Pipe Formulas

Overview

Engineering reference data for Pipe Formulas 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

Pipe Cross-Section Data

Cross-Section Properties Formulas

The following formulas relate to the geometric properties of a pipe's circular cross-section.

Section Modulus The section modulus ($S$) is a geometric property of a cross-section used in the design of beams or flexural members, describing its strength in bending.

$S = \frac{I}{c} = \frac{\pi (d_o^4 - d_i^4)}{32 d_o} \approx 0.0982 \frac{(d_o^4 - d_i^4)}{d_o}$

Transverse Metal Area The cross-sectional area of the pipe wall itself.

$A_m = \frac{\pi}{4} (d_o^2 - d_i^2)$

Transverse Internal Area (Flow Area) The internal cross-sectional area available for fluid flow.

$A_a = \frac{\pi d_i^2}{4} \approx 0.7854 d_i^2$

Internal & External Surface Area per Unit Length Surface areas per foot of pipe length.

$A_i = \frac{\pi d_i}{12} \quad (\text{ft}^2 \text{ per ft})$ $A_o = \frac{\pi d_o}{12} \quad (\text{ft}^2 \text{ per ft})$

Internal & External Circumference

$C_i = \pi d_i$ $C_e = \pi d_o$

Variables: $d_o$ = outside diameter (in), $d_i$ = inside diameter (in), $I$ = moment of inertia ($in^4$).

Interactive Charts

References

• Original Source