Pressure Drop Calculations in Medium and High Pressure Gas Pipelines

1 lutego 2026 | Gas

Calculating pressure drop in medium and elevated pressure gas pipelines (0.1-16 bar) requires the application of appropriate formulas that account for gas compressibility. In this article, we compare different calculation methods used worldwide and show how the Polish standard PN-76/M-34034 results compare to American methods (Weymouth, Panhandle, AGA).

If you need to quickly calculate pressure drop in a gas pipeline, use our medium and high pressure gas pipeline calculator.

Introduction to Gas Pipeline Calculations

Gas flow in pipelines differs fundamentally from liquid flow. As a compressible medium, gas changes its density and velocity along the pipeline as pressure drops. This phenomenon requires more complex equations than the classical Darcy-Weisbach equation for incompressible flows.

When designing medium pressure gas pipelines, the following must be considered:

Inlet pressure (P₁) - pressure at the pipeline entrance
Volumetric flow rate (Q) - at normal or standard conditions
Internal pipe diameter (D) - in mm or inches
Pipeline length (L) - in meters or miles
Relative gas density (d) - ratio of gas density to air density
Flow temperature (T) - affects viscosity and gas density
Pipe roughness (k) - depends on material and surface condition

PN-76/M-34034 Method (Polish Standard)

The Polish standard PN-76/M-34034 is based on the general isothermal equation for compressible gas flow. The method uses the Darcy-Weisbach equation for pressure loss calculations and the Colebrook-White equation for determining the friction factor λ. Below is the complete calculation algorithm.

Step 1: Input Data Preparation

Before starting calculations, all quantities must be converted to appropriate units:

Absolute pressure - gauge pressure plus atmospheric pressure:

$P_{abs} = P_{gauge} + 1.01325 \text{[bar]}$

Absolute temperature in Kelvin:

T_K = T_C + 273.15 \text{[K]}

Relative roughness - ratio of absolute roughness to diameter:

$\varepsilon = \frac{k} {D}$

Step 2: Individual Gas Constant

The gas constant for a specific gas is calculated based on its relative density (ratio of gas density to air density):

$R = \frac{R_u}{M} = \frac{R_u}{d \cdot M_{air}} = \frac{8314.46}{d \cdot 28.97} \text{ [J/(kg}\cdot\text{K)]}$

Where:

R_u = 8314.46 J/(kmol·K) - universal gas constant
M_air = 28.97 kg/kmol - molar mass of air
d - relative gas density [-]

For high-methane natural gas (d = 0.6), the gas constant is approximately 480 J/(kg·K).

Step 3: Gas Velocity at Inlet

The gas velocity at the inlet point is calculated from the continuity equation, converting flow from normal conditions (P_n = 101325 Pa, T_n = 273.15 K) to actual conditions:

$w_1 = \frac{Q_n \cdot P_n \cdot T}{A \cdot P_1 \cdot T_n}$

Where:

Q_n - volumetric flow rate at normal conditions [m³/s]
A - pipe cross-sectional area [m²]
P₁ - absolute pressure at inlet [Pa]
T - flow temperature [K]

Step 4: Kinematic Viscosity

The kinematic viscosity of gas depends on pressure and temperature. It is calculated from dynamic viscosity and gas density at flow conditions:

$\nu = \frac{\mu}{\rho}$

Where gas density at flow conditions:

$\rho = \rho_n \cdot d \cdot \frac{P_{abs}}{P_n} \cdot \frac{T_n}{T}$

With air density at normal conditions ρ_n = 1.293 kg/m³.

Step 5: Reynolds Number

The Reynolds number determines the flow regime:

$Re = \frac{w_1 \cdot D}{\nu}$

Where D is the internal pipe diameter in meters.

Step 6: Friction Factor λ

The choice of friction factor formula depends on the Reynolds number:

Laminar flow (Re ≤ 2300):

$\lambda = \frac{64} {Re}$

Transitional flow (2300 < Re ≤ 4000):

\lambda = 0.0025 \cdot \sqrt[3]{Re}

Turbulent flow (Re > 4000) - Colebrook-White equation (solved iteratively):

$\frac{1}{\sqrt{\lambda}} = -2 \log_{10} \left( \frac{2.51}{Re \cdot \sqrt{\lambda}} + \frac{k}{3.72 \cdot D} \right)$

The Colebrook-White equation is implicit - λ appears on both sides. It is solved iteratively (e.g., Newton-Raphson method), starting from an initial value of λ = 0.02.

Step 7: Gas Velocity at Outlet (Iterative)

A key element of the PN-76 method is accounting for gas velocity changes along the pipeline. As pressure drops, the gas expands and accelerates. The outlet velocity w₂ is calculated from the isothermal equation:

$R \cdot T \cdot \left(\frac{1}{w_1^2} - \frac{1}{w_2^2}\right) - 2 \cdot \ln\frac{w_2}{w_1} = \frac{\lambda \cdot L}{D}$

Where:

R - individual gas constant [J/(kg·K)]
T - temperature [K]
L - pipeline length [m]
D - diameter [m]

This equation is also solved iteratively using the Newton-Raphson method, finding w₂ > w₁.

Step 8: Pressure Drop Calculation

Knowing the inlet and outlet velocities, the pressure drop is calculated from:

$\Delta P = P_1 \cdot \left(1 - \frac{w_1} {w_2}\right)$

Final pressure:

P_2 = P_1 - \Delta P

Algorithm Summary

The PN-76 method is the most physically accurate because it:

Accounts for gas density changes along the pipeline
Calculates the actual velocity increase from w₁ to w₂
Uses the accurate Colebrook-White equation for friction factor
Uses normal conditions as the reference point for flow

The disadvantage of the method is the need to solve two iterative equations (Colebrook-White and isothermal equation), which requires computational calculations.

