Buoyancy Analysis & Concrete Coating Requirements – Gas

Introduction

A submerged pipeline’s tendency to float is governed by a balance of weights: the steel pipe itself, the water it displaces, any liquid it carries, and the backfill above it. This calculator evaluates that balance with the pipe treated as empty — a deliberately conservative assumption that both sets aside the stabilizing weight of any product and accounts for periods when the line may be out of service.

From that balance the calculator sizes the concrete coating required to hold the line down. It solves for the concrete coating thickness that makes the coated, empty pipe heavy enough to overcome buoyancy while still meeting the specified safety factor and negative buoyancy margin against the weight of water displaced.

The analysis is driven by the unit weight of water entered in PLTB; it does not account for water depth or depth of burial.

Determine Bare Pipe Weight

W_{pipe}=10.68\,(D-t)\,t \quad [\text{lbs/ft}]

W_{pipe}=10.68\,(D-t)\,t \quad [\text{lbs/ft}]

Where:
D − Pipe outside diameter (in)
t − Pipe wall thickness (in)

Determine Volume of Corrosion Coating

V_{corr}=\frac{\pi\,(D+2t_{corr})^2}{4(144)}-\frac{\pi D^2}{4(144)} \quad [\text{ft}^3]

V_{corr}=\frac{\pi\,(D+2t_{corr})^2}{4(144)}-\frac{\pi D^2}{4(144)} \quad [\text{ft}^3]

Where:
t_corr = Corrosion coating thickness (in)

Determine Required Concrete Coating Thickness

The coating is sized against a design water unit weight that folds in both the safety factor and the negative buoyancy margin:

\gamma = \rho_{w}\cdot SF\cdot\left(1+\frac{\%b}{100}\right)

\gamma = \rho_{w}\cdot SF\cdot\left(1+\frac{N}{100}\right)

Where:
γ = Design water unit weight (lb/ft³)
ρ_w = Specific weight of water (lb/ft³)
SF = Safety factor
%b = Negative buoyancy (%)

The required thickness t_con is the larger real root of the quadratic A·t_con² + B·t_con + C = 0. The coefficients below produce a thickness in feet, which is then converted to inches:

\begin{aligned}
A &= \pi\,(\gamma-\rho_{con})\\[2pt]
B &= \frac{\pi}{12}\,(D+2t_{corr})\,(\gamma-\rho_{con})\\[2pt]
C &= \frac{\pi}{144}\left[\frac{\gamma}{4}\,(D+2t_{corr})^2-\rho_{corr}\,(D\,t_{corr}+t_{corr}^2)\right]-W_{pipe}
\end{aligned}

\begin{aligned} A &= \pi\,(\gamma-\rho_{con})\\ B &= \frac{\pi}{12}\,(D+2t_{corr})\,(\gamma-\rho_{con})\\ C &= \frac{\pi}{144}\left[\frac{\gamma}{4}\,(D+2t_{corr})^2-\rho_{corr}\,(D\,t_{corr}+t_{corr}^2)\right]-W_{pipe} \end{aligned}

t_{con}=\max\!\left(\frac{-B \pm \sqrt{B^{2}-4AC}}{2A}\right)\times 12 [\text{in}]

t_{con}=\max\!\left(\frac{-B \pm \sqrt{B^{2}-4AC}}{2A}\right)\times 12 \quad [\text{in}]

Where:
t_con = Concrete coating thickness (in)
ρ_con = Concrete coating specific weight (lb/ft³)
ρ_corr = Corrosion coating specific weight (lb/ft³)

Before a thickness is reported, two conditions are tested:

• If the concrete coating density is less than the design water unit weight (ρ_con < γ), no solution is possible — the concrete is not dense enough to overcome buoyancy.
• If C < 0, the pipe already fulfills the specified safety factors without concrete coating, so no coating is necessary.

