The internal diameter of the restriction or pipe opening.
The pressure drop across the orifice (Inlet Pressure – Outlet Pressure).
Standard Water: 1000, Hydraulic Oil: ~870, Air (sea level): ~1.225.
Typically 0.60-0.62 for sharp-edged orifices, 0.98 for smooth nozzles.
Calculation Results
Flow Rate (Liters/min):–
Flow Rate (m³/hour):–
Flow Rate (Gallons/min – US):–
Est. Fluid Velocity:–
function calculateFlowRate() {
// 1. Get Input Values
var diameterInput = document.getElementById("fr_diameter").value;
var pressureInput = document.getElementById("fr_pressure").value;
var densityInput = document.getElementById("fr_density").value;
var cdInput = document.getElementById("fr_coefficient").value;
// 2. Validate Inputs
if (diameterInput === "" || pressureInput === "" || densityInput === "" || cdInput === "") {
alert("Please fill in all fields to calculate the flow rate.");
return;
}
var d_mm = parseFloat(diameterInput);
var p_bar = parseFloat(pressureInput);
var rho = parseFloat(densityInput);
var cd = parseFloat(cdInput);
if (d_mm <= 0 || p_bar < 0 || rho <= 0 || cd <= 0) {
alert("Please enter valid positive numbers.");
return;
}
// 3. Perform Calculations (SI Units)
// Convert Diameter from mm to meters
var d_meters = d_mm / 1000;
// Calculate Area (A) in m²: PI * (r^2) = PI * (d/2)^2
var area_m2 = Math.PI * Math.pow((d_meters / 2), 2);
// Convert Pressure from Bar to Pascals (Pa)
// 1 Bar = 100,000 Pa
var p_pascals = p_bar * 100000;
// Bernoulli Principle / Orifice Equation:
// Q = Cd * A * sqrt(2 * DeltaP / rho)
// Result Q is in m³/s (Cubic meters per second)
var velocity_theoretical = Math.sqrt((2 * p_pascals) / rho);
var flow_m3s = cd * area_m2 * velocity_theoretical;
// Actual Velocity at Vena Contracta (approx)
var velocity_actual = velocity_theoretical * cd;
// Note: strictly speaking v = Q/A, but A varies at vena contracta.
// For display purposes, v = Q / OrificeArea is often used for bulk velocity through the hole.
var velocity_bulk = flow_m3s / area_m2;
// 4. Convert Results to Display Units
// m³/s to Liters per Minute (LPM): * 60,000
var flow_lpm = flow_m3s * 60000;
// m³/s to m³/hour: * 3600
var flow_m3h = flow_m3s * 3600;
// LPM to US Gallons per Minute (GPM): / 3.78541
var flow_gpm = flow_lpm / 3.78541;
// 5. Update UI
document.getElementById("res_lpm").innerHTML = flow_lpm.toFixed(2) + " LPM";
document.getElementById("res_m3h").innerHTML = flow_m3h.toFixed(2) + " m³/h";
document.getElementById("res_gpm").innerHTML = flow_gpm.toFixed(2) + " GPM";
document.getElementById("res_velocity").innerHTML = velocity_bulk.toFixed(2) + " m/s";
document.getElementById("results").style.display = "block";
}
Understanding Flow Rate and Pressure
Calculating flow rate from pressure is a fundamental task in fluid dynamics, hydraulic engineering, and plumbing. This calculator uses the physical relationship between pressure drop and flow velocity across an orifice or restriction to determine the volumetric flow rate.
Whether you are sizing a hydraulic nozzle, checking a water pipe leak rate, or designing a pneumatic system, understanding the variables involved is crucial for accurate estimation.
The Physics: Bernoulli's Principle
The relationship between pressure and flow through an orifice is derived from Bernoulli's principle. In simple terms, as a fluid is forced through a smaller opening (an orifice), the potential energy (pressure) is converted into kinetic energy (velocity).
The standard formula used in this calculator is:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
Q: Flow Rate (m³/s)
Cd: Discharge Coefficient (accounts for turbulence and friction)
A: Cross-sectional Area of the orifice (m²)
ΔP: Pressure Difference across the orifice (Pa)
ρ (rho): Fluid Density (kg/m³)
Key Input Variables
1. Pressure Difference (ΔP)
This is not just the system pressure, but the difference between the pressure before the orifice and the pressure after it. If you are discharging water into the open air (atmosphere), the "Outlet Pressure" is effectively zero gauge pressure, so your Pressure Difference is simply your gauge reading.
2. Discharge Coefficient (Cd)
Theoretical equations assume fluids are perfect and frictionless. In reality, energy is lost to turbulence and viscosity. The Discharge Coefficient adjusts for this.
0.60 – 0.62: Standard sharp-edged orifice (most common for drilled holes).
Heavier fluids require more pressure to achieve the same velocity.
Water: 1000 kg/m³
Hydraulic Oil: ~850-900 kg/m³
Diesel: ~830 kg/m³
Air: ~1.225 kg/m³ (highly variable with pressure/temp)
Practical Example
Imagine you have a water tank pressurized to 3 Bar. There is a leak through a small hole with a diameter of 5 mm.
Diameter: 5 mm
Pressure: 3 Bar
Fluid: Water (1000 kg/m³)
Coefficient: 0.61 (irregular hole)
Using the calculator, you would find that approximately 17.5 Liters per Minute of water is being lost through that small hole. This illustrates why pressure management is critical in leak prevention.