Pipe Sizing Calculator

Detailed Description

This calculator determines the minimum internal cross-sectional area and corresponding pipe diameter required to carry a given compressed air flow at or below a specified design velocity. All formulas use U.S. customary units.

Correct pipe sizing is critical for efficient compressed air distribution:

• Undersized pipes create excessive pressure drop, wasting energy and reducing available pressure at end-use equipment.
• Oversized pipes increase capital cost and reduce air velocity, which can allow condensate to accumulate rather than being carried to drain points.
• Main headers are typically designed for 20 ft/s; velocity should never exceed 30 ft/s in any distribution segment.

The calculation applies Boyle's Law to convert the free-air volumetric flow rate to the compressed-air flow at operating pressure, then uses the continuity equation to find the pipe area that limits velocity to the design value.

Relevant formulas are documented below.

Cross-Sectional Area

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Minimum internal pipe area to limit compressed-air velocity to the design value.

The formula derives from the continuity equation applied to a compressible fluid. The free-air flow rate \(Q\) is first converted to the actual compressed-air volumetric flow at operating pressure using Boyle's Law:

\begin{equation}\label{eq:boyles-law} Q_{compressed} = Q \cdot \dfrac{P_{atm}}{P_{line} + P_{atm}}\end{equation}

The required cross-sectional area at the design velocity is:

\begin{equation}\label{eq:cross-sectional-area} A_{ft^2} = \dfrac{Q_{compressed}}{v \cdot k_{60}}\end{equation}

Converting from ft² to in² by multiplying by \(k_{144}\):

\begin{equation}\label{eq:pipe-sizing-area} A = \frac{k_{144} \cdot Q \cdot P_{atm}}{v \cdot k_{60} \cdot (P_{line} + P_{atm})} \end{equation}

Symbols

\(A\)	Minimum required internal cross-sectional area \([\unit{ \inch\squared}]\)
\(k_{144}\)	Square inches per square foot (144) \([\unit{ \inch\squared\per\squareFoot}]\)
\(Q\)	Volumetric free-air flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric (absolute) pressure \([\unit{ \psia}]\)
\(v\)	Maximum allowable compressed-air design velocity \([\unit{ \foot\per\second}]\)
\(k_{60}\)	Seconds per minute (60) \([\unit{ \second\per\minute}]\)
\(P_{line}\)	Operating gauge pressure in the pipe \([\unit{ \psig}]\)

Note

\(P_{line} + P_{atm}\) converts gauge pressure to absolute pressure (Boyle's Law requires absolute pressures). The combined factor \(k_{144} / k_{60} = 2.4\) converts the area from ft²·min/s to in².

Pipe Diameter

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Internal pipe diameter corresponding to the computed cross-sectional area.

Assumes a circular pipe cross-section. The relationship between internal diameter and cross-sectional area for a circle is:

\(A = k_c \cdot D^2\)

Solving for the diameter:

\begin{equation}\label{eq:pipe-sizing-diameter} D = \sqrt{\frac{A}{k_c}} \end{equation}

Symbols

\(D\)	Minimum required internal pipe diameter \([\unit{ \inch}]\)
\(A\)	Cross-sectional area (from \eqref{eq:pipe-sizing-area}) \([\unit{ \inch\squared}]\)
\(k_c\)	Circle area factor (0.78 \(\approx \pi/4\)) \([\unit{ \unitless}]\)

Note

The factor \(k_c = 0.78\) is an industry-standard rounded approximation of \(\pi / 4 \approx 0.7854\) used in U.S. customary compressed air pipe sizing practice. The resulting diameter is the minimum internal (bore) diameter; the next larger standard nominal pipe size should be selected for the actual installation.

Modules
	Pipe Cross-Sectional Area Formula
	Minimum internal pipe area to limit compressed-air velocity to the design value.
	Pipe Diameter Formula
	Internal pipe diameter corresponding to the computed cross-sectional area.

Files
file	pipe_sizing.h
	Declarations for compressed air pipe sizing calculations.

Namespaces
namespace	pipe_sizing
	Compressed air pipe sizing calculator.

Classes
struct	pipe_sizing::Input
	Input parameters for the pipe sizing calculation. More...
struct	pipe_sizing::Result
	Result of the pipe sizing calculation. More...