Estimate discharge flow rate based on pressure and opening diameter.
0.98 – Smooth Nozzle
0.80 – Short Tube
0.61 – Sharp Edged Orifice
0.92 – Fire Nozzle
Calculation Results
Flow Rate (GPM):–
Flow Rate (Liters/min):–
Water Velocity (ft/sec):–
Estimated Output (Gallons/Hour):–
function calculateFlow() {
// Retrieve input values
var pressure = parseFloat(document.getElementById('pressurePsi').value);
var diameter = parseFloat(document.getElementById('diameterIn').value);
var cd = parseFloat(document.getElementById('coeffCd').value);
// Validation
if (isNaN(pressure) || isNaN(diameter) || pressure < 0 || diameter <= 0) {
alert("Please enter valid positive numbers for Pressure and Diameter.");
return;
}
// Calculation using Torricelli's Law variant for flow through an orifice
// Formula: Q (GPM) = 29.83 * Cd * d^2 * sqrt(P)
// Where P is PSI, d is inches
var flowGPM = 29.83 * cd * Math.pow(diameter, 2) * Math.sqrt(pressure);
// Conversions
var flowLPM = flowGPM * 3.78541;
var flowGPH = flowGPM * 60;
// Calculate Velocity
// Formula: Velocity (ft/s) = (0.408 * Q(gpm)) / d(in)^2
// Note: This is derived from Q = v * A
var velocity = (0.408 * flowGPM) / Math.pow(diameter, 2);
// Display Results
document.getElementById('resGPM').innerHTML = flowGPM.toFixed(2) + " GPM";
document.getElementById('resLPM').innerHTML = flowLPM.toFixed(2) + " L/min";
document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " ft/s";
document.getElementById('resGPH').innerHTML = flowGPH.toFixed(0).replace(/\B(?=(\d{3})+(?!\d))/g, ",") + " GPH";
// Show results container
document.getElementById('resultsArea').style.display = "block";
}
Understanding Water Pressure vs. Flow Rate
When designing plumbing systems, irrigation setups, or analyzing industrial fluid dynamics, the relationship between water pressure (measured in PSI) and flow rate (measured in GPM) is fundamental. While often used interchangeably in casual conversation, they are distinct physical properties that interact in specific ways governed by fluid mechanics.
The Core Difference
Pressure (PSI): This is the potential energy of the water. It represents the force exerted by the water against the walls of the pipe or container. Think of it as how "hard" the water is pushing.
Flow Rate (GPM): This is the kinetic result—the actual volume of water moving through a specific point over time. It represents how "much" water is moving.
Analogy: Think of electricity. Voltage is like Pressure (the push), and Amperage is like Flow Rate (the current moving). You can have high voltage with no current flowing if the switch is off (closed valve).
How to Calculate Flow Rate from Pressure
To determine how much water will flow through an opening (like a nozzle, a leak, or a pipe end) given a specific pressure, we use a derivation of Torricelli's Law. The formula used in this calculator is:
Q = 29.83 × Cd × d² × √P
Where:
Q: Flow rate in Gallons Per Minute (GPM).
Cd: Discharge Coefficient. This accounts for friction and turbulence caused by the shape of the opening. A perfect opening is 1.0, but most real-world sharp-edged orifices are around 0.61.
d: Diameter of the opening in inches.
P: Pressure in pounds per square inch (PSI).
Why Diameter Matters More Than Pressure
You might notice from the formula that the diameter (d) is squared, while the pressure (P) is only a square root. This means that changing the pipe size has a significantly larger impact on flow rate than changing the pressure.
For example, doubling the pressure increases flow by roughly 41% (√2). However, doubling the diameter increases the flow by 300% (2² = 4 times the area)!
Common Discharge Coefficients (Cd)
The "efficiency" of the opening affects the calculation:
0.61 (Sharp Edged): A standard hole drilled in a tank or pipe with sharp edges.
0.80 (Short Tube): A short length of pipe extending from a tank.
0.98 (Smooth Nozzle): A carefully tapered nozzle designed to maximize flow efficiency (like a fire hose nozzle).
Applications of This Calculation
This calculator is useful for:
Irrigation: Determining which sprinkler heads to use based on available water pressure.
Plumbing: Estimating flow from a showerhead or faucet at different household pressures.
Leak Analysis: Estimating how much water is lost through a hole of a specific size in a pressurized pipe.
Pressure Washing: calculating the required nozzle size to achieve a specific PSI given a pump's GPM rating.
Important Limitations
This calculator assumes the pressure supplied is the dynamic pressure at the point of discharge. In long pipe runs, friction causes pressure loss (head loss) as water travels. If you have 50 PSI at the source but a 100-foot garden hose, the pressure at the nozzle will be lower than 50 PSI due to friction. To account for pipe length friction, one would need to use the Hazen-Williams equation.