The internal diameter of the pipe opening or nozzle.
Efficiency of flow. 0.98 for smooth nozzles, 0.60 for sharp-edged orifices.
Calculation Results
Required Pressure (PSI):–
Required Pressure (Bar):–
Fluid Velocity (ft/sec):–
function calculatePressure() {
// 1. Get input values
var flowRateGPM = parseFloat(document.getElementById('flowRate').value);
var diameterInches = parseFloat(document.getElementById('diameter').value);
var dischargeCoef = parseFloat(document.getElementById('dischargeCoef').value);
// 2. Validate inputs
if (isNaN(flowRateGPM) || flowRateGPM <= 0) {
alert("Please enter a valid Flow Rate greater than 0.");
return;
}
if (isNaN(diameterInches) || diameterInches <= 0) {
alert("Please enter a valid Diameter greater than 0.");
return;
}
if (isNaN(dischargeCoef) || dischargeCoef 1) {
alert("Please enter a Discharge Coefficient between 0.01 and 1.0.");
return;
}
// 3. Define Constants
var densityWaterKgM3 = 997; // Density of water at room temp
// 4. Convert Units to SI (Meters, Seconds) for calculation
// 1 GPM = 6.30902e-5 m^3/s
var flowRateM3S = flowRateGPM * 0.0000630902;
// 1 Inch = 0.0254 Meters
var diameterMeters = diameterInches * 0.0254;
// 5. Calculate Area (A = pi * r^2)
var radiusMeters = diameterMeters / 2;
var areaM2 = Math.PI * Math.pow(radiusMeters, 2);
// 6. Calculate Pressure using Bernoullis/Orifice equation rearranged
// Q = Cd * A * sqrt(2 * P / rho)
// P = (0.5 * rho) * (Q / (Cd * A))^2
var velocityTerm = flowRateM3S / (dischargeCoef * areaM2);
var pressurePascals = 0.5 * densityWaterKgM3 * Math.pow(velocityTerm, 2);
// 7. Convert Results to imperial/readable units
// 1 Pascal = 0.000145038 PSI
// 1 Pascal = 0.00001 Bar
var pressurePSI = pressurePascals * 0.000145038;
var pressureBar = pressurePascals / 100000;
// Velocity in ft/s (1 m/s = 3.28084 ft/s)
// Note: Real fluid velocity is Q/A, but effective velocity for pressure calc includes Cd.
// We usually display the physical velocity Q/A for reference.
var physicalVelocityM3S = flowRateM3S / areaM2;
var velocityFtS = physicalVelocityM3S * 3.28084;
// 8. Display Results
document.getElementById('resPsi').innerHTML = pressurePSI.toFixed(2) + " PSI";
document.getElementById('resBar').innerHTML = pressureBar.toFixed(2) + " Bar";
document.getElementById('resVelocity').innerHTML = velocityFtS.toFixed(2) + " ft/s";
document.getElementById('results').style.display = 'block';
}
Understanding Water Flow Rate and Pressure
Calculating the relationship between water flow rate and pressure is essential for hydraulic engineering, irrigation planning, plumbing, and fire fighting operations. This calculator helps determine the pressure required at a nozzle or orifice to achieve a specific flow rate given the diameter of the opening.
How the Calculation Works
The conversion relies on the principles of fluid dynamics, specifically the orifice discharge equation derived from Bernoulli's principle. The formula expresses the relationship between the flow rate ($Q$), the area of the opening ($A$), and the pressure drop ($\Delta P$).
The Formula:
$$ P = \frac{\rho}{2} \left( \frac{Q}{C_d \cdot A} \right)^2 $$
Q (Flow Rate): The volume of water moving per unit of time (e.g., Gallons Per Minute).
A (Area): The cross-sectional area of the pipe or nozzle opening ($\pi r^2$).
Cd (Discharge Coefficient): A dimensionless number representing the efficiency of the nozzle. A perfect nozzle is 1.0. Typical smooth fire nozzles are around 0.97-0.99, while sharp-edged orifices are around 0.60-0.62.
$\rho$ (Density): The density of water (approx 8.33 lbs/gal or 997 kg/m³).
Example Calculation
Let's say you want to determine the pressure required to push 100 GPM through a nozzle with a 1-inch tip.
Flow Rate: 100 GPM
Diameter: 1.0 Inch
Coefficient: 0.98 (Standard smooth nozzle)
Using the calculator above, this scenario requires approximately 40.8 PSI of pressure at the nozzle tip. If you reduced the nozzle size to 0.75 inches while trying to maintain 100 GPM, the required pressure would jump significantly due to the restriction, requiring roughly 129 PSI.
Key Factors Influencing Pressure
1. Nozzle Diameter
Diameter has the most significant impact on pressure. Because area is a function of the square of the radius, halving the diameter reduces the area by a factor of four, which drastically increases the pressure required to maintain the same flow rate.
2. Discharge Coefficient ($C_d$)
The shape of the opening matters. A smooth, tapered nozzle ($C_d \approx 0.98$) allows water to flow efficiently. A rough hole or a sharp-edged orifice ($C_d \approx 0.60$) creates turbulence, requiring more pressure to push the same amount of water through.
Common Applications
Fire Fighting: Determining pump pressures needed to supply fire hoses with specific GPM ratings.
Irrigation: Selecting pumps that can provide enough pressure for sprinkler heads to operate at their rated flow.
Pressure Washing: Calculating the nozzle tip size needed to achieve a specific PSI at a specific flow rate.