🕳️

Orifice Flow Calculator

Reference: Torricelli / Bernoulli
🕳️ MECH
Free orifice flow calculator. Find discharge flow rate (GPM), velocity and area for flow through an orifice under a given head, using Q = Cd·A·√(2gh). US units, worked examples.
Inputs
Enter the orifice diameter, the head of fluid above the orifice, and the discharge coefficient (0.61 for a sharp-edged orifice). The calculator returns the flow rate, discharge velocity and orifice area.
Results
Calculation confidence: Planning-levelSuitable for early design, estimating and feasibility checks. Verify the final design against the governing code and a licensed engineer before construction or procurement.
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Torricelli / Bernoulli
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ℹ About This Calculator

Flow through an orifice — a sharp-edged hole in a tank, plate or restriction — follows the classic Torricelli/Bernoulli relationship, and this calculator computes the discharge flow rate, velocity and orifice area from the orifice diameter, the driving head and the discharge coefficient. It works in US units (inches, feet, GPM) and applies to tank drainage, orifice-plate metering, weir and outlet sizing, and any situation where a fluid discharges under a head through a small opening.

The theoretical discharge velocity from an orifice under a head h is √(2gh) — the same speed an object would reach falling from height h. Real flow is reduced by the discharge coefficient Cd, which accounts for the vena contracta (the flow contracting just past the opening) and friction. A sharp-edged orifice has Cd ≈ 0.61, a rounded or well-designed nozzle approaches 0.98, and a short tube is about 0.80. The discharge coefficient makes the orifice both a flow restriction and, when calibrated, a flow-measurement device.

Orifice Flow Formula

Torricelli / Bernoulli

Q = Cd · A · √(2gh), where Cd = discharge coefficient (≈0.61 sharp-edged, 0.98 rounded), A = orifice area (ft²), g = 32.2 ft/s², h = head above the orifice (ft). Actual velocity = Cd·√(2gh). Convert ft³/s to GPM by ×448.8.

Worked Example

A 1-inch sharp-edged orifice (Cd = 0.61) discharges under 10 ft of head. Area A = π×(0.5/12)² = 0.00545 ft². Velocity √(2×32.2×10) = 25.4 ft/s. Flow Q = 0.61 × 0.00545 × 25.4 = 0.0844 cfs = about 38 GPM.

Frequently Asked Questions

How do I calculate flow through an orifice? +
Use Q = Cd·A·√(2gh), where Cd is the discharge coefficient, A is the orifice area in ft², g is 32.2 ft/s², and h is the head of fluid above the orifice in feet. Compute the area from the diameter, find the theoretical velocity √(2gh), multiply by Cd and the area to get flow in ft³/s, then multiply by 448.8 to convert to GPM. The head, not the pipe pressure, drives the flow.
What is the discharge coefficient? +
The discharge coefficient (Cd) is a factor less than 1 that corrects the ideal orifice flow for real effects — mainly the vena contracta (the jet contracting just downstream of the opening) and friction. A sharp-edged orifice has Cd ≈ 0.61, a rounded nozzle approaches 0.98, and a short re-entrant tube is about 0.80. Using the right Cd for the orifice geometry is essential for an accurate flow prediction.
What is the velocity of flow from an orifice? +
The theoretical velocity is √(2gh), which is the same speed an object would reach falling freely from the head height h — a result known as Torricelli's theorem. The actual velocity is slightly lower, equal to Cd times the theoretical velocity, because of friction and the contraction of the jet. For 10 ft of head the theoretical velocity is about 25.4 ft/s.
What is an orifice plate used for? +
An orifice plate is a thin plate with a precise hole installed in a pipe to measure flow: the pressure drop across the plate relates to the flow rate through the orifice equation. It is one of the most common and economical flow meters in industrial and HVAC systems. The same physics also makes orifices useful as flow restrictors, balancing devices and pressure-reducing elements.
Does the head or the pressure drive orifice flow? +
For a tank or reservoir discharging to atmosphere, the head (height of fluid above the orifice) drives the flow through Q = Cd·A·√(2gh). For an orifice in a pressurized pipe, the differential pressure across the orifice drives it, and the equation is rewritten as Q = Cd·A·√(2·ΔP/ρ). Both are the same Bernoulli relationship expressed with head or pressure as the driving potential.
How does orifice size affect flow? +
Flow is proportional to the orifice area, which grows with the square of the diameter, so doubling the orifice diameter roughly quadruples the flow at the same head. Flow also increases with the square root of the head, so quadrupling the head only doubles the flow. This square-law dependence on diameter makes the orifice a sensitive way to set or measure flow.
Is this orifice flow calculator accurate? +
It applies the exact orifice discharge equation Q = Cd·A·√(2gh), so it is accurate when you use the correct discharge coefficient for your orifice geometry. The main uncertainty is Cd, which should match a sharp-edged (0.61), rounded (0.98) or tube (0.80) orifice. For metering applications, orifice plates are calibrated to standards (ISO 5167 / ASME MFC) for precise coefficients.

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