Determine Volume of Concrete Coating

V_{con}=\frac{\pi}{4(144)}\left[(D+2t_{corr}+2t_{con})^2-(D+2t_{corr})^2\right] \quad [\text{ft}^3]

V_{con}=\frac{\pi}{4(144)}\left[(D+2t_{corr}+2t_{con})^2-(D+2t_{corr})^2\right] \quad [\text{ft}^3]

Determine Total Volume of Pipe in Air Including Corrosion and Concrete Coating

V_{total}=\frac{\pi\,(D+2(t_{corr}+t_{con}))^2}{4(144)} \quad [\text{ft}^3]

V_{total}=\frac{\pi\,(D+2(t_{corr}+t_{con}))^2}{4(144)} \quad [\text{ft}^3]

Determine Total Weight of Pipe in Air, Including Weight of Corrosion and Concrete Coating

W_{total}=W_{pipe}+V_{corr}\,\rho_{corr}+V_{con}\,\rho_{con} \quad [\text{lbs/ft}]

W_{total}=W_{pipe}+V_{corr}\,\rho_{corr}+V_{con}\,\rho_{con} \quad [\text{lbs/ft}]

Where:
ρ_corr = Corrosion coating specific weight (lb/ft³)
ρ_con = Concrete coating specific weight (lb/ft³)

Determine Weight of Displaced Water

W_{water}=V_{total}\,\rho_{w} \quad [\text{lbs/ft}]

W_{water}=V_{total}\,\rho_{w} \quad [\text{lbs/ft}]

Where:
ρ_w = Specific weight of water (lb/ft³)

Determine the Difference (Weight of Submerged Pipe)

F=W_{total}-W_{water} \quad [\text{lbs/ft}]

F=W_{total}-W_{water} \quad [\text{lbs/ft}]

A positive result means the coated, empty pipe is negatively buoyant — it sinks — by that net weight per foot.

Determine Weight Per Joint

W_{joint}=W_{total}\cdot L \quad [\text{lbs/joint}]

W_{joint}=W_{total}\cdot L \quad [\text{lbs/joint}]

Where:
L = Pipe length per joint (ft)

Verify Negative Buoyancy

As a final check, the achieved negative buoyancy margin is computed and compared against the target value entered as an input. When the coating has been sized correctly, the achieved margin equals the specified negative buoyancy:

\%b=\left(\frac{W_{total}}{W_{water}\cdot SF}-1\right)\times 100 \quad [\%]

N=\left(\frac{W_{total}}{W_{water}\cdot SF}-1\right)\times 100 \quad [\%]

Where:
%b = Negative buoyancy margin (%)
W_total = Weight of pipe in air (lbs/ft)
W_water = Weight of displaced water (lbs/ft)
SF = Safety factor

Case Guide

Part 1: Create Case

Input Parameters

• Nominal Outside Diameter (in): (0.625” – 48”)
• Wall Thickness (in): (0.068” – >2”)
• Pipe Grade: (24,000 psi – 80,000 psi) (if unknown use Grade A 24,000)
• Pipe Length (ft/joint)
• Water Density (lb/ft³): (59 – 64)
• Concrete Coating Density (lb/ft³): (50 – 170)
• Corrosion Coating Density (lb/ft³): (50 – 100)
• Safety Factor (e.g., 1.15)
• Negative Buoyancy (%) (e.g., 1)
• Corrosion Coating Thickness (mil): (1 – 50 mils)

Part 2: Outputs/Reports

Results

• Pipe Weight (lbs/ft)
• Total Volume (ft³)
• Corrosion Coating Volume (ft³)
• Concrete Coating Thickness (in): (0.25” – 8.5”)
• Concrete Coating Volume (ft³)
• Weight of Pipe in Air (lbs/ft): (21 – 1750)
• Weight of Water Displaced (lbs/ft): (3 – 1600)
• Weight of Submerged Pipe (lbs/ft): (2 – 250)
• Weight Per Joint (lbs/joint): (800 – 70,000)

References

• ASME B31.8 – Gas Transmission and Distribution Piping Systems
• API 5L, API 5LS and API 5LX – Specification of Pipe Grade
• ASTM – Various – Weld Joint Factor
• CFR Code Part 192
• USDA-SCS Modified (Permissible Velocity of Water and Soil Erodibility)
• FHWA-HEC
• Pipeline Rules of Thumb Handbook
• Timoshenko, S – Theory of Elasticity Anchor Force

FAQ