Flow Rate Through an Orifice Calculator

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Orifice Flow Rate Calculator

Calculate the volumetric flow rate of a liquid discharging through an orifice based on Bernoulli's principle.

The diameter of the hole or aperture.
Height of fluid above the center of the orifice.
Typical values: 0.61 for sharp-edged, 0.98 for well-rounded.

Calculation Results

Orifice Area: –
Theoretical Velocity: –
Flow Rate (m³/s): –
Flow Rate (Liters/min): –
Flow Rate (Gallons/min): –

Understanding Flow Rate Through an Orifice

The flow rate through an orifice is a fundamental concept in fluid mechanics, widely used in engineering to measure fluid flow rates in pipes, tanks, and reservoirs. Whether you are designing a drainage system, calibrating a carburetor, or managing water treatment facilities, understanding how to calculate discharge through an aperture is critical.

The Flow Rate Formula

This calculator uses the standard orifice equation derived from Bernoulli's principle and Torricelli's law. The formula for Volumetric Flow Rate ($Q$) is:

Q = Cd × A × √(2 × g × h)

Where:

  • Q = Volumetric flow rate (m³/s)
  • Cd = Coefficient of Discharge (dimensionless)
  • A = Cross-sectional area of the orifice (m²)
  • g = Acceleration due to gravity (9.81 m/s²)
  • h = Pressure head or height of fluid above the orifice center (m)

Key Inputs Explained

Orifice Diameter: This is the size of the opening. Even a small increase in diameter leads to a significant increase in flow because the area increases with the square of the diameter ($A = \pi \times r^2$).

Pressure Head: This represents the potential energy of the fluid. In an open tank, it is the height of the liquid surface above the hole. In a pressurized pipe, it is the pressure converted into meters of head.

Discharge Coefficient ($C_d$): Real fluids have friction and viscosity. The $C_d$ accounts for these losses.

  • 0.60 – 0.62: Sharp-edged orifices (standard).
  • 0.95 – 0.98: Rounded/Nozzle-shaped orifices (high efficiency).

Example Calculation

Imagine a water tank with a 50mm (0.05m) sharp-edged hole at the bottom. The water level is 4 meters above the hole. Using a $C_d$ of 0.61:

  1. Area (A): $\pi \times (0.025)^2 \approx 0.001963\ m^2$
  2. Velocity ($\sqrt{2gh}$): $\sqrt{2 \times 9.81 \times 4} \approx 8.86\ m/s$
  3. Flow Rate (Q): $0.61 \times 0.001963 \times 8.86 \approx 0.0106\ m^3/s$

This converts to roughly 636 Liters per minute.

function calculateFlowRate() { // 1. Get DOM elements var diamInput = document.getElementById("orificeDiameter"); var headInput = document.getElementById("pressureHead"); var cdInput = document.getElementById("dischargeCoeff"); var resultBox = document.getElementById("calcResults"); // 2. Parse values var d_mm = parseFloat(diamInput.value); var h_m = parseFloat(headInput.value); var cd = parseFloat(cdInput.value); // 3. Validation if (isNaN(d_mm) || isNaN(h_m) || isNaN(cd)) { alert("Please enter valid numeric values for all fields."); return; } if (d_mm <= 0 || h_m < 0 || cd <= 0) { alert("Values must be positive numbers."); return; } // 4. Constants var g = 9.81; // Gravity m/s^2 // 5. Calculation Logic // Convert diameter from mm to meters var d_m = d_mm / 1000; var radius_m = d_m / 2; // Calculate Area (A = pi * r^2) in m^2 var area_m2 = Math.PI * Math.pow(radius_m, 2); // Calculate Theoretical Velocity (V = sqrt(2gh)) in m/s var velocity_ms = Math.sqrt(2 * g * h_m); // Calculate Flow Rate Q = Cd * A * V (m^3/s) var q_m3s = cd * area_m2 * velocity_ms; // Conversions var q_lpm = q_m3s * 60000; // 1 m^3 = 1000 L, per sec to per min = *60 var q_gpm = q_lpm / 3.78541; // Liters to US Gallons // 6. Display Results document.getElementById("resArea").innerHTML = (area_m2 * 10000).toFixed(2) + " cm²"; document.getElementById("resVelocity").innerHTML = velocity_ms.toFixed(2) + " m/s"; document.getElementById("resFlowM3s").innerHTML = q_m3s.toFixed(5); document.getElementById("resFlowLpm").innerHTML = q_lpm.toFixed(2); document.getElementById("resFlowGpm").innerHTML = q_gpm.toFixed(2); // Show result container resultBox.style.display = "block"; }

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