pipe_sizing Namespace Reference

Compressed air pipe sizing calculator. More...

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

Functions
Result	calculate (const Input &input)
	Calculates the minimum pipe cross-sectional area and diameter for a compressed air system.

Variables
constexpr double	kCircleAreaFactor = 0.78
	Industry-standard approximation of \(\pi / 4\) used in pipe diameter calculations.

Detailed Description

This namespace provides a single calculation that determines the minimum internal pipe size needed to carry a given compressed air flow at a specified design velocity:

• Cross-Sectional Area – the minimum internal area required so that the compressed air velocity does not exceed the design limit.
• Pipe Diameter – the internal diameter corresponding to the computed area, assuming a circular cross-section.

Note

A design velocity of 20 ft/s is recommended for main headers; the velocity should not exceed 30 ft/s in any branch.

See also

Pipe Sizing Calculator

Function Documentation

calculate()

Result pipe_sizing::calculate

(

const Input &

input

)

Applies the continuity equation to convert a free-air flow rate to the compressed-air volumetric flow at operating pressure, then sizes the pipe so that the resulting velocity does not exceed the design limit.

Cross-Sectional Area:

\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}

Pipe Diameter:

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

where:

\(A\)	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 pressure \([\unit{ \psia}]\)
\(v\)	Design velocity (maximum allowable) \([\unit{ \foot\per\second}]\)
\(k_{60}\)	Seconds per minute (60) \([\unit{ \second\per\minute}]\)
\(P_{line}\)	Operating gauge pressure in the pipe \([\unit{ \psig}]\)
\(D\)	Minimum required internal pipe diameter \([\unit{ \inch}]\)
\(k_c\)	Circle area factor (0.78 \approx \pi/4) \([\unit{ \unitless}]\)

Note

The factor \(P_{atm} / (P_{line} + P_{atm})\) compresses the free-air volume to the actual volume at operating pressure (Boyle's Law). The factor \(k_{144} / k_{60} = 144 / 60 = 2.4\) converts units from ft²·min/s to in². \(k_c = 0.78\) is the industry-standard rounded approximation of \(\pi / 4 \approx 0.7854\) used in U.S. customary pipe sizing.

Parameters

[in]

input

Input parameters

Returns

Result containing cross-sectional area in in² and pipe diameter in in.

Variable Documentation

kCircleAreaFactor

constexpr double pipe_sizing::kCircleAreaFactor = 0.78

inlineconstexpr

This factor relates the cross-sectional area of a circular pipe to its diameter squared: \(A = k_c \cdot D^2\), so \(D = \sqrt{A / k_c}\). The value 0.78 is a rounded approximation of \(\pi / 4 \approx 0.7854\) used in U.S. customary pipe sizing practice.

Definition at line 45 of file pipe_sizing.h.