Water (Liquid) – 997 kg/m³
Oil (Hydraulic/Diesel) – ~850 kg/m³
Gasoline – ~700 kg/m³
Air (Sea Level) – 1.225 kg/m³
Custom Density
PSI (Pounds/sq inch)
Bar
Pascal (Pa)
Kilopascal (kPa)
Inches
Millimeters (mm)
Centimeters (cm)
Typ: 0.60-0.65 for sharp edges, 0.98 for smooth nozzles.
Flow Rate (GPM):–
Flow Rate (Liters/min):–
Flow Rate (m³/hour):–
Flow Velocity (m/s):–
function updateDensity() {
var selector = document.getElementById('fluidType');
var densityInput = document.getElementById('densityInput');
if (selector.value !== 'custom') {
densityInput.value = selector.value;
}
}
function calculateFlow() {
// 1. Get Inputs
var pVal = parseFloat(document.getElementById('pressureInput').value);
var pUnit = document.getElementById('pressureUnit').value;
var dVal = parseFloat(document.getElementById('diameterInput').value);
var dUnit = document.getElementById('diameterUnit').value;
var density = parseFloat(document.getElementById('densityInput').value);
var cd = parseFloat(document.getElementById('cdInput').value);
// Validation
if (isNaN(pVal) || isNaN(dVal) || isNaN(density) || isNaN(cd)) {
alert("Please enter valid numeric values for all fields.");
return;
}
if (pVal < 0 || dVal <= 0 || density <= 0) {
alert("Pressure must be positive, and Diameter/Density must be greater than zero.");
return;
}
// 2. Convert Pressure to Pascals (Pa)
var pressurePa = 0;
if (pUnit === "PSI") {
pressurePa = pVal * 6894.76;
} else if (pUnit === "BAR") {
pressurePa = pVal * 100000;
} else if (pUnit === "PA") {
pressurePa = pVal;
} else if (pUnit === "KPA") {
pressurePa = pVal * 1000;
}
// 3. Convert Diameter to Meters (m)
var diameterM = 0;
if (dUnit === "INCH") {
diameterM = dVal * 0.0254;
} else if (dUnit === "MM") {
diameterM = dVal / 1000;
} else if (dUnit === "CM") {
diameterM = dVal / 100;
}
// 4. Calculate Area (m^2)
// Area = pi * r^2 = pi * (d/2)^2
var area = Math.PI * Math.pow((diameterM / 2), 2);
// 5. Calculate Flow Rate (Q) in Cubic Meters per Second (m^3/s)
// Formula: Q = Cd * A * sqrt(2 * Pressure / Density)
// This is derived from Bernoulli's principle for flow through an orifice
var q_m3s = cd * area * Math.sqrt((2 * pressurePa) / density);
// 6. Calculate Velocity (v) in m/s at the opening
// v = Q / A (effective) or just sqrt(2*P/rho) * Cd implicitly
var velocity = q_m3s / area; // Average velocity through the area
// 7. Convert Output Units
// m3/s to m3/h
var q_m3h = q_m3s * 3600;
// m3/s to Liters/min (1 m3 = 1000 L, 60s in min)
var q_lpm = q_m3s * 1000 * 60;
// m3/s to GPM (US Gallons) (1 m3 approx 264.172 US gallons)
var q_gpm = q_m3s * 264.172 * 60;
// 8. Display Results
document.getElementById('resGPM').innerHTML = q_gpm.toFixed(2) + " gal/min";
document.getElementById('resLPM').innerHTML = q_lpm.toFixed(2) + " L/min";
document.getElementById('resM3H').innerHTML = q_m3h.toFixed(2) + " m³/h";
document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " m/s";
document.getElementById('results').style.display = "block";
}
How to Convert Pressure to Flow Rate
Understanding the relationship between fluid pressure and flow rate is essential for engineers, plumbers, and technicians working with hydraulic or pneumatic systems. While pressure and flow are distinct properties, they are intrinsically linked by the physical characteristics of the system, such as pipe size and fluid density.
Quick Summary: Pressure (PSI or Bar) creates the force that moves fluid. The flow rate (GPM or L/min) is how much fluid actually moves. To convert one to the other, you must know the size of the opening (orifice) the fluid passes through and the density of the fluid.
The Calculation Formula
This calculator utilizes Torricelli's Law derived from Bernoulli's Principle, which describes the flow of a fluid through an orifice (a hole or restriction). The general formula used is:
Q = Cd × A × √(2 × ΔP / ρ)
Where:
Q: Flow rate (Volumetric flow).
Cd: Discharge Coefficient. This accounts for friction and turbulence. A perfect theoretical hole is 1.0. A sharp-edged hole is typically 0.60 to 0.62. A smooth nozzle might be 0.98.
A: Cross-sectional area of the opening (calculated from the diameter).
ΔP: Pressure difference across the opening (e.g., Pressure inside pipe minus atmospheric pressure).
ρ (rho): Fluid density (Water is ~997 kg/m³).
Why is the Discharge Coefficient (Cd) Important?
If you enter a pressure and diameter into a theoretical formula without a discharge coefficient, the result will be higher than real-world conditions. Real fluids experience friction. As water passes through a sharp hole, the flow stream contracts (vena contracta), effectively reducing the area. The standard value of 0.62 is used in this calculator as a safe baseline for sharp-edged orifices.
Example Calculation
Let's say you have a water pipe (Density = 997 kg/m³) with a pressure of 50 PSI discharging through a 0.5-inch hole.
Convert Pressure: 50 PSI ≈ 344,738 Pascals.
Convert Diameter: 0.5 inches = 0.0127 meters.
Calculate Area: A = π × (0.00635)² ≈ 0.0001267 m².
Apply Formula: Assuming a Cd of 0.62.
Result: The flow rate would be approximately 19.7 GPM (Gallons Per Minute).
Key Factors Affecting Flow
1. Pressure Difference: Doubling the pressure does not double the flow rate. Because flow is proportional to the square root of pressure, you need four times the pressure to double the flow.
2. Orifice Diameter: Small changes in diameter have a massive impact. Since Area is a function of the radius squared, doubling the diameter increases the area (and potentially the flow) by a factor of four.
3. Fluid Density: Heavier fluids (like mercury or heavy oil) flow slower than lighter fluids (like water or gasoline) under the same pressure.
Common Applications
Fire Hoses: Calculating water output at the nozzle based on pump pressure.
Irrigation: Determining GPM for sprinkler heads based on water line PSI.
Hydraulics: Sizing orifices to control the speed of hydraulic cylinders.
Leak Estimation: Estimating how much fluid is lost through a puncture or crack in a pressurized tank.