</sub> &gt; 200,000  (Table 9.28)<br />\
C = C&#8734; + b/R<sup>n</sup><sub>D</sub> (Eq. 9.49)<br />\
&beta;<sub>1</sub> = [1 + (C<sub>0</sub>/S<sub>M</sub>)<sup>2</sup>]<sup>-1/4</sup> (Eq. 9.83)<br />\
&beta;<sub>n</sub> = [1 + (C<sub>n-1</sub>/S<sub>M</sub>)<sup>2</sup>]<sup>-1/4</sup> (Eq. 9.84)<br />\
d<sub>measure</sub>= (&beta;D)/F<sub>ad</sub> (Eq. 9.51)\
</p>\
<p>\
<p><em>List of Symbols:</em></p>\
&alpha;<sub>p</sub>: coefficient of thermal expansion for pipe material in in/(in <sup>o</sup>F)<br />\
&alpha;<sub>pe</sub>: coefficient of thermal expansion for primary element material in in/(in <sup>o</sup>F)<br />\
&beta;<sub>0</sub>: beta approximation<br />\
&beta;: beta ratio<br />\
b: Reynolds number correction term (Table 9.1)<br />\
C&#8734;: discharge coefficient at an infinite Reynolds number<br />\
D: pipe internal diameter (ID) at flowing conditions<br />\
D<sub>measure</sub>: normal pipe ID as measured at ambient conditions<br />\
d: primary element bore at flowing conditions<br />\
d<sub>measure</sub>: primary element bore measured at ambient conditions<br />\
F<sub>aD</sub>: pipe thermal expansion factor<br />\
F<sub>ad</sub>: orifice thermal expansion factor<br />\
F<sub>p</sub>: correction for liquid compressibility (assumed 1)<br />\
G<sub>b</sub>: specific gravity at base conditions (Table 9.1)<br />\
G<sub>f</sub>: specific gravity at base conditions, uncorrected for pressure<br />\
h<sub>w</sub>: differential pressure in inches of water at 68<sup>o</sup> F, 14.7 PSIA<br />\
&mu;<sub>cP</sub>: absolute viscosity in centipoises<br />\
N<sub>vG</sub>: N factor for flowing volume with specific-gravity determination, liquids, determined by flow rate units <sub>v</sub><br />\
q<sub>v</sub>: volumeric flow rate calculated at standared (gas) or base (liquid) temperature and pressure, where <sub>v</sub> is units<br />\
R<sup>n</sup><sub>D</sub>: Reynolds number exponent n is constant and depends on the primary element (Table 9.1)\
</p>";
}