Default 0.62 for sharp-edged orifice. Use 0.98 for smooth nozzles.
Flow Rate (Liters/min):–
Flow Rate (m³/hour):–
Flow Rate (US GPM):–
Est. Fluid Velocity:–
function calculateFlowRate() {
// Get input values
var pressureBar = document.getElementById('calc_pressure').value;
var diameterMm = document.getElementById('calc_diameter').value;
var cd = document.getElementById('calc_cd').value;
// Validation
if (pressureBar === "" || diameterMm === "" || cd === "") {
alert("Please fill in all fields (Pressure, Diameter, and Cd).");
return;
}
var P_bar = parseFloat(pressureBar);
var D_mm = parseFloat(diameterMm);
var Cd = parseFloat(cd);
if (isNaN(P_bar) || isNaN(D_mm) || isNaN(Cd) || P_bar < 0 || D_mm 1 Bar = 100,000 Pa
var P_pa = P_bar * 100000;
// Convert Diameter: mm to meters
var D_m = D_mm / 1000;
// Calculate Area (A) in m²
// A = π * (d/2)²
var Area = Math.PI * Math.pow((D_m / 2), 2);
// Calculate Velocity (v) using Bernoulli's principle / Torricelli's Law
// v = sqrt(2 * P / rho)
// Note: This assumes discharge to atmosphere (0 gauge pressure)
var velocity = Math.sqrt((2 * P_pa) / rho);
// Calculate Flow Rate (Q) in m³/s
// Q = Cd * A * v
var Q_m3s = Cd * Area * velocity;
// Unit Conversions for Output
// m³/s to Liters/min (1 m³/s = 60,000 L/min)
var Q_lpm = Q_m3s * 60000;
// m³/s to m³/hour (1 m³/s = 3600 m³/h)
var Q_m3h = Q_m3s * 3600;
// m³/s to US Gallons per Minute (1 m³/s ≈ 15850.32 GPM)
var Q_gpm = Q_m3s * 15850.32;
// Display Results
document.getElementById('res_lpm').innerHTML = Q_lpm.toFixed(2) + " L/min";
document.getElementById('res_m3h').innerHTML = Q_m3h.toFixed(2) + " m³/h";
document.getElementById('res_gpm').innerHTML = Q_gpm.toFixed(2) + " GPM";
document.getElementById('res_velocity').innerHTML = velocity.toFixed(2) + " m/s";
// Show results container
document.getElementById('results').style.display = "block";
}
Understanding Water Flow Rate Calculations
Calculating the water flow rate through a pipe or orifice based on pressure and diameter is a fundamental task in fluid dynamics, plumbing, and irrigation engineering. While many professionals look for a "water flow rate calculator pressure and diameter PDF" or chart, using a dynamic digital calculator provides significantly more accurate results tailored to your specific variables.
Note on Physics: This calculator uses the orifice discharge formula derived from Bernoulli's principle. It assumes the water is being discharged from a pressurized system into the atmosphere (or a lower pressure zone).
The Formula Behind the Calculation
To determine the flow rate ($Q$) when you know the pressure ($P$) and the opening diameter ($d$), we typically use a variation of Torricelli's Law adjusted by a discharge coefficient ($C_d$).
The core equation is:
Q = Cd × A × √(2ΔP / ρ)
Q: Flow rate (Volumetric flow)
Cd: Discharge Coefficient (accounts for energy losses and contraction of the flow stream)
A: Cross-sectional area of the opening ($\pi \cdot r^2$)
ΔP: Pressure difference (Gauge pressure at the opening)
ρ: Fluid density (Water ≈ 997 kg/m³)
Why Diameter Matters More Than Pressure
When analyzing the inputs, you will notice that doubling the pressure does not double the flow rate; it only increases it by a factor of approximately 1.41 (the square root of 2). However, doubling the diameter of the pipe or nozzle increases the cross-sectional area by a factor of 4, which roughly quadruples the flow rate.
This is why pipe sizing is the most critical factor in system design. A small increase in diameter yields a massive gain in flow capacity, whereas increasing pump pressure yields diminishing returns.
Using the Discharge Coefficient ($C_d$)
In real-world physics, water doesn't flow perfectly efficiently through a hole. Friction and turbulence reduce the actual flow compared to the theoretical maximum.
0.60 – 0.62: Standard sharp-edged orifice (like a hole drilled in a tank or pipe).
0.80 – 0.85: Short tube or slightly rounded edges.
0.95 – 0.98: Smooth, well-designed nozzles (like fire hose nozzles).
This calculator defaults to 0.62, which is the industry standard safety factor for general openings, but you can adjust it if you are using high-efficiency nozzles.
Replacing Static PDF Charts
Historically, engineers relied on "pressure vs. flow" PDF tables. These charts are limited because they usually offer fixed intervals (e.g., 10mm, 20mm, 30mm). If you have a 17mm opening or 3.4 Bar of pressure, a PDF chart forces you to guess or interpolate. This calculator solves that problem by computing the exact physics for any numeric input instantly.