Positive Displacement Pump Flow Rate Calculation

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Positive Displacement Pump Flow Rate Calculator

Imperial (in³/rev & GPM) Metric (cm³/rev & LPM)
Typical range: 85% to 95%

Calculation Results

function updateLabels() { var units = document.getElementById('calcUnits').value; var dispLabel = document.getElementById('displacementLabel'); if (units === 'imperial') { dispLabel.innerText = 'Pump Displacement (cubic inches per revolution)'; } else { dispLabel.innerText = 'Pump Displacement (cm³ per revolution)'; } } function calculatePDSlow() { var displacement = parseFloat(document.getElementById('displacement').value); var rpm = parseFloat(document.getElementById('rpm').value); var efficiency = parseFloat(document.getElementById('efficiency').value); var units = document.getElementById('calcUnits').value; var resDiv = document.getElementById('flowResult'); var theoreticalPara = document.getElementById('theoreticalResult'); var actualPara = document.getElementById('actualResult'); if (isNaN(displacement) || isNaN(rpm) || isNaN(efficiency) || displacement <= 0 || rpm <= 0) { alert('Please enter valid positive numbers for all fields.'); return; } var theoreticalFlow; var actualFlow; var unitShort; if (units === 'imperial') { // Formula: (in³/rev * RPM) / 231 = GPM theoreticalFlow = (displacement * rpm) / 231; unitShort = ' GPM'; } else { // Formula: (cm³/rev * RPM) / 1000 = LPM theoreticalFlow = (displacement * rpm) / 1000; unitShort = ' LPM'; } actualFlow = theoreticalFlow * (efficiency / 100); theoreticalPara.innerHTML = 'Theoretical Flow Rate: ' + theoreticalFlow.toFixed(3) + unitShort; actualPara.innerHTML = 'Actual Flow Rate (' + efficiency + '% Efficiency): ' + actualFlow.toFixed(3) + unitShort; resDiv.style.display = 'block'; }

Understanding Positive Displacement Pump Flow Calculations

Positive displacement (PD) pumps operate by trapping a fixed amount of fluid and forcing (displacing) that volume into the discharge pipe. Unlike centrifugal pumps, the flow rate of a PD pump is directly proportional to its speed (RPM), regardless of the system pressure, assuming perfect efficiency.

The Mathematical Formula

To calculate the flow rate of a positive displacement pump, you must account for the mechanical displacement of the pump chambers and the speed at which the pump cycles. The standard formulas used in this calculator are:

  • Imperial: Flow (GPM) = [Displacement (in³/rev) × Speed (RPM)] / 231
  • Metric: Flow (LPM) = [Displacement (cm³/rev) × Speed (RPM)] / 1000

The constant 231 is used in the imperial formula because there are 231 cubic inches in one US gallon. In the metric system, 1000 is used as there are 1000 cubic centimeters in one liter.

What is Volumetric Efficiency?

In a perfect world, a pump would deliver 100% of its displaced volume. However, in real-world applications, internal leakage (often called "slip"), fluid compressibility, and cavitation reduce the output. Volumetric Efficiency is the ratio of the actual flow delivered to the theoretical flow. High-viscosity fluids typically result in higher volumetric efficiency because they leak less through internal clearances.

Practical Example

Imagine a hydraulic gear pump with a displacement of 3.0 cubic inches per revolution running at 1,800 RPM with an estimated efficiency of 92%.

  1. Theoretical Flow: (3.0 × 1,800) / 231 = 23.376 GPM
  2. Actual Flow: 23.376 × 0.92 = 21.506 GPM

In this scenario, the "slip" or loss due to internal clearances is approximately 1.87 GPM.

Key Factors Influencing Flow Rate

  • Fluid Viscosity: Thinner fluids increase slip, lowering actual flow.
  • System Pressure: Higher discharge pressures force more fluid back through internal clearances, reducing volumetric efficiency.
  • Wear and Tear: As internal components wear, clearances increase, leading to significant flow loss.

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