Example Data Table
| Case | Shape | Dimensions | Velocity method | Area (m²) | Velocity (m/s) | Total flow (m³/s) |
|---|---|---|---|---|---|---|
| A | Circular | D = 0.10 m | Known v | 0.007854 | 12.0 | 0.094248 |
| B | Rectangular | 0.12 m × 0.08 m | Known v | 0.009600 | 9.5 | 0.091200 |
| C | Circular | D = 75 mm | From ΔP | 0.004418 | ≈ 20.4 | ≈ 0.0901 |
Formula Used
- Exit area: circular A = π·D²/4, rectangular A = W·H.
- Volumetric flow: Q = A·v (per exit), Qtotal = Q·N.
- Mass flow: ṁ = ρ·Q.
- Velocity from pressure drop: v = Cd·√(2·ΔP/ρ).
- Delivered capacity: Qdel = Qtotal·Availability ÷ Safety.
How to Use This Calculator
- Select the outlet shape and enter its dimensions with correct units.
- Choose a velocity method: measured velocity or pressure-derived estimate.
- Select the fluid option; provide temperature and pressure for air, or density for custom fluids.
- Enter number of exits, availability factor, and a safety factor for conservative sizing.
- Press Calculate to see results above the form, then export CSV or PDF.
Sizing objectives and design context
Exit capacity is typically reported as volumetric flow (m³/s) at the outlet plane. For ventilation exhausts, nozzle discharges, or relief duct terminations, the sizing target often comes from required air changes, contaminant capture, or equipment purge needs. This calculator standardizes results in SI units, then applies availability and safety factors so a conservative delivered capacity can be compared against the design requirement.
Geometry effects on capacity
Outlet area drives capacity linearly through Q = A·v. A 100 mm circular outlet has an area of 0.007854 m², while a 120×80 mm rectangle provides 0.009600 m², a 22% increase. When space constraints force smaller outlets, adding parallel exits may be more effective than raising velocity, because high velocities increase noise, vibration, and downstream losses.
Velocity methods and pressure data
If exit velocity is measured with an anemometer or taken from a fan curve, the “Known velocity” option provides a direct estimate. When only pressure drop is available, the calculator estimates velocity using v = Cd·√(2·ΔP/ρ). For example, with ΔP = 800 Pa, air density near 1.2 kg/m³, and Cd = 0.98, the predicted velocity is about 35.8 m/s. Use realistic Cd values to reflect fittings and contraction losses.
Fluid density and operating conditions
Mass flow depends on density: ˙m = ρ·Q. For gases, density changes with temperature and absolute pressure. The built-in air estimate uses the ideal gas relationship ρ = p/(R·T), which is appropriate for dry air in many engineering checks. For liquids such as water, a nominal 998 kg/m³ provides a practical baseline, while “Custom density” supports process fluids, humid air, or mixed gases.
Risk controls, reporting, and validation
Availability accounts for fouling, blockage, or partial operation; a value of 0.90 represents 10% expected degradation. Safety factor (for example 1.10) reduces the delivered figure to avoid optimistic sizing. Exported CSV and PDF outputs document assumptions, making reviews faster. Always validate critical designs using measured pressure, certified fan performance, and applicable standards for noise and safety. For commissioning, log inlet conditions, instrument uncertainty, and repeat measurements across several operating points before signoff.
FAQs
1) What does “delivered capacity” mean here?
Delivered capacity is the conservative estimate after applying Availability and Safety: Qdel = Qtotal × Availability ÷ Safety. Use it when comparing against required flow so degradation and uncertainty are already accounted for.
2) When should I use the pressure-drop velocity option?
Use it when you know the differential pressure across the outlet and the fluid density, but not the velocity. Provide a realistic discharge coefficient to capture contraction and loss effects.
3) How do I choose a discharge coefficient (Cd)?
Start with 0.60–0.75 for sharp-edged or high-loss exits, 0.80–0.95 for smoother transitions, and approach 1.00 only for well-conditioned, low-loss nozzles. If unsure, pick a lower value and validate.
4) Why are results shown in SI units only?
SI units avoid conversion errors and keep formulas consistent. You can enter dimensions in common units, but the calculator converts them internally and reports area, velocity, flow, and mass flow in standard SI.
5) Does this include compressibility or choked flow?
No. It uses a Bernoulli-based estimate suitable for low Mach numbers and modest pressure drops. For high-pressure gas discharge, sonic conditions, or code-required relief sizing, use specialized compressible-flow methods.
6) How can I improve accuracy for an installed system?
Measure outlet velocity profiles, confirm effective area, record temperature and pressure, and compare against fan curves. Update availability using observed fouling rates and recalibrate Cd using test data.