Formula to Calculate Flow Rate of Pump

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Hydraulic Pump Flow Rate Calculator

Calculation Results

Theoretical Flow Rate (GPM): –
Actual Flow Rate (GPM): –
Metric Flow Rate (L/min): –

Formula to Calculate Flow Rate of a Pump

Understanding the flow rate of a hydraulic pump is essential for sizing system components, determining actuator speeds, and ensuring the efficiency of your hydraulic circuit. The flow rate is primarily determined by the pump's displacement (size) and the speed at which it is driven.

The Flow Rate Formula

For positive displacement pumps (like gear, vane, or piston pumps), the flow rate is calculated using the displacement per revolution and the rotational speed (RPM). The standard formula for US Gallons Per Minute (GPM) is:

Q (GPM) = (D × N) / 231

Where:

  • Q = Theoretical Flow Rate in Gallons Per Minute (GPM)
  • D = Pump Displacement in cubic inches per revolution (in³/rev)
  • N = Pump drive speed in Revolutions Per Minute (RPM)
  • 231 = Conversion constant (231 cubic inches = 1 Gallon)

Accounting for Efficiency

The formula above calculates the theoretical flow rate. In the real world, pumps are not 100% efficient due to internal leakage and fluid slippage, especially at higher pressures. To find the Actual Flow Rate, you must apply the Volumetric Efficiency factor:

Actual Q = Theoretical Q × (Efficiency % / 100)

Most new hydraulic pumps operate with a volumetric efficiency between 85% and 95%. As pumps wear out, this efficiency decreases, leading to lower flow rates.

Example Calculation

Let's calculate the flow rate for a standard hydraulic setup:

  • Displacement: 2.5 in³/rev
  • Speed: 1750 RPM (standard electric motor speed)
  • Efficiency: 95%

Step 1: Calculate Theoretical Flow
(2.5 × 1750) / 231 = 18.94 GPM

Step 2: Apply Efficiency
18.94 × 0.95 = 17.99 GPM (Actual)

function calculateFlowRate() { // Get input values var displacement = parseFloat(document.getElementById('displacement').value); var rpm = parseFloat(document.getElementById('rpm').value); var efficiency = parseFloat(document.getElementById('efficiency').value); // Validation if (isNaN(displacement) || isNaN(rpm) || isNaN(efficiency)) { alert("Please enter valid numbers for all fields."); return; } if (displacement <= 0 || rpm <= 0 || efficiency 100) { alert("Please ensure values are positive and efficiency is between 0 and 100."); return; } // 1. Calculate Theoretical Flow (GPM) // Formula: (Displacement * RPM) / 231 var theoreticalGPM = (displacement * rpm) / 231; // 2. Calculate Actual Flow (GPM) based on efficiency var actualGPM = theoreticalGPM * (efficiency / 100); // 3. Convert Actual Flow to Liters Per Minute (LPM) // 1 GPM = 3.78541 LPM var metricLPM = actualGPM * 3.78541; // Display Results document.getElementById('results').style.display = 'block'; document.getElementById('theoGPM').innerHTML = theoreticalGPM.toFixed(2); document.getElementById('actualGPM').innerHTML = actualGPM.toFixed(2); document.getElementById('metricLPM').innerHTML = metricLPM.toFixed(2); }

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