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INTRODUCTION

Pitot Static Tube

Prof. J.J Atkinson was the first one who came up with qualitative approach of resistance of mine airways and parameters governing it in 1854.

When air flows through a duct be it a ventilation pipe, a tunnel, a shaft with steel work or timber in it or a stope, the pressure required to force or draw the air through the duct depends not only on the uniform air friction, but also on the size, length, and shape of the duct, side wall of the ducts, nature of the obstruction in it and the velocity and density of the air. All the above factors have been unicorported.

In the flow equation for air at standard density.

According to Atkinson’s equation:

  • The pressure ‘P’ required to overcome friction is directly proportional to the area of the rubbing surface. i.e. P ∝ S
    Where, S = rubbing surface. (m2)
  • The pressure ‘P’ required to overcome friction is directly proportional to the square of the velocity of the air. i.e. P ∝ V2
    Where, V = air velocity. (m/sec)
  • The pressure ‘P’ required to overcome friction is inversely proportional to the area of cross–section of the airways. i.e. P ∝ 1 / A. (m2)
    Where, A = area of cross section.
  • The pressure ‘P’ required to overcome friction varies with the degree of roughness of the rubbing surface. i.e. P ∝ K
    Where, K = coefficient of friction. (kg/m3)

All the above four laws of mine air friction are combined in the following equation, which is known as Atkinsons equation. Atkinson’s equation is also called SQUARE LAW because the pressure drop is proportional to the square of the volume of air-flow rate.

Ventilating pressure overcoming friction or pressure loss due to friction.

P=KSV2/A

since Q=A*V

P=KSQ2/A3

P=(KS/A3)*Q3

P=RQ2

Where, R=KS/A3 = Atkinson’s resistance or frictional resistance of airway. (Ns2/m8)

Q = Quantity of air passing through the ventilation duct. (m3/sec)

K = Atkinson’s friction factor or coefficient of Atkinson’s resistance. (Ns2/m4)

Purpose of Atkinson’s friction factor:

  • In underground mining, development includes making galleries, drifts and panels. Many times, we may seal some part of mining areas. All these aspects are to be taken into account while planning of a mine. At this stage, we have to make an approximation of the resistance that would be encountered and then the subsequent cost of ventilation, the power of fans to be setup, etc.
  • To do estimation of resistance as well as cost of ventilating mine galleries or airways even when their construction has not started.
  • To plan the shortest possible mine airway network with highest effectiveness, determination of coefficient of friction factor is must required.