13.2: Air Flow Rate in Pneumatic Systems
- Page ID
- 116680
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Air flow rate in pneumatics is the measure of how much air moves through a system or past a specific point within a certain timeframe. This rate can be quantified either by weight or by volume, though volume is most used in pneumatic applications. Flow rate essentially determines how well a pneumatic system can operate, and it directly affects actuator speed and system responsiveness.
Units of Measurement for Air Flow Rate
For larger air flows, the most common units of measurement are cubic feet per minute (CFM) in the English system and cubic meters per minute (CMM) in the International System of Units (S.I.). For smaller flow rates, the timeframe is typically extended to an hour, using cubic feet per hour (CFH) or cubic meters per hour (CMH). These measurements allow technicians to gauge and compare air flow across various applications and systems efficiently. In the U.S., it is most common to use cubic feet per minute (CFM).
Since air is compressible, the volume flow rate of air must be defined at a specific pressure. To standardize and accurately size pneumatic components, flow rates are defined at specific pressures. In pneumatic systems, three pressure-related terms are often used to define air volumes:
1. Volume at a Given Pressure
When measuring the air volume at the system’s current pressure. For example, imagine the flow through a tube is described as 3 CFM at 44.1 PSIa (30 PSIg+14.7psi). This means that a volume of three cubic feet of air at a pressure of 44 psi passes by a certain point each minute.
Power output devices, such as pneumatic tools, commonly specify flow rate requirements in this manner. In this case, the pressure specified is the pressure that would exist at the inlet to the tool.
2. Free Air Volume
Free air volume describes the amount of volume the air flowing in the tube would occupy if it were allowed to expand to atmospheric conditions. For example, if we were to describe the air flow rate of a compressed gas in terms of free air, the volume flow rate would be much larger because the pressure of free air is lower.
For instance, when compressed air is expanded to atmospheric conditions, its volume increases due to the pressure drop.
In many cases, the pressures in branch circuits of a pneumatic system are different. For this reason, free air is often used to describe the airflow in these branch circuits even though the airflow in each branch is not at free air pressure. This allows designers to perform tasks such as calculating the total flow needed from the air compressor.
For example, free airflow at a given pressure can be determined using Boyle's Law:
VFA=P1×V1PSIa
where P1 is the pressure in the tube, V1 is the flow rate of air in the tube, and PSIa (14.7 PSIa) is the standard atmospheric pressure.
Conversion of Air Volumes at Pressure to Free Air Volumes
To convert a measured volume at a given pressure to free air volume, use Boyle’s Law by rearranging to calculate the free air volume, VFA , as follows:
VFA=P1×V114.7 psia VFA=14.7 PSIa P1×V1
where P1 is the initial pressure in psia, and V1 is the flow rate at that pressure. This conversion allows for direct comparisons in free air terms, regardless of the system’s pressure.
3. Standard Volume
Air volume is measured at standard conditions, typically at a specific temperature and pressure. To standardize measurements for comparison across systems, standard volume is used. A standard cubic foot of air (SCF) represents air at specific conditions: 14.7 psia (sea level pressure), 68°F, and 36% relative humidity. At sea level, free air and standard air are usually within 5% of each other. By referencing air volumes under these standard conditions, pneumatic components can be consistently compared. For example, the flow rate might be specified in “standard” cubic feet per minute (SCFM), which helps engineers select air compressors and other components with comparable flow ratings.
It is important to use a consistent pressure-based definition throughout calculations to maintain accuracy.
Free Air vs. Standard Air
There is often confusion between free air and standard air. Free air refers to the atmospheric air entering the compressor, whose properties vary with temperature, humidity, and altitude. In contrast, standard air refers to air at defined, unchanging conditions. Because ambient air properties fluctuate, free air volumes are typically converted to standard volumes to maintain consistency when comparing flow rates and component ratings across systems.