Buoyancy Analysis & Concrete Weight Spacing – Liquid

Introduction

The Buoyancy Analysis & Concrete Weight Spacing calculator is used to determine the weight spacing needed to keep a pipeline from floating. Supported weights in the calculator are not limited to concrete, and can be constructed of any material, provided the user knows the total mass and volume of each weight.

By default, the calculator determines the weight spacing needed to achieve a zero net buoyancy on the pipe, with a safety factor added for conservatism. Users can also specify the negative percent buoyancy they would like to pipe to have after weights are installed. It is important to note that increasing the safety factor artificially makes the pipe more buoyant for the sake of conservatism; users who who prefer to build their conservatism directly into the negative buoyancy may opt to use a safety factor of 1 to make the results more physical.

Buoyancy Force

We start by calculating the upward buoyancy force on the pipe:

F_B=\frac{\pi}{4}\left(\frac{D_o}{12 [\text{in/ft}]} \right)^2\gamma_w, \text{ where}

F_B=\frac{\pi}{4}\left(\frac{D_o+t_c}{12 [\text{in/ft}]} \right)^2\gamma_w, \text{ where}

𝐹_𝐵 − Buoyancy Force (lbf/ft)
𝐷_𝑜 − Pipe outside diameter (without coating) (in)
t_c – Corrosion coating thickness (in)
𝛾_𝑤 − Unit weight of fluid/water (lb/ft³)

Weight of Steel Pipe in the Air

Before calculating the weight spacing necessary to oppose the buoyancy force, we first account for all downward forces on the pipe. The weight of the steel pipe in air is given as:
W_P=\pi(D_{o}-t)t \gamma_P, \text{ where}

W_P=\pi(D_{o}-t)t \gamma_{P}, \text{ where}

𝑊_𝑃 − Weight of bare pipe in air (lbf/ft)
𝐷_𝑜 − Pipe outside diameter (without coating) (in)
𝑡 − Pipe wall thickness (in)
𝛾_P − Unit weight of steel (3.400 lb/[ft*in²])

Weight of Pipe Coating in the Air

The weight of the pipe coating in air is given as:

W_c= \frac{ \pi(D_o+t_c)t_c}{(12[\text{in/ft}])^2}\gamma_c,\text{ where}

W_c= \frac{ \pi(D_o+t_c)t_c}{(12[\text{in/ft}])^2}\gamma_c,\text{ where}

𝑊_𝑐 − Weight of coating in air (lbf/ft)
𝐷_𝑜 − Pipe outside diameter (without coating) (in)
t_c – Corrosion coating thickness (in)
𝛾_𝑐 − Unit weight of coating (lb/ft³)

The unit weight of many common corrosion coatings is conveniently accessible underneath the “Unit Weight of Corrosion Coating” dropdown menu. Manual values for the corrosion coating can still be specified.

Weight of Product in the Pipe

The weight of the product in the pipe is given as:

W_{pr}=\frac{\pi}{4} \left( \frac{D_{o}-2t}{12 [\text{in/ft}]} \right)^2 \gamma_{pr}, \text{ where}

W_{pr}=\frac{\pi}{4} \left( \frac{D_{o}-2t}{12 [\text{in/ft}]} \right)^2 \gamma_{pr}, \text{ where}

𝑊_𝑝𝑟 − Weight of product in pipe (lbf/ft)
𝐷_𝑜 − Pipe outside diameter (without coating) (in)
𝑡 − Pipe wall thickness (in)
𝛾_𝑝𝑟 − Unit weight of product in pipe (lb/ft³)

Downward Force of the Pipe

Without installing weights, the total downward force on the pipe is the sum of weights given in the previous section:

F_P=W_P+W_c+W_{pr}, \text{where}

F_P=W_P+W_c+W_{pr}, \text{where}

F_𝑃 − Total downward force on the pipe without weights (lbf/ft)
𝑊_𝑃 − Weight of bare pipe in air (lbf/ft)
𝑊_𝑐 − Weight of coating in air (lbf/ft)
𝑊_𝑝𝑟 − Weight of product in pipe (lbf/ft)

Net Controlling Force

The net controlling force on the pipe is the difference between the buoyancy force, and the downward force on the pipe without weights.

F_{net}=(F_B-F_p)f_s, \text{ where}

F_{net}=(F_B-F_p)f_s, \text{ where}

𝐹_𝑛𝑒𝑡 − Net controlling force (lbf/ft)
𝐹_𝐵 − Buoyancy Force (lbf/ft)
F_𝑃 − Total downward force on the pipe without weights (lbf/ft)
f_s = Safety Factor

Downward Force of the Weight

The force of an individual weight on the pipe is given as:

F_{wt}=V_{wt}(\gamma_{wt}-\gamma_w), \text{ where}

F_{wt}=V_{wt}(\gamma_{wt}-\gamma_w), \text{ where}

F_wt − Downward force of a single weight (lbf)
𝑉_𝑤𝑡 − Volume of a single weight (ft³)
𝛾_𝑤𝑡 − Unit weight of a single weight (lb/ft³)
𝛾_𝑤 − Unit weight of fluid/water (lb/ft³)

Weight Spacing

Once we know the downward force of a single weight, we can calculate the concrete weight spacing necessary to reach the given negative percent buoyancy:

L_{wt}=\frac{1}{f_s}\frac{F_{wt}}{(1+\%b)F_b-F_p}, \text{where}

L_{wt}=\frac{1}{f_s}\frac{F_{wt}}{(1+\%b)F_b-F_p}, \text{where}

L_𝑤𝑡 − Calculated weight spacing
f_s − Safety factor
%b − Negative percent buoyancy (defaulted to 0%)
𝐹_wt − Downward force of a single weight (lbf)
𝐹_𝐵 − Buoyancy Force (lbf/ft)
F_𝑃 − Total downward force on the pipe without weights (lbf/ft)

Safety Factor and Negative Percent Buoyancy are both applied in the Calculated Weight Spacing. In instances where Negative percent buoyancy remains the primary parameter under consideration a Safety factor of “1” should be applied to negate the effect of Safety Factor in the calculation.

Case Guide

Part 1: Create Case

Input Parameters

• Nominal Pipe Diameter (in): (0.625” – 48”)
• Wall Thickness (in): (0.068” – 2”)
  • Reduced Wall Thickness (in): (0.068” – 2”)
• Pipe Grade
• Internal Pipe Diameter (in): (0.49” – 46”)
• Location Class
• Design Factor
• Corrosion Coating Thickness (in): (1 mil – 50 mils)
• Unit Weight of Water: (59 – 64) (lbs/ft³)
• Density of Weight: (90 – 150) (lbs/ft³)
• Unit Weight of Corrosion Coating: (50 – 100) (lbs/ft³)
• Unit Weight of Product in the Pipe: (50-100) (lbs/ft³)
• Volume of Weight (ft³)
• Safety Factor
• Manual Negative Buoyancy – Defaulted to 0, if value not entered

Part 2: Outputs/Reports

Results

• Weight of Pipe in Air: (21 – 1750) (lbf/ft)
• Buoyancy Force (lbf/ft)
• Weight of Coating in Air (lbf/ft)
• Weight of Product in Pipe (lbf/ft)
• Downward Force of the Pipe (lbf/ft)
• Net Controlling Force: (-4 – 255) (lbf/ft)
• Downward Force of the Weight (lbf)
• Weight Spacing (ft)

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
• MMS Regulations
• USDA-SCS Modified (Permissible Velocity of Water and Soil Erodibility)
• FHWA-HEC
• Pipeline Rules of Thumb Handbook

FAQ