pneumatic_valve Namespace Reference

Pneumatic valve flow rate and flow coefficient (Cv) calculations. More...

Classes
struct	CvInput
	Input parameters for the valve flow coefficient (Cv) calculation. More...
struct	CvResult
	Result of the valve flow coefficient (Cv) calculation. More...
struct	FlowRateInput
	Input parameters for the flow rate calculation (Cv = 1). More...
struct	FlowRateResult
	Result of the flow rate calculation (Cv = 1). More...

Functions
FlowRateResult	calculateFlowRate (const FlowRateInput &input)
	Calculates the air flow rate through a pneumatic valve with unit flow coefficient (Cv = 1).
CvResult	calculateCv (const CvInput &input)
	Calculates the valve flow coefficient (Cv) for a pneumatic valve.

Variables
constexpr double	kAirFlowFactor = 0.6875
	Empirical air flow constant for dry air at standard conditions (60°F, 14.696 psia).

Detailed Description

This namespace provides two calculation modes for pneumatic valve sizing in compressed air distribution systems:

• Flow Rate – calculates the theoretical air flow rate through a valve with a unit flow coefficient (Cv = 1) given the inlet and outlet pressures. For a valve with a known Cv, multiply the result by that value.
• Flow Coefficient (Cv) – calculates the dimensionless valve flow coefficient when the actual flow rate and operating pressures are known. Use this to select or verify a valve for a given application.

Both calculations use the simplified compressible-flow pneumatic valve formula with an empirically derived air flow constant for dry air at standard conditions.

See also

Pneumatic Valve Calculator

Function Documentation

calculateCv()

CvResult pneumatic_valve::calculateCv

(

const CvInput &

input

)

Rearranges the pneumatic valve flow formula to solve for the dimensionless valve flow coefficient Cv when the actual flow rate and operating pressures are known. A higher Cv indicates a valve with lower flow restriction. Select a valve whose rated Cv meets or exceeds the calculated value.

\begin{equation}\label{eq:pneumatic-valve-cv} C_v = \frac{Q}{k_{flow} \cdot \sqrt{(P_{in} - P_{out}) \cdot (P_{in} + P_{out})}} \end{equation}

where:

\(C_v\)	Dimensionless valve flow coefficient \([\unit{ \unitless}]\)
\(Q\)	Measured or required air flow rate \([\unit{ \scfm}]\)
\(k_{flow}\)	Empirical air flow constant for dry air at standard conditions (0.6875) \([\unit{ \scfm\per\psi}]\)
\(P_{in}\)	Inlet (upstream) absolute pressure \([\unit{ \psia}]\)
\(P_{out}\)	Outlet (downstream) absolute pressure \([\unit{ \psia}]\)

Note

Cv is a dimensionless sizing coefficient with implicit unit dependence on the formula constant \(k_{flow}\). Pressures must be in psia (absolute). Select a valve whose catalog Cv equals or exceeds the calculated value.

Parameters

[in]

input

CvInput

Returns

CvResult containing the dimensionless valve flow coefficient.

calculateFlowRate()

FlowRateResult pneumatic_valve::calculateFlowRate

(

const FlowRateInput &

input

)

Uses the simplified compressible-flow pneumatic valve formula to compute the theoretical air flow rate for a valve with Cv = 1. The formula is equivalent to \(Q = k_{flow} \cdot \sqrt{P_{in}^2 - P_{out}^2}\), a form commonly found in pneumatic system design references. For a valve with a specific Cv, multiply the result by that Cv value.

\begin{equation}\label{eq:pneumatic-valve-flow-rate} Q = k_{flow} \cdot \sqrt{(P_{in} - P_{out}) \cdot (P_{in} + P_{out})} \end{equation}

where:

\(Q\)	Air flow rate through the valve (Cv = 1) \([\unit{ \scfm}]\)
\(k_{flow}\)	Empirical air flow constant for dry air at standard conditions (0.6875) \([\unit{ \scfm\per\psi}]\)
\(P_{in}\)	Inlet (upstream) absolute pressure \([\unit{ \psia}]\)
\(P_{out}\)	Outlet (downstream) absolute pressure \([\unit{ \psia}]\)

Note

The factored form \(\sqrt{(P_{in}-P_{out})(P_{in}+P_{out})}\) is algebraically identical to \(\sqrt{P_{in}^2 - P_{out}^2}\). The constant \(k_{flow} = 0.6875\) is empirically derived for dry air at standard conditions (60°F, 14.696 psia). Pressures must be in psia (absolute). To find the flow through a valve with a specific Cv, multiply \(Q\) by that Cv.

Parameters

[in]

input

FlowRateInput

Returns

FlowRateResult containing the flow rate in scfm.

Variable Documentation

kAirFlowFactor

constexpr double pneumatic_valve::kAirFlowFactor = 0.6875

inlineconstexpr

This constant combines the isentropic flow factor for dry air, standard air density, and the necessary unit conversions to produce a dimensional factor valid for U.S. customary inputs (pressures in psia, flow rate in scfm). It appears in the standard simplified pneumatic valve flow formula used in industrial compressed air system design. \([\unit{\scfm\per\psi}]\)

Definition at line 45 of file pneumatic_valve.h.