Mass Flow Rate Calculation Formula

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Mass Flow Rate Calculator

kg/m³
m/s
mm
Please enter valid positive numbers for all fields.

Calculation Results:

Mass Flow Rate (kg/s):
Mass Flow Rate (kg/hr):
Volumetric Flow Rate (m³/hr):
Cross-Sectional Area (cm²):
function calculateMassFlow() { // Get input values var density = parseFloat(document.getElementById('fluidDensity').value); var velocity = parseFloat(document.getElementById('flowVelocity').value); var diameterMM = parseFloat(document.getElementById('pipeDiameter').value); var errorDiv = document.getElementById('mfrError'); var resultDiv = document.getElementById('mfrResult'); // Validation logic if (isNaN(density) || isNaN(velocity) || isNaN(diameterMM) || density <= 0 || velocity <= 0 || diameterMM <= 0) { errorDiv.style.display = "block"; resultDiv.style.display = "none"; return; } errorDiv.style.display = "none"; // 1. Calculate Area from Diameter (mm to meters) // Formula: A = PI * (d/2)^2 // Convert diameter mm to meters: d / 1000 var diameterM = diameterMM / 1000; var radiusM = diameterM / 2; var areaM2 = Math.PI * Math.pow(radiusM, 2); // Calculate Area in cm2 for display var areaCm2 = areaM2 * 10000; // 2. Calculate Volumetric Flow Rate (Q = v * A) // Unit: m³/s var volFlowRateM3S = velocity * areaM2; // Convert to m³/h var volFlowRateM3H = volFlowRateM3S * 3600; // 3. Calculate Mass Flow Rate (m_dot = rho * Q) // Unit: kg/s var massFlowRateKgS = density * volFlowRateM3S; // Unit: kg/h var massFlowRateKgH = massFlowRateKgS * 3600; // Display Results document.getElementById('resKgS').innerText = massFlowRateKgS.toFixed(4) + " kg/s"; document.getElementById('resKgH').innerText = massFlowRateKgH.toFixed(2) + " kg/h"; document.getElementById('resM3H').innerText = volFlowRateM3H.toFixed(2) + " m³/h"; document.getElementById('resArea').innerText = areaCm2.toFixed(2) + " cm²"; resultDiv.style.display = "block"; }

Understanding the Mass Flow Rate Calculation Formula

Mass flow rate is a critical parameter in fluid dynamics, engineering, and process control. Unlike volumetric flow rate, which measures the volume of fluid passing a point per unit of time, mass flow rate measures the actual mass of the substance. This distinction is vital in systems where temperature or pressure changes affect fluid density, such as in natural gas pipelines or steam turbines.

The Core Formula

To calculate the mass flow rate ($\dot{m}$), you typically need to know the fluid's density, the flow velocity, and the cross-sectional area of the pipe or duct through which it flows. The fundamental equation is:

$\dot{m} = \rho \cdot A \cdot V$

Where:

  • $\dot{m}$ (m-dot): Mass flow rate (typically in kg/s or lb/s).
  • $\rho$ (rho): Density of the fluid (kg/m³).
  • $A$: Cross-sectional area of the flow (m²).
  • $V$: Velocity of the flow (m/s).

How to Use This Calculator

Our tool simplifies the calculation by allowing you to input the pipe diameter directly rather than manually calculating the cross-sectional area. Here is a step-by-step guide to the inputs:

  1. Fluid Density ($\rho$): Enter the density of the substance. For example, water at room temperature is approximately 997 kg/m³, while air is roughly 1.225 kg/m³.
  2. Flow Velocity ($V$): Enter the average speed at which the fluid travels through the pipe, measured in meters per second.
  3. Pipe Inner Diameter ($d$): Input the internal diameter of the pipe in millimeters. The calculator automatically converts this to area (in square meters) for the physics calculation.

Mass Flow Rate vs. Volumetric Flow Rate

The relationship between mass flow rate ($\dot{m}$) and volumetric flow rate ($Q$) is defined by density:

$\dot{m} = \rho \cdot Q$

Volumetric flow rate is often easier to measure directly with flow meters, but mass flow rate is the law of conservation of mass in action. In combustion engines, for instance, the specific mass of air (oxygen) determines how much fuel can be burned efficiently, regardless of the air's volume which changes with altitude and temperature.

Common Applications

  • HVAC Systems: Determining the mass of air moved to calculate cooling or heating loads.
  • Chemical Processing: Ensuring precise stoichiometry in reactions where reactants are fed via pipes.
  • Aerospace: Calculating fuel consumption rates for rocket engines or jet turbines.
  • Water Treatment: Monitoring the mass of water processed through filtration membranes.

Example Calculation

Let's say you have water flowing through a 50mm diameter pipe at a speed of 2 m/s.

  • Density of water $\approx 1000$ kg/m³.
  • Diameter = 50mm = 0.05 meters.
  • Area $A = \pi \times (0.05/2)^2 \approx 0.001963$ m².
  • Mass Flow Rate $\dot{m} = 1000 \times 0.001963 \times 2 = 3.926$ kg/s.

Using the calculator above will give you this result instantly, along with conversions to kg/h and volumetric flow rates.

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