Orifice Flow Discharge Calculator
Calculates the volumetric flow rate through an orifice plate or opening given the upstream-to-downstream pressure difference. Used in flow metering, tank drainage design, and hydraulic control systems.
About this calculator
Flow through an orifice is governed by Torricelli's theorem extended to pressurised systems. The formula is: Q = Cd × A × √(2 × ΔP / ρ), where Q is volumetric flow rate (m³/s), Cd is the dimensionless discharge coefficient, A is the orifice cross-sectional area (m²), ΔP is the pressure difference across the orifice (Pa), and ρ is the fluid density (kg/m³). The term √(2ΔP/ρ) represents the theoretical maximum velocity through the orifice, derived from Bernoulli's equation. The discharge coefficient Cd (typically 0.6–0.65 for sharp-edged orifices, up to 0.98 for well-rounded nozzles) corrects for vena contracta — the narrowing of the jet downstream — and viscous losses. A higher Cd means the orifice passes more flow for the same pressure drop. Orifice plates are widely used in pipeline flow measurement because ΔP can be measured easily with a differential pressure transmitter.
How to use
Water (density 1000 kg/m³) discharges through a sharp-edged circular orifice with a diameter of 0.04 m (area = π/4 × 0.04² ≈ 0.001257 m²). The pressure difference is 5000 Pa and the discharge coefficient is 0.62. Apply Q = Cd × A × √(2 × ΔP / ρ). Step 1: 2 × ΔP / ρ = 2 × 5000 / 1000 = 10. Step 2: √10 ≈ 3.162 m/s. Step 3: Q = 0.62 × 0.001257 × 3.162 ≈ 0.00246 m³/s (2.46 L/s). Enter the area, Cd, pressure difference, and density to reproduce this result immediately.
Frequently asked questions
What is the discharge coefficient for an orifice plate and what affects its value?
The discharge coefficient (Cd) accounts for the difference between the theoretical and actual flow through an orifice. Its value depends primarily on orifice geometry: sharp-edged orifices have Cd ≈ 0.60–0.65, rounded-entry nozzles reach 0.95–0.98, and Venturi meters achieve up to 0.99. Reynolds number also matters — at low Re (viscous flow) Cd drops noticeably, while at high Re it stabilises. Beta ratio (orifice-to-pipe diameter ratio) and the exact tap locations for measuring ΔP further influence Cd. Calibrated values from ISO 5167 standards should be used for custody-transfer metering applications.
How does fluid density affect the flow rate through an orifice for the same pressure drop?
Density appears in the denominator under the square root in the orifice equation, so a denser fluid produces a lower velocity — and therefore lower volumetric flow — for the same ΔP. However, the mass flow rate (ṁ = ρQ) scales as √ρ, meaning denser fluids actually deliver more mass per second. For example, replacing water (1000 kg/m³) with a fluid twice as dense halves the velocity term (√(2ΔP/2ρ) = velocity/√2), reducing Q by 29%, but mass flow increases by 41%. This distinction matters for energy balance calculations and when sizing orifice meters for different process fluids.
When should I use an orifice plate versus a Venturi meter for flow measurement?
Orifice plates are lower cost, easier to install and replace, and suit a wide range of pipe sizes, making them the default choice for many industrial metering applications. Their main drawback is a higher permanent pressure loss — typically 60–80% of the measured ΔP is lost — increasing pumping costs. Venturi meters recover most of the pressure (permanent loss only 10–15% of ΔP) because of their gradual diffuser section, so they are preferred for large, continuous-flow systems where energy savings justify the higher purchase cost. Orifice plates also require more straight pipe upstream to ensure a stable velocity profile, whereas Venturi meters are somewhat less sensitive to upstream disturbances.