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.
Potential energy = kinetic energy
mgh = ½ mu² ..... (1)
u = √(2gh) …… (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 second²
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 (Co).
V = 4.559 × A × Co × √(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
Imperial System
For engineers that prefer to use the imperial system of measurements, the orifice flow formula is generally expressed as:
V = 1656 × A × Co × √(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)
Co = 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 16°C) = 998.94 Kg/m³
- Weight of air (at 16°C & 1013.25 mbar) = 1.2212 Kg/m³