After a demand event empties the tank from \(P_{in}\) to \(P_{out}\), the metering valve continues to supply air at \(Q_{metered}\) while the system pressure recovers. The refill time is the time required to re-pressurize the tank volume \(V_{cf}\) from \(P_{out}\) back to \(P_{in}\) at the constant metered flow rate. The intermediate computation yields a time in minutes (since \(Q_{metered}\) is in cfm); multiplying by 60 converts to seconds.

\begin{equation}\label{eq:receiver-tank-metered-storage-refill} T_{refill} = \frac{60 \cdot V_{cf} \cdot (P_{in} - P_{out})}{Q_{metered} \cdot P_{atm}} \end{equation}

where \(V_{cf} = V_{required} \cdot k_{cf}\) is the tank volume in cubic feet.

Symbols

\(T_{refill}\)	Tank refill time \([\unit{ \second}]\)
\(60\)	Seconds per minute conversion \([\unit{ \second\per\minute}]\)
\(V_{cf}\)	Tank volume in cubic feet \([\unit{ \cubicFoot}]\)
\(k_{cf}\)	Cubic feet per gallon (0.133681) \([\unit{ \cubicFoot\per\gallon}]\)
\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(P_{in}\)	Initial tank pressure \([\unit{ \psi}]\)
\(P_{out}\)	Final tank pressure \([\unit{ \psi}]\)
\(Q_{metered}\)	Metering valve flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)