Atkinson resistance
Encyclopedia
Atkinson resistance is commonly used in mine ventilation
to characterise the resistance to airflow of a duct of irregular size and shape, such as a mine roadway. It has the symbol
and is used in the square law for pressure drop,
where (in English units)
One atkinson is defined as the resistance of an airway which, when air flows along it at a rate of 1,000 cubic feet per second, causes a pressure drop of one pound-force
per square foot.
The unit is named after J J Atkinson, who published one of the earliest comprehensive mathematical treatments of mine ventilation. Atkinson based his expressions for airflow resistance on the more general work of Chézy
and Darcy
who defined frictional pressure drop as
where
The practicalities of mine ventilation led Atkinson to group some of these variables into one all-encompassing term:
The resulting term is one that can be easily calculated from the results of two simple measurements: a pressure survey by the gauge and tube method and a flowrate survey with a counting anemometer. This is a major strength and is the reason why Atkinson resistance remains in use today.
A complete definition of Atkinson resistance
in more common fluid flow terms is as follows:
in which
in addition to the terms defined above.
Atkinson also defined a friction factor (Atkinson friction factor
) used for airways of fixed section such as shafts. It accounts for Fanning friction factor, density and the constant
and relates to Atkinson resistance by
Despite its weakness with regards to density changes, the use of Atkinson resistance is so widespread in the mining industry that a corresponding term in metric units
has also been defined. It, too, is termed the atkinson resistance but the unit was given the name gaul (for reasons unknown). The earliest known use of the name is a 1971 British Coal memorandum on metrication, VB/CIRC/71(26).
One gaul is defined as the resistance of an airway which, when air (of density 1.2 kg/m³) flows along it at a rate of one cubic metre per second, causes a pressure drop of one pascal
. The gaul has units of N·s2/m8, or alternatively Pa·s2/m6.
It uses the same basic equation as its Imperial counterpart, but with slightly different dimensions
:
where
The metric and Imperial resistances are related by
where
is the standard acceleration of gravity (metres per second squared).
The metric equivalent is now more widely used than the original Imperial definition. Most suppliers quote resistances of flexible temporary ventilation ducts in gauls/100 m and in most mine ventilation software programs, branch resistances are given in gauls.
Underground mine ventilation
Underground mine ventilation provides a flow of air to the underground workings of a mine of sufficient volume to dilute and remove noxious gases . The source of these gases are equipment that runs on diesel engines, blasting with explosives, and the orebody itself...
to characterise the resistance to airflow of a duct of irregular size and shape, such as a mine roadway. It has the symbol
and is used in the square law for pressure drop,where (in English units)
-
is pressure drop (pounds per square foot), -
is the air density in the duct (pounds per cubic foot), -
is the standard air density (0.075 pound per cubic foot), -
is the resistance (atkinsons), -
is the rate of flow of air (thousands of cubic feet per second).
One atkinson is defined as the resistance of an airway which, when air flows along it at a rate of 1,000 cubic feet per second, causes a pressure drop of one pound-force
Pound-force
The pound force is a unit of force in some systems of measurement including English engineering units and British gravitational units.- Definitions :...
per square foot.
The unit is named after J J Atkinson, who published one of the earliest comprehensive mathematical treatments of mine ventilation. Atkinson based his expressions for airflow resistance on the more general work of Chézy
Antoine de Chézy
Antoine de Chézy was a French hydraulics engineer. He is known for the Chézy formula, which concerned the velocity of pipe flow. He died in 1798 after being director of the École nationale des ponts et chaussées for less than a year. His son was the orientalist Antoine-Léonard de Chézy.-References:...
and Darcy
Henry Darcy
Henry Philibert Gaspard Darcy was a French engineer who made several important contributions to hydraulics.-Biography:...
who defined frictional pressure drop as
where
-
is pressure drop, -
is the density of the fluid in question (water, air, oil etc.), -
is the Fanning friction factor, -
is the length of the duct, -
is the perimeter of the duct, -
is the area of the duct, -
is the velocity of the fluid.
The practicalities of mine ventilation led Atkinson to group some of these variables into one all-encompassing term:
- Area and perimeter were incorporated because mine airways are of irregular shape, and both vary along the length of an airway.
- velocity
was replaced by the ratio of flowrate to area (
) because variations in area cause variations in velocity. Area was then incorporated into the denominator of the Atkinson resistance term. - Length of the airway was incorporated. This may have been a step too far, as most of his successors chose to give values of Atkinson resistance in terms of atkinsons per unit length (often 100 or 1000 yards).
- The term
was incorporated, which later authors definitely considered a step too far (e.g. McPherson, 1988). In Atkinson's time not only were all British mines shallow enough that the density of air could be considered constant, but fan design was primitive enough that variations in density would make no measurable difference to the amount of motive power required. Atkinson did not foresee that his methods would be applied several miles underground, where air is 30–50% denser than it is at the surface. Density variations of this magnitude can alter the power consumption of colliery ventilation fans by hundreds of kilowattsWattThe watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
.
The resulting term is one that can be easily calculated from the results of two simple measurements: a pressure survey by the gauge and tube method and a flowrate survey with a counting anemometer. This is a major strength and is the reason why Atkinson resistance remains in use today.
A complete definition of Atkinson resistance
in more common fluid flow terms is as follows:in which
-
is hydraulic radiusManning formulaThe Manning formula, known also as the Gauckler–Manning formula, or Gauckler–Manning–Strickler formula in Europe, is an empirical formula for open channel flow, or free-surface flow driven by gravity...
, -
is hydraulic diameter and -
is Darcy friction factor
in addition to the terms defined above.
Atkinson also defined a friction factor (Atkinson friction factor
Atkinson friction factor
Atkinson friction factor is a measure of the resistance to airflow of a duct. It is widely used in the mine ventilation industry but is rarely referred to outside of it....
) used for airways of fixed section such as shafts. It accounts for Fanning friction factor, density and the constant
and relates to Atkinson resistance by
- where
is Atkinson friction factor and the other terms are as defined above.
Despite its weakness with regards to density changes, the use of Atkinson resistance is so widespread in the mining industry that a corresponding term in metric units
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
has also been defined. It, too, is termed the atkinson resistance but the unit was given the name gaul (for reasons unknown). The earliest known use of the name is a 1971 British Coal memorandum on metrication, VB/CIRC/71(26).
One gaul is defined as the resistance of an airway which, when air (of density 1.2 kg/m³) flows along it at a rate of one cubic metre per second, causes a pressure drop of one pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
. The gaul has units of N·s2/m8, or alternatively Pa·s2/m6.
It uses the same basic equation as its Imperial counterpart, but with slightly different dimensions
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
:
where
-
is pressure drop (pascals), -
is the air density in the air duct (kilograms per cubic metre), -
is the standard air density (1.2 kilograms per cubic metre), -
is the resistance of the air path (gauls), -
is the rate of flow of air (cubic metres per second).
The metric and Imperial resistances are related by
where
is the standard acceleration of gravity (metres per second squared).The metric equivalent is now more widely used than the original Imperial definition. Most suppliers quote resistances of flexible temporary ventilation ducts in gauls/100 m and in most mine ventilation software programs, branch resistances are given in gauls.
Further reading
- Atkinson, J J, Gases met with in Coal Mines, and the general principles of Ventilation Transactions of the Manchester Geological Society, Vol. III, p.218, 1862
- McPherson, M J, Subsurface Ventilation and Environmental Engineering, Chapman & Hall, 1993, ISBN 0412353008