AGA – Partially Turbulent

The AGA – Partially Turbulent pipe flow calculator computes volumetric flow rate, pressure drop, or pipe sizing for gas transmission systems operating under partially turbulent flow conditions. Based on the American Gas Association smooth pipe law, this equation accounts for relative pipe roughness using the smooth pipe friction factor formulation. It is moderately conservative compared to other transmission-style equations and is best suited for transmission pipelines where Reynolds Number-dependent friction losses are significant.

Theory and Background

Pipe flow equations for natural gas systems are derived from a general fundamental flow relationship: the volumetric flow through a pipe segment is proportional to the pressure drop across the segment, divided by the combined resistance of the pipe and gas. The higher the pressure drop, the greater the flow rate; the higher the resistance, the lower the flow rate.

Various equations have been developed to reflect specific flow regimes and application conditions. The AGA – Partially Turbulent equation was developed specifically for transmission systems where flow is in the partially turbulent (smooth pipe) regime. Unlike the AGA – Fully Turbulent variant, which uses a fixed or variable wall roughness parameter (rough pipe law), the Partially Turbulent form applies the smooth pipe law to determine the friction transmission factor. This means the friction factor is Reynolds Number-dependent, making the equation sensitive to gas viscosity and flow velocity.

Flow Regimes and Equation Selection

The flow regime in a pipeline is characterized by the Reynolds Number (Re), which describes the ratio of inertial to viscous forces in the flowing gas. At lower Reynolds Numbers, viscous effects dominate (laminar flow). As Reynolds Number increases, flow transitions through partially turbulent to fully turbulent conditions. In the partially turbulent regime, the friction factor depends on both the Reynolds Number and, to a lesser extent, pipe wall roughness — captured here via the smooth pipe law approximation.

The AGA – Partially Turbulent equation is applicable to transmission systems operating in this regime. It is Reynolds Number dependent, meaning results will vary with changes in gas viscosity, flow rate, and pipe diameter. For fully turbulent conditions, the AGA – Fully Turbulent or AGA – Turbulent equations are more appropriate. The Gas Processors Suppliers Association Engineering Data Book notes that when used with an efficiency of approximately 0.90, the Panhandle-A equation (another smooth-pipe transmission equation) approximates the partially turbulent general flow equation, providing a useful cross-check.

Elevation Adjustment

When an elevation difference exists between the inlet and outlet of a pipe segment, and the pressure difference term (ΔP) is expressed as the difference of squared pressures (P₁² − P₂²), the pressure difference term in the flow equation is replaced with an elevation-corrected form:

\Delta P = P_1^2 - e^S \times P_2^2

\Delta P = P_1^2 – e^S \times P_2^2

Where:
S = Elevation compensation factor
e = Napier’s constant, 2.71828
P₁ = Inlet (upstream) pressure, psia
P₂ = Outlet (downstream) pressure, psia

The elevation compensation factor is computed as:

S = \frac{0.0375 \cdot SG \cdot (E_1 - E_2)}{T_F \times Z}

S = \frac{0.0375 \cdot SG \cdot (E_1 – E_2)}{T_F \times Z}

Where:
SG = Specific gravity of gas
E₁ = Pipe inlet (upstream) elevation, ft
E₂ = Pipe outlet (downstream) elevation, ft
T_F = Average gas flowing temperature, °R
Z = Compressibility factor

Equivalent Length Adjustment

When pipe fittings or components with different equivalent diameters are included in a calculation, their equivalent lengths must be adjusted to a common reference diameter. The adjustment ensures that each component produces the same pressure drop under the new reference diameter as it would under its original diameter and length. For all pipe flow equations other than IGT-Improved, Mueller, Panhandle-A, and Panhandle-B, the diameter exponent used is 5.000:

L_{EQ} = L \times \left[\frac{D_{EQ}}{D}\right]^{EXP_D}

L_{EQ} = L \times \left[\frac{D_{EQ}}{D}\right]^{EXP_D}

Where:
L_EQ = Adjusted equivalent length, ft
L = Original length or equivalent length associated with D, ft
D_EQ = Target equivalent diameter, in
D = Original diameter or equivalent diameter associated with L, in
EXP_D = 5.000 for AGA – Partially Turbulent and all other equations not specifically listed

AGA – Partially Turbulent Flow Equation

As implemented in GASCalc, the American Gas Association – Partially Turbulent flow equation applies the smooth pipe law to determine the friction/transmission factor. The general flow equation form is:

Q = 117.38 \times \frac{T_B}{P_B} \times \sqrt{\frac{1}{f}} \times\sqrt{\frac{\Delta P}{SG \times T_F \times L \times Z}} \times D^{2.5} \times E

Q = 117.38 \times \frac{T_B}{P_B} \times \sqrt{\frac{1}{f}} \times\sqrt{\frac{\Delta P}{SG \times T_F \times L \times Z}} \times D^{2.5} \times E

