ATKINSON'S EQUATION
Before discussing Atkinson's formual/equation . we have to understand the LAW'S OF MINE AIR FRICTION,
then we can easily understand Atkinson's equation.
LAW'S OF MINE AIR FRICTION :
For air to flow between two points - There must be difference of pressure between two points.[The difference of pressure is called ventilating pressure ]
It is the pressure producing ventilation and is expended in overcoming the frictional resistance between the two points.
The frictional resistance depends upon:
1. The dimensions of the airways (Cross section area , Perimeter , Length).
2. Velocity of the airway
3. Nature of the airway.
The relationship between these various factors was given by J. J . Atkinson's in 1854 in the form of following four laws which are called laws of mine air friction.
If Pressure P required to overcome friction- Then
LAW 1 : Pressure(P) directly proportional to the area of the rubbing surface(S).
Where (S)rubbing surface = perimeter(p) × length(l)
LAW 2 : Pressure(P) directly proportional to the square of the velocity of air (v).
LAW 3 : Pressure(P) inversely proportional to the area of the cross section of the airway(A).
LAW 4 : Pressure(P) varies with the degree of roughness of the rubbing surface, OR , in other words , on the coefficient of friction(K) of the airway.
Atkinson's equation
All the above four laws of mine air friction are combined in the Equation, which is known as Atkinson's Equation.
Ventilation pressure overcoming friction or pressure loss due to friction =
" P = KSV²/A "
Where ,
P is in Pascal.
K = coefficient of friction of the airway in Ns²/m⁴.
K= (f × density of air )/8 kg/m³.
S= area of rubbing surface in m²
= Perimeter × Length
= 2(w+h) × l (for rectangular roadway)
V= velocity of air current in m/s.
A= Area of cross section of the airway in m².
Another form of Atkinson's equation
We have- P = KSV²/A
and Q = A×V so, V = Q/A
Then , " P = KSQ²/A³ " ...............
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