IGE Rec 3 – Low Pressure

The IGE Rec 3 – Low Pressure pipe flow calculator computes volumetric flow rate, pressure drop, or pipe sizing for low-pressure gas distribution systems operating at or below 1.1 psig (75 mBar). Developed by the British Gas Engineers Institute and documented in Standard IGE/TD/3, this equation is a modified version of the IGE Rec 3 – General (Medium Pressure) formulation adapted for the low-pressure regime. It uses a polynomial smooth pipe law friction factor that is Reynolds Number dependent and expresses pressure difference as a simple linear drop rather than a difference of squared pressures.

This equation is applicable only to systems operating at pressures at or below 1.1 psig (75 mBar); for higher-pressure distribution systems use the IGE Rec 3 – Medium Pressure or IGE Rec 3 – General equations.

Theory and Background

All gas pipe flow equations are ultimately derived from a general fundamental relationship: volumetric flow through a pipe segment is proportional to the pressure drop across it, divided by the combined resistance of the pipe geometry and gas properties. The greater the pressure drop, the higher the flow; the greater the resistance, the lower the flow.

The Institution of Gas Engineers and Managers (IGEM) Recommendation 3 series provides three related equations tailored to different pressure bands in British gas distribution practice. The three variants are:

At low pressures (at or below approximately 1.1 psig), the difference between gauge and absolute pressures is relatively large, meaning the squared-pressure form (P₁² − P₂²) can introduce error. The Low Pressure variant therefore uses a simple linear pressure difference (P₁ − P₂), which is a more appropriate approximation in this regime. This is the key structural distinction between the Low Pressure and Medium Pressure variants of the IGE Rec 3 equation.

Reynolds Number Dependence

Like the Medium Pressure variant, the Low Pressure equation is Reynolds Number dependent — the smooth pipe law friction factor is a function of the Reynolds Number. This means results are sensitive to gas viscosity, flow rate, and pipe diameter. The friction factor is computed via a polynomial approximation to the smooth pipe curve, making the equation explicit (non-iterative) while still capturing the Reynolds Number dependence of the partially turbulent regime.

Elevation Adjustment

When an elevation difference exists between the inlet and outlet of a pipe segment where the pressure difference is expressed as P₁² − P₂², the ΔP term is replaced with an elevation-corrected form. For the IGE Rec 3 – Low Pressure equation the pressure difference is expressed linearly (P₁ − P₂), so the standard elevation adjustment using the S-factor applies to the squared-pressure equations (Medium Pressure and General variants). Users should consult the elevation adjustment documentation within GASCalc when elevation differences are significant in low-pressure applications.

Equivalent Length Adjustment

When pipe fittings or components with different equivalent diameters are combined in a single calculation, their equivalent lengths are adjusted to a common reference diameter. For the IGE Rec 3 – Low Pressure equation, the diameter exponent used in this adjustment is 5.000 (the default for all equations other than IGT-Improved, Mueller, Panhandle-A, and Panhandle-B):

L_{EQ} = L \times \left[\frac{D_{EQ}}{D}\right]^{5.000}

L_{EQ} = L \times \left[\frac{D_{EQ}}{D}\right]^{5.000}

Where:
L_EQ = Adjusted equivalent length, feet
L = Original length or equivalent length associated with D, feet
D_EQ = Target equivalent diameter, inches
D = Original diameter or equivalent diameter associated with L, inches

IGE Rec 3 – Low Pressure Flow Equation

As implemented in GASCalc, the Institution of Gas Engineers Recommendation 3 – Low Pressure flow equation is:

Q = 165.94 \times \frac{T_B}{P_B^{0.5}} \times \left(\frac{1}{f_{spl}}\right)^{0.5} \times \left(\frac{\Delta P}{SG \times T_F \times L \times Z}\right)^{0.5} \times D^{2.5} \times E

Q = 165.94 \times \frac{T_B}{P_B^{0.5}} \times \left(\frac{1}{f_{spl}}\right)^{0.5} \times \left(\frac{\Delta P}{SG \times T_F \times L \times Z}\right)^{0.5} \times D^{2.5} \times E

Where:
Q = Volumetric flow rate at the specified base pressure and temperature, cfh
T_B = Base temperature, Rankine
P_B = Base pressure, psia
f_spl = Smooth pipe law friction factor, dimensionless
ΔP = Pressure drop across the pipe segment (linear), psia
SG = Specific gravity, dimensionless
T_F = Average gas flowing temperature, Rankine
L = Pipe length, feet
Z = Compressibility factor, dimensionless
D = Inside pipe diameter, inches
E = Pipe efficiency, decimal

Pressure Difference Term

A critical distinction of the Low Pressure variant is that ΔP is expressed as a linear pressure difference rather than a difference of squared pressures:

\Delta P = P_1 - P_2

\Delta P = P_1 – P_2

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

This contrasts with the Medium Pressure and General variants, which use ΔP = P₁² − P₂². The linear form is appropriate at low pressures where the absolute pressure values are small relative to atmospheric pressure, and the squared-pressure approximation would introduce meaningful error.

