Orifice Discharge Calculator

Inputs

Discharge method

Choose submerged if downstream water level exists.

Orifice shape

Area changes based on selected shape.

Units

Changing units refreshes labels only.

Diameter (mm)

For circular openings. Use inside diameter.

Upstream head h₁ (m)

Vertical head above orifice centerline.

Downstream head h₂ (m)

Used only for submerged discharge.

Number of orifices

Total Q = Q₁ × count.

Discharge coefficient C_d

Typical sharp-edged: 0.60–0.65 (check specs).

Gravity g (m/s²)

Default matches standard gravity.

Fluid density ρ (kg/m³)

Water ≈ 1000; slurry may be higher.

Kinematic viscosity ν (m²/s) (optional)

Water at ~20°C ≈ 1.0e-6 m²/s.

Project notes (optional)

Notes appear in the PDF report.

Reset

Formula used

The calculator applies the standard sharp-edged orifice relationship: Q = C_d · A · √(2 g Δh)

Q = discharge (m³/s)
C_d = discharge coefficient (dimensionless)
A = orifice area (m²)
g = gravity (m/s²)
Δh = head difference (m); free: Δh = h₁, submerged: Δh = h₁ − h₂

Use manufacturer data or testing for C_d when accuracy matters.

How to use this calculator

Select Free discharge for flow to air, or Submerged with backwater.
Pick the shape and enter the opening size in the shown units.
Enter head h₁ above the orifice centerline; add h₂ for submerged.
Set C_d based on the orifice edge and approach conditions.
Click Calculate Discharge, then export CSV/PDF if needed.

Discharge coefficient selection

Use C_d to capture contraction and losses at the opening. Sharp‑edged plates commonly fall near 0.60–0.65, while well‑rounded inlets can be higher. Match C_d to the same edge condition, approach flow, and installation details. If the orifice is partly blocked by screens or corrosion, apply a conservative C_d or reduce effective area. Record the assumed value for review.

Head measurement on site

Measure head from the upstream water surface to the orifice centerline, not the invert. For sumps and tanks, confirm the reference point after any berms or pump drawdown. For submerged flow, include downstream head and use Δh = h₁ − h₂. Small head errors can change discharge because velocity scales with √Δh.

Area determination and tolerances

Enter clear opening dimensions, using inside diameter for circular holes and net width × height for slots. For field‑cut openings, measure in two directions and use the minimum when safety is critical. When multiple orifices exist, confirm each opening is identical; otherwise compute per opening and sum flows. The tool converts to m² internally, helping compare unit sets without rounding bias.

Submergence and backpressure effects

Submergence reduces driving head and can suppress aeration at the jet, changing observed patterns. Use the submerged option when tailwater covers the opening or when discharge enters a conduit with backpressure. If tailwater rises during storms, evaluate several h₂ values to understand worst‑case capacity. For critical control, consider a safety margin or field verification when turbulence is high.

Reporting and QA workflow

After calculating, export CSV for logs and PDF for approvals. Include notes, measurement dates, and instrument accuracy. Compare computed flow against pump curves, meter readings, or tank level change rates to validate assumptions. If results differ, revisit head reference, effective area, and C_d. Store exports in the job folder so inspectors can trace inputs and assumptions later without delay. A repeatable record improves commissioning, supports change orders, and reduces schedule risk during dewatering.

FAQs

1) What is the main formula used for discharge?

The calculator uses Q = Cd × A × √(2gΔh). Cd represents losses, A is opening area, g is gravity, and Δh is the driving head between upstream and downstream water levels.

2) When should I use the submerged option?

Use it when tailwater covers the opening or when downstream pressure resists flow. The calculator then uses Δh = h1 − h2, so backwater directly reduces the predicted discharge.

3) Which head reference point should I measure from?

Measure vertically from the upstream water surface to the orifice centerline. For submerged cases, also measure downstream water surface to the same centerline to obtain h2 consistently.

4) Can I work in inches and feet?

Yes. Select Imperial units to enter sizes in inches and heads in feet. The tool converts inputs internally to SI units to compute discharge and then reports flow in multiple convenient units.

5) Why is viscosity optional, and what does it affect?

Viscosity is only used to estimate an approximate Reynolds number for circular orifices. It does not change the discharge equation here, but it helps flag when flow conditions may differ from typical sharp‑edged assumptions.

6) How do I handle multiple orifices with different sizes?

If openings differ, calculate each orifice separately using its own area and head, then add the individual discharges. If all openings are identical, enter the count to scale the per‑orifice discharge automatically.

Example data table

Case	Method	Shape	Size	h₁	h₂	C_d	Orifices	Estimated Q (m³/s)	Estimated Q (L/s)
A	Free	Circular	50 mm	1.2 m	0	0.62	1	0.0023	2.3
B	Submerged	Rectangular	120 × 80 mm	1.5 m	0.5 m	0.60	2	0.0081	8.1
C	Free	Circular	2.5 in	5 ft	0	0.63	1	0.0072	7.2