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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.

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