Advanced Orifice Flow Rate Calculator

Calculator Inputs

The page uses a single-column layout overall. The calculator fields use a responsive 3-column, 2-column, and 1-column arrangement.

Opening Shape

Driving Input

Discharge Coefficient, Cd

Diameter (mm)

Width (mm)

Height (mm)

Head Above Orifice (m)

Pressure Drop (kPa)

Fluid Density (kg/m³)

Dynamic Viscosity (mPa·s)

Gravity (m/s²)

Number of Identical Orifices

Upstream Diameter (mm, optional)

Example Data Table

Scenario	Shape	Opening	Driver	Cd	Flow (L/s)	Re
Lab Water Jet	Circular	Ø 20.0 mm	1.80 m head	0.62	1.157	73,530
Rectangular Plate Opening	Rectangular	30.0 mm × 15.0 mm	18.00 kPa	0.64	3.472	80,978
Process Drain Array	Circular	Ø 12.0 mm	35.00 kPa	0.61	3.415	44,429

Formula Used

Opening area
Circular: A = πd² / 4
Rectangular: A = w × h

Ideal exit velocity
Head input: v = √(2gh)
Pressure input: v = √(2ΔP / ρ)

Actual flow rate
Q = Cd × A × v

Optional approach correction
When an upstream diameter is entered, the calculator applies
Correction = 1 / √(1 - β⁴), where β = d_eq / D_upstream

Supporting outputs
Pressure-head relation: ΔP = ρgh
Mass flow: ṁ = ρQ
Reynolds number: Re = ρvD_h / μ

These equations work best for incompressible liquids and practical coefficient-based estimates. Very low heads, submerged discharge, gases, cavitation, or detailed meter standards need specialized treatment.

How to Use This Calculator

Select the opening shape and choose whether flow is driven by liquid head or pressure drop.
Enter the geometry, discharge coefficient, fluid properties, and the number of identical openings.
Add an upstream diameter only when you want an approach velocity correction.
Press Calculate Flow Rate to display results above the form.
Review flow, velocity, Reynolds number, and time-based output values.
Use the CSV and PDF buttons to save the current calculation report.

FAQs

1) What equation does the calculator apply?

It uses Q = Cd × A × √(2gh) for head input and Q = Cd × A × √(2ΔP/ρ) for pressure input. An optional beta-based correction adjusts velocity when an upstream diameter is supplied.

2) Why is the discharge coefficient important?

The coefficient captures contraction and energy losses at the opening. Even small Cd changes can shift flow noticeably, so measured or published values should be used whenever accuracy matters.

3) Can I use rectangular openings?

Yes. The tool supports circular and rectangular openings. For rectangular cases, it also estimates a hydraulic diameter so Reynolds number remains useful for comparing operating conditions.

4) Is this calculator suitable for gases?

No. The current model assumes incompressible liquid flow. Gas discharge requires compressible-flow equations, expansion factors, and choking checks that are outside this page.

5) Why does Reynolds number appear in the results?

It helps you compare regimes and judge whether viscosity might influence performance. It is informative here, but it does not replace calibration data or detailed standards.

6) What does upstream diameter change?

When you enter it, the calculator applies an approach velocity correction using the beta ratio. Leave it blank for large-reservoir style discharge without that correction.

7) Can multiple orifices be combined in one estimate?

Yes. The tool multiplies single-opening area by the number of identical openings. Real systems may still show interaction effects, spacing losses, or shared pressure changes.

8) Why might measured flow differ from this estimate?

Real installations may include edge wear, partial submergence, nonuniform head, air entrainment, viscosity shifts, and instrument uncertainty. Field calibration is the best accuracy check.