Pipe Volume
Engineering fundamentals for inventory and operations calculations
1. Volume Calculation
Pipe internal volume is calculated from the inside diameter and length. Various unit conversions are needed for practical applications.
Basic Formulas
Volume per foot of pipe:
V = π × d² / 4 × (1 ft)
Practical formulas:
V (gal/ft) = 0.0408 × d²
V (bbl/ft) = 0.000971 × d²
V (ft³/ft) = 0.00545 × d²
V (liters/m) = 0.7854 × d² [d in cm]
Where d = inside diameter (inches)
Inside Diameter
d = D - 2t
Where:
d = Inside diameter (inches)
D = Outside diameter (inches)
t = Wall thickness (inches)
Unit Conversions
| From |
To |
Multiply by |
| ft³ |
gallons |
7.481 |
| ft³ |
barrels (42 gal) |
0.1781 |
| gallons |
barrels |
0.02381 |
| ft³ |
liters |
28.317 |
| gallons |
liters |
3.785 |
| barrels |
liters |
159.0 |
2. Volume Reference Tables
Standard Pipe Volumes
| NPS |
OD (in) |
Wall (Std) |
ID (in) |
gal/ft |
bbl/mile |
| 2" |
2.375 |
0.154 |
2.067 |
0.174 |
21.9 |
| 4" |
4.500 |
0.237 |
4.026 |
0.661 |
83.4 |
| 6" |
6.625 |
0.280 |
6.065 |
1.501 |
189.4 |
| 8" |
8.625 |
0.322 |
7.981 |
2.599 |
327.9 |
| 10" |
10.750 |
0.365 |
10.020 |
4.098 |
517.0 |
| 12" |
12.750 |
0.375 |
12.000 |
5.875 |
741.2 |
| 16" |
16.000 |
0.375 |
15.250 |
9.489 |
1,197 |
| 20" |
20.000 |
0.375 |
19.250 |
15.12 |
1,907 |
| 24" |
24.000 |
0.375 |
23.250 |
22.05 |
2,782 |
| 30" |
30.000 |
0.375 |
29.250 |
34.90 |
4,403 |
| 36" |
36.000 |
0.375 |
35.250 |
50.71 |
6,398 |
| 42" |
42.000 |
0.500 |
41.000 |
68.60 |
8,655 |
Quick Reference: Volume per Mile
Volume per mile:
V (gal/mile) = 0.0408 × d² × 5,280 = 215.4 × d²
V (bbl/mile) = 5.129 × d²
Example: 24" × 0.500" wall (ID = 23")
V = 5.129 × 23² = 2,715 bbl/mile
3. Gas Volume at Pressure
For gas pipelines, volume must account for compressibility. The actual gas quantity depends on pressure, temperature, and composition.
Gas Inventory Calculation
Standard cubic feet in pipeline:
SCF = V_pipe × (P / P_std) × (T_std / T) × (1 / Z)
Where:
V_pipe = Physical pipe volume (ft³)
P = Operating pressure (psia)
P_std = Standard pressure (14.73 psia)
T = Operating temperature (°R)
T_std = Standard temperature (520°R = 60°F)
Z = Compressibility factor
Simplified:
SCF = V_pipe × P × 35.37 / (T × Z)
Line Pack
Line pack (MMSCF):
LP = 0.0283 × d² × L × P_avg / (T × Z)
Where:
d = Inside diameter (inches)
L = Length (miles)
P_avg = Average pressure (psia) = (P₁ + P₂) / 2
T = Average temperature (°R)
Rule of thumb:
LP ≈ d² × L × P_avg / 1,000,000 [rough estimate, MMSCF]
Example: Gas Pipeline Inventory
Given: 24" × 0.500" pipeline, 100 miles, avg pressure 800 psia, 70°F, Z = 0.88
Physical volume:
d = 24 - 1.0 = 23 in
V = 0.00545 × 23² × 5,280 × 100 = 15.23 MM ft³
Line pack:
T = 70 + 460 = 530°R
SCF = 15.23×10⁶ × 800 × 35.37 / (530 × 0.88)
SCF = 924 MMSCF
Operating significance: Line pack represents stored gas that can be withdrawn by lowering pressure. A 100 psi pressure change in this example releases/absorbs ~115 MMSCF.
4. Applications
Common Uses
| Application |
Purpose |
| Hydrotesting |
Calculate water volume needed for test |
| Purging/inerting |
Determine nitrogen volume for displacement |
| Pigging |
Estimate pig travel time at given flow rate |
| Batch tracking |
Calculate batch interface location |
| Line pack |
Gas storage capacity in pipeline |
| Blowdown |
Gas release volume for depressuring |
| Chemical treatment |
Inhibitor/biocide dosing volume |
Hydrotest Water Requirements
Water volume:
V_water = V_pipe × (1 + compression factor)
Compression factor ≈ 0.03 per 1000 psi test pressure
(Water compresses ~3% at 1000 psi)
Fill time estimate:
t (hours) = V_pipe (gal) / Q_fill (gal/hr)
Pig Travel Time
Travel time:
t = V_pipe / Q
For liquids:
t (hours) = V (bbl) / Q (bbl/hr)
t (hours) = L (miles) × 5.129 × d² / Q (bbl/hr)
For gas (at flow velocity):
t (hours) = L (miles) × 5,280 / (v × 3,600)
Where v = gas velocity (ft/s)
5. System Volume
Total system volume includes pipe plus vessels, headers, and fittings.
Vessel Volumes
Horizontal cylinder:
V = π × D² × L / 4
Sphere:
V = π × D³ / 6
2:1 Elliptical head:
V_head = 0.1309 × D³ (each head)
Hemispherical head:
V_head = π × D³ / 12 (each head)
Fitting Equivalent Volumes
| Fitting |
Equivalent Pipe Length |
| 90° elbow (LR) |
1.5 × D |
| 90° elbow (SR) |
1.0 × D |
| 45° elbow |
0.7 × D |
| Tee (through) |
1.0 × D |
| Tee (branch) |
1.5 × D |
| Gate valve (open) |
0.5 × D |
| Ball valve (open) |
0.1 × D |
Partially Filled Horizontal Pipe
Volume at depth h:
V/L = r² × arccos((r-h)/r) - (r-h) × √(2rh - h²)
Quick reference:
25% full: V = 0.147 × V_full
50% full: V = 0.500 × V_full
75% full: V = 0.853 × V_full
Where r = d/2 (radius), h = liquid depth
📐 Partial Volume Geometry
Cross-section of horizontal pipe showing: circular cross-section with radius r, liquid depth h measured from bottom, wetted perimeter arc, liquid surface width (chord), and shaded area representing liquid volume. Include formula for area calculation. Show examples at 25%, 50%, and 75% fill levels.
References
- ASME B36.10M – Welded and Seamless Wrought Steel Pipe
- API MPMS Chapter 2 – Tank Calibration
- GPSA Engineering Data Book, Section 17