Fluid inventory in straight pipe

Calculate contained volume and liquid mass from actual internal diameter and total straight length.

How this calculation works

This geometry-based calculation estimates the liquid inventory in a full length of circular pipe. Enter the actual internal diameter, the total straight length of that bore and liquid density. The diameter is converted from millimeters to meters before calculating cross-sectional area. Multiplying area by length gives cubic meters, which are then converted to liters; multiplying by density gives contained liquid mass. Because area depends on diameter squared, selecting the correct bore matters. Nominal pipe size and outside diameter are not interchangeable with internal diameter. Use separate calculations where sections have different bores and account independently for fittings, equipment and tanks. The model assumes a completely filled, constant circular cross-section. Its inventory result does not determine required storage capacity or expansion-vessel sizing.

Inputs and units

Actual internal diameter (mm)
Total pipe length (m)
Liquid density (kg/m³)

Method and formula

V = π(Dinternal/1000)² L/4; liters = 1000V; liquid mass = density × V, with V in m³.

Worked example

Example inputs

Actual internal diameter: 50 mm
Total pipe length: 100 m
Liquid density: 1000 kg/m³

Calculation steps

Internal diameter = 50 / 1000 = 0.05 m. Cross-sectional area = π × 0.05² / 4 ≈ 0.001963495408 m².
Volume = 0.001963495408 × 100 ≈ 0.1963495408 m³ = 196.349541 L.
Liquid mass = 1000 × 0.1963495408 ≈ 196.349541 kg.

Example results

Contained liquid volume: 196.3495408 L
Contained liquid mass: 196.3495408 kg

Assumptions

Pipe is completely full; bore is circular and constant along the entered length.

Limitations

Enter internal diameter, not nominal size or outside diameter.
Equipment, fittings and tanks are excluded; this does not size storage or expansion vessels.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

DOE Fundamentals: Fluid Flow: Continuity and Bernoulli energy balance; centrifugal pumps, equations 3-19 through 3-25; series and parallel piping