Page 120 - Air and gas Drilling Field Guide 3rd Edition

5.5 Compressor Shaft Power Requirements 111

For engineering calculations, Equation (5-1) is often simplified to the form
P R e T
¼ (5-11)
S g
g
R u
R e ¼ ; (5-12)
m w
where R e is the engineering gas constant for API standard condition air
(53.36 lb-ft/lb- R, 29.31 N-m/N-K) and S g is the specific gravity of the particular

gas used (for API standard condition air S g ¼ 1.0).

Equation (5-11) can be simplified further by defining R (lb-ft/lb- R, N-m/N-K)
as the gas constant for any specified gas (e.g., air, natural gas, nitrogen). There-
fore, the gas constant for any gas is approximately
R e
R g ¼ : (5-13)
S g
Substituting Equation (5-13) into Equation (5-11) yields
P
¼ R g T: (5-14)
g
The specific volume and specific weight of a gas are related by
1
v ¼ : (5-15)
g
Substituting Equation (5-15) into Equation (5-14) yields
Pv ¼ R g T (5-16)

or, specifically,
Pv 1 ¼ R g T 1 : (5-17)
Using the definitions for a polytropic process given earlier and Equation (5-17),
then Equation (5-10) can be reduced to
k 1
2 3
ð 2
P 2 k 7
R g T 1 6
Pdv ¼ 4 15: (5-18)
1 k 1 P 1
Again, using the definitions for a polytropic process and Equation (5-16), then
a general relationship between P and T can be obtained. This is
k 1

P 2 k T 2
¼ : (5-19)
P 1 T 1
Substituting Equation (5-19) into Equation (5-18) yields
ð 2
R g T 1 T 2 R g
Pdn ¼ 1 ¼ ðT 2 T 1 Þ: (5-20)
1 k 1 T 1 k 1