How to Calculate Flow Rate from Psi

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Flow Rate From PSI Calculator

Smooth Bore Nozzle (0.99) Sharp Edged Orifice (0.90) Average Valve (0.80) Square Edged Orifice (0.62)

Calculated Flow Rate:

How to Calculate Flow Rate from PSI

In fluid dynamics, the relationship between pressure (PSI) and flow rate (GPM) is determined by the size of the opening (orifice) the fluid is passing through. This calculation is essential for irrigation systems, fire protection engineering, and industrial plumbing.

The Discharge Formula

The standard formula to calculate the flow rate of water discharging into the atmosphere from an orifice is:

GPM = 29.7 × d² × √P × Cd

  • GPM: Gallons Per Minute
  • d: Diameter of the orifice in inches
  • P: Pressure at the orifice in PSI (Pounds per Square Inch)
  • Cd: Discharge Coefficient (accounts for friction and turbulence)

Step-by-Step Calculation Example

Scenario: You have a 1/2-inch (0.5″) nozzle operating at 40 PSI using a smooth bore tip (Cd = 0.99).

  1. Square the diameter: 0.5 × 0.5 = 0.25
  2. Find the square root of the pressure: √40 ≈ 6.32
  3. Multiply by the constant: 29.7 × 0.25 × 6.32 × 0.99
  4. Result: ≈ 46.47 GPM

The Pressure-Flow Relationship

It is important to remember that flow rate is proportional to the square root of the pressure. This means that to double your flow rate through the same nozzle, you must increase the pressure by four times. Conversely, if you double the diameter of the hole, the flow rate increases by four times because diameter is squared in the formula.

Common Discharge Coefficients (Cd)

Orifice Type Typical Cd
Smooth Bore Nozzle 0.99
Circular Orifice (Short tube) 0.82
Square-edged Orifice 0.62
function calculateFlow() { var d = parseFloat(document.getElementById("orifice_dia").value); var p = parseFloat(document.getElementById("pressure_psi").value); var cd = parseFloat(document.getElementById("coeff").value); if (isNaN(d) || isNaN(p) || d <= 0 || p <= 0) { alert("Please enter valid positive numbers for diameter and pressure."); return; } // Formula: GPM = 29.7 * d^2 * sqrt(P) * Cd var dSquared = d * d; var sqrtP = Math.sqrt(p); var gpm = 29.7 * dSquared * sqrtP * cd; // Convert to LPM (1 GPM = 3.78541 Liters) var lpm = gpm * 3.78541; // Display Results document.getElementById("flowResult").style.display = "block"; document.getElementById("gpm_val").innerHTML = gpm.toFixed(2) + " GPM (US Gallons)"; document.getElementById("lpm_val").innerHTML = "Equivalent to " + lpm.toFixed(2) + " LPM (Liters Per Minute)"; }

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