Pressure Diameter Flow Rate Calculator

Pressure, Diameter & Flow Rate Calculator

0.61 (Sharp Edged Orifice) 0.80 (Average Pipe/Nozzle) 0.98 (Well-rounded Nozzle) A value representing the efficiency of the flow opening.

Calculated Flow Results:

Gallons Per Minute (GPM): 0

Liters Per Minute (L/min): 0

Velocity: 0 ft/s

Understanding Fluid Flow from Pressure and Diameter

In fluid dynamics, the relationship between pressure, pipe diameter, and flow rate is governed by Bernoulli's principle and the Law of Continuity. This calculator uses the orifice flow equation, which is the industry standard for estimating how much water or fluid will exit a pipe or nozzle at a specific pressure.

The Calculation Formula

The core formula used in this calculator for water is:

Q = 29.84 × Cd × d² × √P

• Q: Flow rate in Gallons Per Minute (GPM)
• Cd: Discharge coefficient (dimensionless)
• d: Inside diameter of the pipe/orifice in inches
• P: Pressure drop or gauge pressure in PSI

Key Factors Influencing Flow

Determining flow rate isn't just about the hole size. Several environmental factors play a role:

1. Static vs. Residual Pressure: Static pressure is the pressure when no water is moving. Residual pressure is the pressure measured while water is flowing. For accurate calculations, use the residual pressure.
2. Pipe Smoothness: Friction loss occurs as water rubs against the interior walls of a pipe. While this calculator assumes a localized exit point, long pipe runs will significantly reduce the actual delivered pressure.
3. Fluid Viscosity: This tool is calibrated for water. Thicker fluids (like oils) will result in lower flow rates at the same pressure and diameter.

Practical Example

If you have a 1-inch pipe (Diameter = 1.0) and a measured pressure of 40 PSI using a standard nozzle (Cd = 0.98), the calculation would look like this:

Q = 29.84 × 0.98 × (1.0)² × √40
Q = 29.84 × 0.98 × 1 × 6.32
Flow Rate ≈ 184.8 GPM

Frequently Asked Questions

What is a Discharge Coefficient (Cd)?

It is a ratio that accounts for the fact that fluid cannot perfectly exit an opening due to turbulence and the contraction of the fluid stream (vena contracta). A perfectly smooth nozzle has a Cd near 0.98, while a rough, sharp-cut pipe end is closer to 0.61.

How does doubling the diameter affect flow?

Because diameter is squared in the equation, doubling the diameter actually quadruples the flow rate, assuming pressure remains constant.

function calculateFluidFlow() { var pressure = parseFloat(document.getElementById("pressure_val").value); var diameter = parseFloat(document.getElementById("diameter_val").value); var cd = parseFloat(document.getElementById("coefficient_val").value); var resultContainer = document.getElementById("flow-result-container"); if (isNaN(pressure) || isNaN(diameter) || pressure <= 0 || diameter <= 0) { alert("Please enter valid positive numbers for Pressure and Diameter."); return; } // Calculation: Q = 29.84 * Cd * d^2 * sqrt(P) var sqrtP = Math.sqrt(pressure); var dSquared = Math.pow(diameter, 2); var gpm = 29.84 * cd * dSquared * sqrtP; // Convert GPM to Liters Per Minute (1 GPM = 3.78541 L/min) var lpm = gpm * 3.78541; // Calculate Velocity (v = Q / A) // Area in square inches = pi * (d/2)^2 // Area in square feet = Area / 144 // Q in cubic feet per second = GPM / 448.83 var areaInches = Math.PI * Math.pow((diameter / 2), 2); var qCFS = gpm / 448.83; var areaSqFt = areaInches / 144; var velocity = qCFS / areaSqFt; // Display Results document.getElementById("gpm_output").innerText = gpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("lpm_output").innerText = lpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("velocity_output").innerText = velocity.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); resultContainer.style.display = "block"; resultContainer.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }