THE COMTHERM ON-LINE TECHNICAL MANUAL

DERIVATION OF THE ORIFICE GAS FLOW FORMULA

The derivation of the orifice flow formula is based on the simple principle that the potential energy of the gas is transferred into kinetic energy at the orifice.

1. So potential energy = kinetic energy

mgh = ½ mu²   ..... (1)

u = √(2gh) …… (2)

2. volume flow

q = ua ….. (3)

q = volume flow in cubic metres per. second
a = area of orifice in square metres
u = gas velocity in metres per. Second
m = mass
h = height in metres of gas column
g = gravity acceleration - 9.8066 metres per. sec.²

From (2) & (3)

q = a × √(2gh) ….. (4)

In practice the following units would be used
A = area of orifice in sq. Centimetres
V= volume flow in cubic metres per. Hour

V = {3600 × A × √(2(9.8066)h)} ÷ 10⁴

V = (1.5943 × A × √(h)) ….. (5)

In practice we do not use h as the height of the gas column but cm of water (mbar to all practical purposes)
p = mbar gas pressure. ( Note : 1 mbar = 0.981 cm w.c. )
Ratio of water weight to air rate = 818. At 160°C & 1 Atmosphere pressure. (1013.25 mbar) (760mm Hg)
d = relative density of gas ( air = 1.0)

h = (p/100) × (818/d) ..... (6)

h = 8.18 × p/d ….. (7)

From (4) & (5)

V = 4.559 × A × √(p/d) ….. (8)

The above formula is theoretical and in practice the shape and design of the orifice affects the actual gas flow.
It is necessary to apply a correction factor to the formula depending on the type of orifice, referred to as the coefficient of discharge (C_o).
Fig 1. shows some typical orifice shapes and the nominal coefficient of discharge associated with that shape. Naturally in practice the actual coefficient will depend on the quality and finish of the orifice.

V = 4.559 × A × C_o × √(p/d) ….. (The orifice flow formula)

V = volume flow in cubic metres per. hour
A = area of orifice in square centimetres
p = gas pressure in mbar.
d = relative density of gas (air = 1.0)
Co = orifice coefficient of discharge

For engineers that prefer to use the imperial system of measurements the orifice flow formula is generally expressed as:

V = 1656 × A × C_o × √ (p/d) …..

V= volume flow in cubic feet per. Hour
A = area of orifice in sq. inches
p = gas pressure in inches w.c.
d= specific gravity of gas (air = 1.0)
C_o = orifice coefficient of discharge

SOME USEFUL FACTS :-

1 cubic metre = 35.3146 cubic ft.
1" w.c. pressure = 2.49089 mbar,
relative density (d) of methane = 0.5548
relative density (d) of North Sea natural gas = 0.6064 (typical)
relative density (d) of propane = 1.5257
relative density (d) of butane = 2.0111
weight of water (at 16C) = 998.94 Kg.m(sup>3
weight of air (at 16C & 1013.25 mbar) = 1.2212 Kg.m³

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