Page 131 - Air and Gas Drilling Manual

Chapter 4: Compressors 4-17
dv
2
2
−
k
Pdv
= − P v
1
1
k
v
∫ 1
∫ 1

The right-hand side of the above equation can be integrated to yield (4-9)
  v  k −1 
Pv
2
− ∫ Pdv = 1 1   1  − 1  (4-10)
1 k −1   v  
 2 
For engineering calculations, Equation 4-1 is often simplified to the form
P = R a T
γ S (4-11)
g
R
R = u (4-12)
a m
w
where R a is the gas constant for API standard condition air (53.36 ft-lb/lb-˚R),
S g is the specific gravity of the particular gas used (for API standard condition
air S g = 1.0).
Equation 4-11 can be further simplified by defining, R (ft-lb/lb-˚R), as the gas
constant for any specified gas (e.g., air, natural gas, nitrogen, etc.). Therefore, the
gas constant for any gas is approximately
R
R = a
S g (4-13)
Substituting Equation 4-13 into Equation 4-11 yields
P = R T (4-14)
γ
The specific volume and specific weight of a gas are related by
v = 1 (4-15)
γ

Substituting Equation 4-15 into Equation 4-14 yields
Pv = R T (4-16)

or, specifically