How to Calculate Flow Rate from Rpm

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Flow Rate from RPM Calculator

Pump Flow Rate & RPM Calculator (Affinity Laws)

Use this calculator to determine the new flow rate of a centrifugal pump or fan when changing the rotational speed (RPM), based on the First Affinity Law.

(GPM, LPM, m³/h – unit stays same)

Calculation Results

New Flow Rate: 0 Units

RPM Change Ratio: 0%

Please enter valid numeric values for all fields. Current RPM must be greater than 0.

How to Calculate Flow Rate from RPM

Calculating flow rate changes based on RPM (Revolutions Per Minute) is a fundamental task in fluid dynamics and hydraulic engineering, particularly when dealing with centrifugal pumps and fans. This relationship is governed by the Pump Affinity Laws.

The Formula

The First Affinity Law states that the flow rate ($Q$) is directly proportional to the rotational speed ($N$) of the impeller. If the impeller diameter remains constant, the formula is:

Q₂ = Q₁ × (N₂ / N₁)

Where:

  • Q₁ = Initial Flow Rate (GPM, LPM, etc.)
  • N₁ = Initial Speed (RPM)
  • Q₂ = New Flow Rate
  • N₂ = New Speed (RPM)

Example Calculation

Imagine you have a water pump running at 1,750 RPM delivering a flow rate of 500 GPM (Gallons Per Minute). You install a Variable Frequency Drive (VFD) and increase the motor speed to 2,000 RPM. What is the new flow rate?

  1. Determine the ratio of speed change: $2000 / 1750 = 1.143$
  2. Multiply the original flow by this ratio: $500 \times 1.143 = 571.5$
  3. The new flow rate is 571.5 GPM.

Important Engineering Considerations

While flow rate changes linearly with speed, other parameters change at different rates according to the Affinity Laws:

Parameter Relationship to Speed Formula
Flow (Q) Directly Proportional (Linear) $Q_2 = Q_1 \times (N_2/N_1)$
Head / Pressure (H) Proportional to Square $H_2 = H_1 \times (N_2/N_1)^2$
Power (P) Proportional to Cube $P_2 = P_1 \times (N_2/N_1)^3$

Note: Because power consumption increases with the cube of the speed, a small increase in RPM requires a significantly larger increase in horsepower.

function calculateFlowRate() { // Get input values var n1 = document.getElementById('currentRPM').value; var q1 = document.getElementById('currentFlow').value; var n2 = document.getElementById('targetRPM').value; // Output elements var resultBox = document.getElementById('resultContainer'); var errorBox = document.getElementById('errorMsg'); var resultFlowSpan = document.getElementById('resultFlow'); var rpmRatioSpan = document.getElementById('rpmRatio'); // Reset display resultBox.style.display = 'none'; errorBox.style.display = 'none'; // Parse values to floats var currentRPM = parseFloat(n1); var currentFlow = parseFloat(q1); var targetRPM = parseFloat(n2); // Validation logic // Ensure all inputs are numbers and Current RPM is not zero (division by zero protection) if (isNaN(currentRPM) || isNaN(currentFlow) || isNaN(targetRPM) || currentRPM === 0) { errorBox.style.display = 'block'; return; } // Calculation Logic: Pump Affinity Law for Flow // Q2 = Q1 * (N2 / N1) var ratio = targetRPM / currentRPM; var newFlow = currentFlow * ratio; // Calculate percentage change for display var percentChange = ((targetRPM – currentRPM) / currentRPM) * 100; var percentSign = percentChange > 0 ? "+" : ""; // Update HTML with results resultFlowSpan.innerHTML = newFlow.toFixed(2); rpmRatioSpan.innerHTML = percentSign + percentChange.toFixed(1); // Show results resultBox.style.display = 'block'; }

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