__General
Gas Flow Equation:__

The General Gas Flow equation, is also called the Fundamental Gas Flow
equation, for the steady-state __isothermal flow__ in a gas pipeline is the basic equation
for relating the pressure drop with flow rate.

The most common form of this equation in the U.S. Customary System (USCS) of units is given in terms of the pipe diameter,
gas properties, __pressures__, temperatures, and flow rate as follows.

Where,

Q = gas flow rate,
measured at standard conditions, ft^{3}/day (SCFD)

f = friction factor,
dimensionless

P_{b} = base pressure,
psia

T_{b}*
*= base
temperature, °R (460 + °F)

P_{1} = upstream
pressure, psia

P_{2} = downstream
pressure, psia

G = gas gravity (air
=
1.00)

T_{f}*
*= average gas
flowing temperature, °R (460 + °F)

L = pipe segment
length, mile

Z = gas
compressibility factor at the flowing temperature, dimensionless

D = pipe inside
diameter, inch

It must be noted that for the pipe segment from
section 1 to section 2, the gas temperature T_{f} is assumed to be
constant (isothermal flow).

__In SI units, the General Flow equation is stated as
follows:__

Where,

Q = gas flow rate,
measured at standard conditions, m^{3}/day

f = friction factor,
dimensionless

P_{b} = base pressure,
kPa

T_{b}= base
temperature, K (273 + °C)

P_{1} = upstream
pressure, kPa

P_{2} = downstream
pressure, kPa

G = gas gravity (air
=
1.00)

T_{f}= average gas
flowing temperature, K (273 + °C)

L = pipe segment
length, km

Z = gas
compressibility factor at the flowing temperature, dimensionless

D = pipe inside
diameter, mm

- Above flow equation relates the
capacity (flow rate or throughput) of a pipe segment of
length L, based on an
upstream pressure of P
_{1}and a downstream pressure of P_{2}.**It is assumed that there is no elevation difference****between the upstream and downstream points; therefore, the pipe segment is****horizontal.**

- We see that for a pipe segment of length L and diameter D, the gas flow rate Q (at standard conditions) depends on several factors. Q depends on gas properties represented by the gravity G and the compressibility factor Z.

- If the gas gravity is increased
(heavier gas), the flow rate will decrease.
Similarly, as the compressibility factor Z increases, the flow rate will
decrease. Also,
as the gas flowing temperature T
_{f}increases, throughput will decrease. Thus, the hotter the gas, the lower the flow rate will be. Therefore, to increase the flow rate, it helps to keep the gas temperature low. The impact of pipe length and inside diameter is also clear. As the pipe segment length increases for given pressure P_{1}and P_{2}, the flow rate will decrease. On the other hand, the larger the diameter, the larger the flow rate will be.

- The term P
_{1}^{2}– P_{2}^{2}represents the driving force that causes the flow rate from the upstream end to the downstream end. As the downstream pressure P_{2}is reduced, keeping the upstream pressure P_{1}constant, the flow rate will increase. It is obvious that when there is no flow rate, P_{1}is equal to P_{2}. It is due to friction between the gas and pipe walls that the pressure drop (P_{1}–P_{2}) occurs from the upstream point 1 to downstream point 2. The friction factor f depends on the internal condition of the pipe as well as the type of flow (laminar or turbulent).

Sometimes the General Flow equation is represented
in terms of the transmission factor F instead of the
friction factor f. This form of
the equation is as follows in USCS Units.

Where, the transmission factor F and
friction factor f are related by

__Then General Flow equation in SI Units,__

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