Air Flow Through an Orifice Calculator
Estimate subsonic airflow, CFM, velocity, and mass flow through a round orifice from diameter, pressure difference, density, and Cd.
How air flow through an orifice is estimated
This air flow through an orifice calculator estimates subsonic airflow through a round orifice using the basic orifice equation. You enter orifice diameter, pressure difference, air density, and discharge coefficient. The calculator converts the diameter and pressure to SI units, calculates area, estimates volume flow, converts it to CFM, and calculates mass flow. It also checks the upstream and downstream absolute pressure ratio to warn about possible choked flow.
The formula Q = Cd A √(2ΔP/ρ) is a practical incompressible estimate. Cd is the discharge coefficient, which accounts for losses, vena contracta, edge shape, and non-ideal flow. A sharp-edged orifice may use a Cd around 0.60 to 0.65, while other shapes can differ. For air, compressibility becomes important when pressure ratios are large, velocities are high, or the flow approaches sonic conditions.
For a deeper reference point, see NASA Glenn’s mass-flow-rate equations reference. The link is included because it explains the background principle or the standard context behind the calculation, not because it replaces the checks needed for a real project.
Formula and worked example
The example is useful because it shows the order of work. First keep all dimensions in one unit system, then calculate the core value, then convert the final result into the units you actually need. This prevents the common problem where a correct formula gives a wrong number because one input was entered in inches while another was treated as millimeters.
Common mistakes, use cases, and limits
A common mistake is using gauge pressure values as if they were absolute pressures for compressible checks. The orifice equation uses pressure difference, but choking checks use absolute pressure ratio. Another mistake is assuming Cd is always 1. Real orifices lose energy, so the effective flow is lower than the ideal flow. People also forget that air density changes with temperature, pressure, and humidity.
Use this calculator for rough leakage estimates, small ventilation openings, test rigs, pneumatic restrictions, dust collector bleed air, and educational fluid mechanics. It is also useful for comparing how flow changes with diameter because area grows with diameter squared.
This page is not a replacement for ISO 5167 sizing, calibrated flow meters, compressible nozzle calculations, or critical-flow analysis. For high-pressure gas, high Mach number, custody transfer, safety relief, or regulated testing, use the correct standard and verified instrumentation.
How to read the result: Do not look only at the large number at the top of the calculator. The smaller rows explain where that number came from and what part of the result may control the decision. In many engineering estimates, the secondary value is the one that prevents a mistake. For example, a total weight may look acceptable while weight per foot affects supports, or a pressure result may look acceptable while velocity, face area, or a warning note shows that the assumption is weak. Read the formula box after every calculation, especially when changing units or using custom material data.
Common questions
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For a rough sharp-edged orifice estimate, 0.60 to 0.65 is common. Use tested data for the actual orifice plate when accuracy matters.
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It matters when pressure drop is large compared with absolute pressure or when velocity becomes a significant fraction of the speed of sound.
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Choked flow occurs when the flow reaches sonic speed at the smallest area, limiting further mass-flow increase from lowering downstream pressure.
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The same form is used for many liquid orifice estimates, but the density, Cd, vapor pressure, and cavitation checks would be different.
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Use the result as an estimating or checking tool only. Final design should be checked against the applicable code, standard, manufacturer data, and a qualified professional review when safety, compliance, or expensive equipment is involved.
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The physical value should stay the same after conversion, but small rounding differences can appear because the calculator rounds displayed values. For purchasing, fabrication, or field work, keep extra significant digits until the final step.
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The most common mistake is mixing units. A formula may expect inches, feet, psi, millimeters, pascals, kilograms, or pounds. This page converts the common options internally, but the input labels still need to be read carefully.
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Yes, when the result is used for sizing, procurement, lifting, field installation, or machine selection. The correct safety factor depends on the code, material variation, uncertainty, wear, environment, and consequence of failure.