Volume Partly Filled Pipes

Overview

Engineering reference data for Volume Partly Filled Pipes in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Liquid Volume Reference Table

The following table provides volume calculations for liquid in partly filled horizontal pipes and tanks, based on liquid level and pipe/tank diameter.

Table Usage Notes

• Empty cells indicate that the liquid level exceeds the pipe diameter for that size (physically impossible).
• The volumes represent the actual liquid volume, not the total tank volume.
• These values assume a perfectly circular and horizontal pipe/tank cross-section.
• For partially filled vertical pipes or tanks with different geometries, different formulas apply.

Interactive Charts

References

• Original Source