Calculate flow rate through an orifice using Q = CdA√(2gh). Supports sharp-edged, beveled, and rounded orifice types with multiple fluids.
When fluid flows through an orifice under a head of liquid, the theoretical jet velocity follows Torricelli's theorem: V = √(2gh). The actual discharge is lower because the jet contracts and loses energy, which is why the formula uses a discharge coefficient Cd.
This calculator applies Q = Cd × A × √(2gh) for a chosen orifice size, head, and fluid. It includes common entrance geometries such as sharp-edged, beveled, and rounded openings, and it lets you compare how changes in diameter or coefficient affect both velocity and flow rate.
That makes it useful for tank drain estimates, outlet sizing, simple irrigation checks, and other first-pass hydraulic problems where the geometry is known but a full pipe-network model would be excessive. It also keeps the theoretical velocity and the corrected discharge side by side so you can see how much the coefficient changes the final flow estimate before using it for design or troubleshooting.
Use this calculator when you need a first-pass flow estimate for a tank outlet, free discharge opening, or simple metering orifice.
It is useful for drain sizing, irrigation hardware, nozzle comparison, and quick hydraulic checks where head and opening diameter are known but a full CFD or piping model is unnecessary. It also helps you compare how much a change in diameter or entrance shape matters before you spend time on a more detailed analysis.
Torricelli's Theorem: V = √(2gh) Actual discharge: Q = Cd × A × √(2gh) Where: • Cd = discharge coefficient (0 to 1) • A = orifice area = πd²/4 (m²) • g = gravitational acceleration (m/s²) • h = head of fluid above orifice (m)
Result: Q ≈ 1.88 L/s (112 L/min)
V_th = √(2 × 9.81 × 2) = 6.26 m/s. A = π/4 × 0.025² = 4.91×10⁻⁴ m². Q = 0.61 × 4.91×10⁻⁴ × 6.26 = 1.88×10⁻³ m³/s, which is about 1.88 L/s or 112 L/min.
Orifice flow is a good first-order model when the discharge is driven mainly by a liquid head and the opening geometry is known. It is especially helpful for comparing candidate diameters or checking whether a target drain time or emitter rate is realistic before moving to a more detailed design.
The largest errors usually come from using the wrong head, ignoring downstream submergence, or assuming Cd stays fixed under every condition. Free-discharge tank outlets, submerged openings, and compressible gas flow are different cases, so make sure the physical setup matches the formula before you rely on the number.
After passing through a sharp-edged orifice, the jet contracts to a cross-section smaller than the orifice. This contracted section (vena contracta) occurs about half a diameter downstream and is the point of minimum pressure and area.
The jet contraction ratio (Cc ≈ 0.64) and velocity coefficient (Cv ≈ 0.97) multiply to give Cd = Cc × Cv ≈ 0.61. Rounded entrances eliminate contraction, raising Cd close to unity.
For low-pressure drops (< 10% of absolute pressure) in gases, the incompressible formula is a reasonable approximation. For higher ratios, use compressible-flow orifice equations.
h = ΔP / (ρg). For water, 1 meter of head = 9.81 kPa. The calculator converts automatically when you select kPa or psi as the unit.
For very small orifices (< 3 mm), surface-tension and viscous effects increase, slightly lowering Cd. For standard industrial sizes (10–100 mm), Cd is essentially constant for a given geometry.
This calculator models free discharge from a tank or reservoir. In-pipe orifice plates additionally involve the approach velocity and beta ratio — see the Differential Pressure calculator for that case.