Page 184 - Standard Handbook Of Petroleum & Natural Gas Engineering

Fluid Mechanics 169

The governing equation for the pressure within a fluid at any depth h is
dP = pgdh (2-46)

where p is the fluid density in mass per unit volume, and g is the acceleration due to
gravity. In engineering calculations it is often convenient to replace the quantity pg
with y, the specific weight, which is a measure of the weight of the fluid per unit
volume.
If y can be considered to be constant, the fluid is said to be incompressible and
Equation 2-46 can be solved to yield

P = P,, + y(h - h,) (2-47)

where h,) is some reference depth, h is depth increasing downward, and P, is the
pressure at h,. In a gas the specific weight of the fluid is a function of pressure and
temperature. The concept of an ideal or perfect gas as one in which the molecules
occupy no volume and the only intermolecular forces are due to intermolecular
collisions leads to the ideal gas law:

y=- PS (2-48)
RT

where P is the absolute pressure in pounds per square foot, T is the temperature in
degrees Rankine, S is the specific gravity (the ratio of the density of the gas in
question to the density of air at standard conditions), and R is Boltzman's constant
(53.3 ft-lb/lb-OR). Under the assumption of an ideal gas at constant temperature,
Equation 2-46 can be solved to yield

(2-49)

If the gas behavior deviates markedly from ideal, the real gas law can be written as

y=- Ps (2-50)
ZRT
where Z is an empirical compressibility factor that accounts for nonideal behavior
(See Volume 2, Chapter 5).
Substituting the real gas law into Equation 2-47 yields

ZT S
-dP = -dh (2-51)
P R
Equation 2-51 can be integrated under the assumption that Z and T are constant to
yield Equation 2-52, or, if extreme accuracy is required, it is necessary to account for
variations in Z and T and a numerical integration may be required.

(2-52)