Calculator
Formula used
The calculator uses the standard orifice/nozzle relation: Q = Cd · A · √(2ΔP/ρ). Total area is A = n · (πd²/4).
If you select head input, it converts using ΔP = ρ g H with g = 9.80665 m/s².
For ideal gases, mass flow is computed with the isentropic model. It automatically selects subsonic or choked flow based on P2/P0 versus the critical ratio.
Volumetric rate at downstream uses Q2 = ṁRT/P. Standard rate uses 101325 Pa and 273.15 K.
How to use this calculator
- Select Liquid or Gas based on your application.
- Enter nozzle diameter, nozzle count, and a realistic Cd.
- For liquids, choose Pressure drop or Head, then fill fluid properties.
- For gases, enter absolute pressures and temperature, then confirm γ and R.
- Press Calculate to show results above the form, then export CSV or PDF if needed.
Example data table
| Case | Mode | Diameter | Nozzles | Cd | ΔP / Pressures | Fluid / Gas | Key output |
|---|---|---|---|---|---|---|---|
| A | Liquid | 12 mm | 1 | 0.62 | 300→100 kPa | Water (ρ≈998) | Q (L/min) computed on submit |
| B | Liquid | 8 mm | 2 | 0.80 | Head: 6 m | Seawater (ρ≈1025) | Velocity, mass flow, Re |
| C | Gas | 6 mm | 1 | 0.90 | P0 400 kPa, P2 100 kPa | Air (γ≈1.4) | ṁ (kg/s), Q2, choked flag |
Discharge fundamentals for liquids
For incompressible flow, discharge comes from pressure energy converted to jet velocity. The calculator applies Q = Cd·A·√(2ΔP/ρ). ΔP may be entered directly or derived from head using ΔP = ρgH. In practice, ΔP should represent the net drop across the nozzle after upstream losses. Jet velocity (v = Q/A) helps check spray reach and erosion potential, while mass flow (ṁ = ρQ) supports pump sizing.
Selecting a realistic discharge coefficient
Cd represents contraction and losses that make real flow lower than the ideal prediction. Sharp-edged orifices often sit near 0.60–0.65, while well-rounded nozzles can exceed 0.90. Use manufacturer data when available and treat Cd as a calibration factor when you have test results. The Reynolds number estimate highlights low-Re conditions where viscosity can depress effective Cd and where additional testing is recommended.
Compressible flow and choking behavior
Gas flow depends on absolute pressure, temperature, γ, and the specific gas constant R. The tool evaluates the critical pressure ratio (2/(γ+1))^(γ/(γ−1)). When P2/P0 falls below this limit, the nozzle chokes and mass flow becomes largely independent of further downstream pressure reduction. This matters for purge, pneumatic, and relief designs. The calculator reports mass flow and estimates downstream volumetric flow via Q2 = ṁRT/P2, plus a standard volumetric rate for reporting.
Unit handling and verification checks
Design data often mixes kPa, bar, psi, and head values across drawings and logs. This calculator converts inputs to consistent SI bases and outputs in your flow unit. Verify by comparing theoretical and Cd-corrected flow, ensuring ΔP is positive, and using absolute gas pressures. If results look high, re-check diameter units and nozzle count; area scales with d².
Documentation for reviews and audits
Engineering reviews demand traceable assumptions and repeatable calculations. After computing, export CSV for quick spreadsheet comparison or PDF for controlled documentation. Record the selected preset, the Cd source, and whether the gas case is choked. For liquid cases, note whether pressure drop or head was used and how upstream losses were treated. Capturing these details simplifies commissioning, supports change control, and accelerates future troubleshooting when performance deviates from expectations.
FAQs
What does the discharge coefficient represent?
Cd accounts for jet contraction and internal losses. Start with vendor data, then tune Cd to match test flow at a known pressure drop. Typical sharp edges are near 0.60–0.65, while streamlined nozzles can exceed 0.90.
Should I enter gauge or absolute pressure?
For liquids, use consistent gauge values because only the pressure difference matters. For gases, enter absolute pressures for P0 and P2, or add atmospheric pressure to gauge readings, otherwise choking and mass flow will be wrong.
Why does gas flow stop increasing as P2 decreases?
When P2/P0 drops below the critical ratio, the nozzle chokes and the throat reaches sonic conditions. Mass flow then depends mainly on P0, T0, γ, R, area, and Cd, not on further reductions in downstream pressure.
How does nozzle count change the discharge?
Total flow scales with total area. If you keep the same diameter, doubling the number of identical nozzles doubles area and approximately doubles discharge or mass flow, assuming the same upstream conditions and Cd.
Is the liquid result accurate for very viscous fluids?
The equation assumes incompressible flow with a Cd that represents losses. Viscosity mainly affects Cd and flow regime; the calculator reports Reynolds number to flag low-Re cases. For highly viscous fluids, use calibrated Cd or test data.
What is included in the CSV and PDF downloads?
Exports include all entered inputs, the computed results, and a timestamp. CSV is convenient for comparing multiple cases in spreadsheets, while PDF is formatted for sharing, review comments, and attaching to calculations packages.