Where:
Q = Volumetric flow rate at the specified base pressure and temperature, ft³/h
T_B = Base temperature, °R
P_B = Base pressure, psia
f = Fanning friction factor
ΔP = Difference of squared pressures across the pipe segment, psia²
SG = Specific gravity
T_F = Average gas flowing temperature, °R
L = Pipe length, ft
Z = Compressibility factor
D = Inside pipe diameter, in
E = Pipe efficiency (0-1)

Pressure Difference Term

For transmission-style calculations where pressures are relatively high, the pressure difference is expressed as the difference of squared pressures:

\Delta P = P_1^2 - P_2^2

\Delta P = P_1^2 – P_2^2

Where:
P₁ = Pipe inlet (upstream) pressure, psia
P₂ = Pipe outlet (downstream) pressure, psia

Reynolds Number

Because the AGA – Partially Turbulent equation uses the smooth pipe law friction factor, which is Reynolds Number dependent, the Reynolds Number must be determined as part of the calculation. GASCalc computes the Reynolds Number using the standard gas pipe flow formulation:

Re = 0.01146 \times \frac{P_B}{T_B} \times \frac{Q \times SG}{D \times \mu}

Re = 0.01146 \times \frac{P_B}{T_B} \times \frac{Q \times SG}{D \times \mu}

Where:
Re = Reynolds Number, dimensionless
P_B = Base pressure, psia
T_B = Base temperature, Rankine
Q = Volumetric flow rate at base conditions, cfh
SG = Specific gravity of the gas, dimensionless
D = Inside pipe diameter, inches
μ = Absolute viscosity of the gas, lbm/ft-sec

The Reynolds Number characterizes the flow regime in the pipe. At lower Reynolds Numbers, viscous forces dominate (laminar flow, Re < 2,000). As Re increases, flow transitions through the partially turbulent regime — where both viscous and inertial effects are significant — and ultimately to fully turbulent flow at very high Reynolds Numbers. The AGA – Partially Turbulent equation is specifically suited to the partially turbulent regime, where the smooth pipe law provides an accurate description of the friction factor. Because Re depends on the flowing conditions (Q, P_AVE, T_F), it is recalculated iteratively by GASCalc as part of the solution process. partially turbulent regime, where both viscous and inertial effects are significant, and ultimately to fully turbulent flow at very high Reynolds Numbers. The AGA – Partially Turbulent equation is specifically suited to the partially turbulent regime, where the smooth pipe law provides an accurate description of the friction factor. Because Re depends on the flowing conditions (Q, P_AVE, T_F), it is recalculated iteratively by GASCalc as part of the solution process.

Smooth Pipe Law Friction Factor

The distinguishing feature of the AGA – Partially Turbulent equation is the use of the smooth pipe law to determine the friction/transmission factor. This is an implicit formulation — the friction factor (1/f)^0.5 appears on both sides — requiring iterative solution:

\sqrt{\frac{1}{f}} = 4\log_{10}\left(\frac{Re}{\sqrt{\frac{1}{f} }} \right) - 0.6

\left(\frac{1}{f}\right)^{0.5} = 4\log_{10}\!\left(\frac{Re}{\left(\frac{1}{f}\right)^{0.5}}\right) – 0.6

Where:
f = Fanning friction factor
Re = Reynolds Number

Because the smooth pipe law friction factor is Reynolds Number dependent, the AGA – Partially Turbulent equation requires knowledge of gas viscosity and the flowing conditions to fully determine the friction factor. GASCalc solves this iteratively as part of the calculation routine.

Gas Properties and Compressibility

The flow resistance in the general pipe flow equation depends on several gas properties: specific gravity (SG), viscosity (μ), and compressibility factor (Z). All equation forms include a specific gravity adjustment. The AGA – Partially Turbulent equation includes compressibility, as implemented in GASCalc, though historically some formulations assumed Z = 1.0 to simplify calculations. Excluding compressibility or assuming it to be unity generally yields conservative results — lower calculated flow rates, higher pressure drops, or larger pipe sizes than the true value.

Pipe Efficiency

All GASCalc pipe flow equations include a hydraulic efficiency term (E). This parameter allows users to tune the equation to better match field-measured results. In most applications, an efficiency less than 1.0 provides a safety factor. If an efficiency below 0.80 or above 1.20 is needed to match field values, this generally indicates either a data entry problem or a poor equation selected for the application.

General Equation Recommendations

The following table summarizes the recommended applications and key characteristics of the AGA – Partially Turbulent equation relative to other commonly used transmission equations. It can be used as a shorthand for what calculations best fit your current case.

No single flow equation accurately reflects all conditions across all gas piping system types. The table below summarizes the go-to recommendations from GASCalc for equation selection by application type:

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

References

• Gas Processors Suppliers Association, Engineering Data Book, Eleventh Edition – FPS, 1998.
• American Gas Association, Gas Engineering and Operating Practices – System Design, GEOP Series Book D-1, 1990.
• Industrial Press, Gas Engineers Handbook, 1965.
• Dejan Brkić, Influence of Friction Factor and Flow Equation on Calculation of Gas Distribution Pipeline Networks.
• B3PE LLC, GASCalc 6.1 Calculation Reference – Pipe Flow, Revision 005, Copyright 2025.

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