# Orifice Plate Mass Flow Formulas - Crane TP410

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#### Robert S.

Short story: I'm trying to compare the result of mass flow formulas using ISO 5167 formulas and formulas from Cranes TP410.

Long Story: I can't figure out where "1891" comes from in the orifice plate mass flow formula documented in Cranes - Technical Paper 410 "Flow of Fluids through Valves, Fittings, and Pipe". I have the 12/01 reprint and in that version the formula is under the section of equations labeled 3-22.

For compressible fluids, the formula is given as

W = 1891 * Y * d1^2 * C * SQRT (dP / V)

W - Mass Flow, lb/hr
Y - Gas Expansion Factor, unitless
C - Discharge Coefficient, unitless
dP - Diff Press across orifice, lb/in^2
V - Specific Volume, ft^3/lb (aka 1/density)
d1 - in, (page 7 refers to the i.d. of the pipe rather than the orifice which is a little confusing itself)

The best guess I have is the following:

d1^2 is the remnant of the Area formula
A = (pi * d^2)/4, so I'm guessing pi/4 is factored into the 1891 number.

To match up units under the SQRT the dP has to be multiplied by 144, so I'm guessing sqrt(144) is also factored into the 1891 number.

To get at density (i.e. compensate for Pressure and Temperature) I end up with the Universal Gas Constant
(1544 (lb * ft^2 abs * ft^3) / (lb * mol * °R)
in the numerator under the SQRT, so I'm guessing sqrt(1544) is also factored into the 1891 number.

At this point I have (pi/4) * SQRT(144 * 1544) but that only comes out to 370.3.

Robert

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#### raju

DP in psi, density in lb/ft3, diameter in inch
=pi()/4 * 144 * sqrt(2*144*32.2)
=1891