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function calculateFlowRate() {
// Get Input Values
var diameterMM = parseFloat(document.getElementById("nozzleDiameter").value);
var pressureBar = parseFloat(document.getElementById("inletPressure").value);
var cd = parseFloat(document.getElementById("dischargeCoeff").value);
var density = parseFloat(document.getElementById("fluidDensity").value);
// Validation
if (isNaN(diameterMM) || diameterMM <= 0) {
alert("Please enter a valid nozzle diameter greater than 0.");
return;
}
if (isNaN(pressureBar) || pressureBar < 0) {
alert("Please enter a valid pressure value.");
return;
}
if (isNaN(cd) || cd 1) {
alert("Discharge Coefficient must be between 0 and 1.");
return;
}
if (isNaN(density) || density meters
var diameterM = diameterMM / 1000;
// Pressure: bar -> Pascals (Pa) -> 1 bar = 100,000 Pa
// We assume pressure drop is equal to gauge pressure (discharging to atmosphere)
var pressurePa = pressureBar * 100000;
// 2. Calculate Cross-Sectional Area (A) in m²
// Area = π * r² = π * (d/2)²
var radiusM = diameterM / 2;
var areaM2 = Math.PI * Math.pow(radiusM, 2);
// 3. Calculate Velocity (v) using Bernoulli's/Torricelli's
// v = Cd * sqrt(2 * P / rho)
var velocityMS = cd * Math.sqrt((2 * pressurePa) / density);
// 4. Calculate Flow Rate (Q) in m³/s
// Q = A * v
var flowM3S = areaM2 * velocityMS;
// 5. Convert Results to User Friendly Units
// Area in mm²
var areaMM2 = areaM2 * 1000000;
// Flow in Liters Per Minute (LPM)
// 1 m³/s = 60,000 LPM
var flowLPM = flowM3S * 60000;
// Flow in Cubic Meters per Hour (m³/h)
// 1 m³/s = 3600 m³/h
var flowM3H = flowM3S * 3600;
// Display Results
document.getElementById("resLPM").innerText = flowLPM.toFixed(2) + " L/min";
document.getElementById("resM3H").innerText = flowM3H.toFixed(3) + " m³/h";
document.getElementById("resVelocity").innerText = velocityMS.toFixed(2) + " m/s";
document.getElementById("resArea").innerText = areaMM2.toFixed(3) + " mm²";
// Show result box
document.getElementById("resultsArea").style.display = "block";
}
How to Calculate Flow Rate Through a Nozzle
Understanding how to calculate the flow rate through a nozzle is essential for engineers, irrigation specialists, and technicians working with fluid dynamics. Whether you are calibrating a pressure washer, designing a fire suppression system, or setting up agricultural sprayers, determining the volumetric flow rate ensures your system operates efficiently and safely.
The flow rate depends primarily on three factors: the size of the nozzle orifice, the fluid pressure at the inlet, and the specific density of the fluid being sprayed.
The Nozzle Flow Equation
The calculation of flow through a nozzle is derived from Bernoulli's principle. For most practical applications involving liquids discharging into the atmosphere, the formula is:
Q = Cd × A × √(2ΔP / ρ)
Where:
- Q = Volumetric Flow Rate (m³/s)
- Cd = Discharge Coefficient (dimensionless)
- A = Cross-sectional Area of the nozzle orifice (m²)
- ΔP = Pressure drop across the nozzle (Pascals). If spraying into open air, this is the Gauge Pressure at the inlet.
- ρ (rho) = Fluid Density (kg/m³). Water is approx 1000 kg/m³.
Understanding the Input Variables
1. Nozzle Diameter & Area
The physical size of the hole is the most significant factor. Even a small increase in diameter results in a large increase in area (since Area is proportional to the square of the diameter), drastically increasing flow.
2. Inlet Pressure
Pressure drives the fluid through the restriction. The relationship is non-linear; to double the flow rate, you must quadruple the pressure. This is why increasing pump pressure is often an inefficient way to gain significantly more volume compared to simply changing the nozzle size.
3. Discharge Coefficient (Cd)
In the real world, friction and turbulence prevent fluid from flowing perfectly. The Discharge Coefficient accounts for these losses.
Most standard smooth nozzles have a Cd between 0.95 and 0.99. Sharp-edged orifices may be closer to 0.60. If you are unsure, 0.98 is a safe standard value for commercial spray nozzles.
Example Calculation
Let's calculate the flow rate for a pressure washer nozzle with the following specs:
- Diameter: 2 mm
- Pressure: 100 bar
- Fluid: Water (1000 kg/m³)
- Cd: 0.98
Step 1: Convert units to SI.
Diameter = 0.002 m. Pressure = 10,000,000 Pascals.
Step 2: Calculate Area (A).
A = π × (0.001)² ≈ 3.14159 × 10⁻⁶ m².
Step 3: Calculate Velocity.
v = 0.98 × √(2 × 10,000,000 / 1000)
v = 0.98 × √20,000 ≈ 0.98 × 141.42 ≈ 138.6 m/s.
Step 4: Calculate Flow (Q).
Q = 3.14159 × 10⁻⁶ × 138.6 ≈ 0.000435 m³/s.
Step 5: Convert to LPM.
0.000435 × 60,000 ≈ 26.1 Liters per Minute.
Applications of Flow Rate Calculation
Irrigation: Ensuring each sprinkler head delivers the correct amount of water to cover a specific crop zone without overwatering.
Firefighting: Determining if a specific hose and nozzle combination can deliver the required gallons per minute (GPM) to extinguish a fire based on the pump's pressure capabilities.
Industrial Cleaning: Matching the nozzle size to the high-pressure pump to prevent pump cavitation or lack of cleaning power.