Smooth Pipe Law Friction Factor

The smooth pipe law friction factor is computed using the same polynomial approximation as the IGE Rec 3 – Medium Pressure equation. The transmission factor (1/f_spl)^0.5 is expressed as an explicit polynomial function of the logarithm of the Reynolds Number, avoiding the iterative solution required by the AGA Partially Turbulent smooth pipe law:

\left(\frac{1}{f_{spl}}\right)^{0.5} = 14.7519 + 3.5657X + 0.0362X^2

\left(\frac{1}{f_{spl}}\right)^{0.5} = 14.7519 + 3.5657X + 0.0362X^2

Where the Reynolds Number argument X is defined as:

X = \log_{10}(Re) - 5

X = \log_{10}(Re) – 5

Where:
f_spl = Smooth pipe law friction factor, dimensionless
X = Shifted log-Reynolds Number argument, dimensionless
Re = Reynolds Number, dimensionless

Because X is centered on log₁₀(Re) = 5 (i.e., Re = 100,000), the polynomial is well-conditioned for the Reynolds Numbers typical of low-pressure distribution systems. The quadratic polynomial form provides a compact, accurate approximation to the smooth pipe law curve across the applicable range without requiring iterative solution.

Comparison: IGE Rec 3 Low Pressure vs. Medium Pressure

The Low Pressure and Medium Pressure variants share the same friction factor formulation but differ in their pressure difference expression and leading coefficient, reflecting the different physical regimes. The Medium Pressure form uses:

Q = 117.3 \times \frac{T_B}{P_B} \times \left(\frac{1}{f_{spl}}\right)^{0.5} \times \left(\frac{\Delta P}{SG \times T_F \times L \times Z}\right)^{0.5} \times D^{2.5} \times E \quad (\Delta P = P_1^2 - P_2^2)

Q = 117.3 \times \frac{T_B}{P_B} \times \left(\frac{1}{f_{spl}}\right)^{0.5} \times \left(\frac{\Delta P}{SG \times T_F \times L \times Z}\right)^{0.5} \times D^{2.5} \times E \quad (\Delta P = P_1^2 – P_2^2)

The Low Pressure form substitutes the linear ΔP = P₁ − P₂ and adjusts the leading coefficient and base pressure exponent accordingly (165.94 and P_B^0.5 vs. 117.3 and P_B). This ensures dimensional consistency when switching from squared-pressure to linear-pressure units. Users should select the appropriate variant based solely on the operating pressure of the system being analyzed.

Gas Properties and Compressibility

The equation includes terms for specific gravity (SG), average flowing temperature (T_F), and compressibility factor (Z). At the low pressures applicable to this equation, compressibility deviates very little from unity (Z ≈ 1.0), and in many practical low-pressure distribution calculations compressibility is set to 1.0 with negligible error. However, GASCalc supports full compressibility calculation if a compressibility factor method is specified in the Base Conditions screen.

Pipe Efficiency

All GASCalc pipe flow equations include a hydraulic efficiency term (E) to allow tuning against field measurements. For most distribution applications an efficiency of 1.0 or slightly below is appropriate. If an efficiency below 0.80 or above 1.20 is required to match field values, this typically indicates either a data entry issue or a poor equation choice for the application.

Equation Variables

Unless otherwise noted, all variables use the following base units:
D = Inside pipe diameter, inches
D_EQ = Equivalent diameter associated with L_EQ, inches
E = Pipe efficiency, decimal
E₁ = Pipe inlet (upstream) elevation, feet
E₂ = Pipe outlet (downstream) elevation, feet
f_spl = Smooth pipe law friction factor, dimensionless
L = Pipe length, feet
L_EQ = Equivalent length, feet
μ = Absolute viscosity, lbm/ft-sec
ΔP = Pressure drop across a pipe segment, psia (linear)
P₁ = Pipe inlet (upstream) pressure, psia
P₂ = Pipe outlet (downstream) pressure, psia
P_ATM = Average atmospheric pressure, psia
P_AVE = Average pressure along the pipeline segment, psia
P_B = Base pressure, psia
Q = Volumetric flow rate at the specified base pressure and temperature, cfh
Re = Reynolds Number, dimensionless
SG = Specific gravity, dimensionless
T_B = Base temperature, Rankine
T_F = Average gas flowing temperature, Rankine
X = Shifted log-Reynolds Number argument = log₁₀(Re) − 5, dimensionless
Z = Compressibility factor, dimensionless

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

References

• The Institution of Gas Engineers and Managers, Steel and PE Pipelines For Gas Distribution, Recommendations on Transmission and Distribution Practice, Standard IGE/TD/3 Edition 4, 2003.
• Gas Processors Suppliers Association, Engineering Data Book, Eleventh Edition – FPS, 1998.
• Industrial Press, Gas Engineers Handbook, 1965.
• B3PE LLC, GASCalc 6.1 Calculation Reference – Pipe Flow, Revision 005, Copyright 2025.

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