Weymouth Method (1912)

The oldest and most widespread empirical method developed by T.R. Weymouth. Formula in US customary units:

$Q = 433.5 \cdot \frac{T_b}{P_b} \cdot E \cdot \sqrt{\frac{P_1^2 - P_2^2}{S \cdot L \cdot T \cdot Z}} \cdot D^{2.667}$

Where:

Q - flow rate [SCFD]
T_b, P_b - base temperature and pressure
E - efficiency factor (0.85-1.0)
S - relative gas density
Z - compressibility factor

The Weymouth method is considered conservative - it gives higher pressure drops than other methods.

Panhandle A Method (1940s)

Developed for US transmission pipelines, suitable for partially turbulent flows (Re 2000-3000):

$Q = 435.87 \cdot E \cdot \left(\frac{T_b}{P_b}\right)^{1.0788} \cdot \left(\frac{P_1^2 - P_2^2}{S^{0.853} \cdot L \cdot T \cdot Z}\right)^{0.5394} \cdot D^{2.6182}$

Panhandle B Method (1956)

Modified version for fully turbulent flow, gives the lowest pressure drops:

$Q = 737 \cdot E \cdot \left(\frac{T_b}{P_b}\right)^{1.02} \cdot \left(\frac{P_1^2 - P_2^2}{S^{0.961} \cdot L \cdot T \cdot Z}\right)^{0.51} \cdot D^{2.53}$

AGA Method (American Gas Association)

Uses the general equation with friction factor calculated by the Colebrook-White method:

$Q = 77.54 \cdot \frac{T_b}{P_b} \cdot \sqrt{\frac{P_1^2 - P_2^2}{S \cdot T \cdot L \cdot Z \cdot f}} \cdot D^{2.5}$

Where f is the Darcy friction factor calculated iteratively from the Colebrook-White equation.

Results Comparison - Practical Analysis

We conducted a detailed comparison of results for three typical design cases. All calculations were performed for high-methane natural gas (type E) with a relative density of 0.6.

Test Cases

Test	Flow Rate	Diameter	Length	Pressure	Temperature
1	300 m³/h	DN 54.5 mm	200 m	5 bar	15°C
2	100 m³/h	DN 50 mm	100 m	5 bar	15°C
3	1000 m³/h	DN 100 mm	1000 m	10 bar	15°C

Pressure Drop Results

Method	Test 1 [bar]	Test 2 [bar]	Test 3 [bar]
PN-76/M-34034	0.0786	0.0073	0.0982
General Isothermal	0.0787	0.0073	0.0982
Weymouth	0.0856	0.0075	0.1016
AGA	0.0706	0.0066	0.0882
Panhandle A	0.0512	0.0050	0.0683
Panhandle B	0.0317	0.0028	0.0451

Percentage Differences vs PN-76

Method	Test 1	Test 2	Test 3	Average
General Isothermal	+0.1%	+0.2%	0.0%	+0.1%
Weymouth	+8.9%	+2.4%	+3.5%	+4.9%
AGA	-10.2%	-10.0%	-10.2%	-10.1%
Panhandle A	-34.9%	-30.9%	-30.5%	-32.1%
Panhandle B	-59.7%	-61.5%	-54.1%	-58.4%

Interpretation of Results

The PN-76/M-34034 method shows virtually perfect agreement (difference < 0.2%) with the general isothermal gas flow equation. This is the most physically accurate method, which accounts for gas expansion along the pipeline and calculates velocity change from w₁ to w₂.

Conservatism Hierarchy of Methods

From most to least conservative:

Weymouth (+5-9% vs PN-76) - gives the highest pressure drops
PN-76 / Isothermal (baseline) - most physically accurate
AGA (-10% vs PN-76) - modern method with Colebrook-White
Panhandle A (-30-35% vs PN-76) - for partial turbulence
Panhandle B (-55-60% vs PN-76) - for full turbulence

Why Such Differences?

Differences between methods result from:

Empirical simplifications - Panhandle A/B omit the explicit friction factor, replacing it with empirical constants
Efficiency factor E - American methods use E = 0.85-0.92 to account for real pipeline imperfections
Base conditions - different standard temperatures (15°C vs 60°F = 15.56°C)
Applicability range - each method was optimized for specific flow conditions

Practical Recommendations

When to Use Which Method?

Application	Recommended Method	Justification
Projects in Poland	PN-76/M-34034	National standard compliance
US transmission pipelines	Panhandle B	Industry standard
Preliminary calculations	Weymouth	Conservative, safe
Detailed analyses	AGA or Isothermal	Physically justified
Low Re (< 3000)	Panhandle A	Optimized for this range

Safety Margin

When designing gas pipelines, it is recommended to:

Use conservative methods (Weymouth, PN-76) for safety
Verify results with at least two methods
Include a 10-20% safety factor for uncertainties

Summary

The PN-76/M-34034 method used in Polish standards is a solid, physically justified calculation method. Results are virtually identical to the general isothermal equation and fall within a reasonable range compared to recognized international methods.

When choosing a calculation method, consider regulatory requirements of the given country, flow characteristics (Reynolds number), required level of conservatism, and availability of input data.

The gas pipeline sizing calculator in our application uses the PN-76/M-34034 method, ensuring compliance with Polish design standards.

References and Sources

PN-76/M-34034 - Principles for calculating pressure losses in gas or liquid flow in pipelines
GPSA Engineering Data Book - Gas Processors Suppliers Association
Menon, E.S. - "Gas Pipeline Hydraulics"
Bąkowski K. - "Gas networks and installations"

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