Calculating Mass Flow Rate Thermodynamics

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Mass Flow Rate Calculator

Calculation Results:

Mass Flow Rate: kg/s

Mass Flow Rate: kg/h

Cross-sectional Area: m²

function calculateMassFlow() { var density = parseFloat(document.getElementById('fluidDensity').value); var velocity = parseFloat(document.getElementById('flowVelocity').value); var diameterMM = parseFloat(document.getElementById('pipeDiameter').value); if (isNaN(density) || isNaN(velocity) || isNaN(diameterMM) || density <= 0 || velocity < 0 || diameterMM <= 0) { alert("Please enter valid positive numerical values for all fields."); return; } // Convert diameter mm to meters var diameterM = diameterMM / 1000; // Calculate Area (A = π * r²) var area = Math.PI * Math.pow((diameterM / 2), 2); // Calculate Mass Flow Rate (m_dot = ρ * v * A) var massFlowKgS = density * velocity * area; var massFlowKgH = massFlowKgS * 3600; document.getElementById('resKgS').innerText = massFlowKgS.toFixed(4); document.getElementById('resKgH').innerText = massFlowKgH.toFixed(2); document.getElementById('resArea').innerText = area.toFixed(6); document.getElementById('mfr-results').style.display = 'block'; }

Understanding Mass Flow Rate in Thermodynamics

In thermodynamics and fluid mechanics, the mass flow rate is the mass of a substance which passes per unit of time. Its unit is typically kilograms per second (kg/s) in the SI system. Understanding this value is critical for sizing pumps, designing heat exchangers, and analyzing propulsion systems.

The Mass Flow Rate Formula

The fundamental equation used in this calculator is:

ṁ = ρ × v × A

  • ṁ (m-dot): Mass flow rate (kg/s)
  • ρ (rho): Density of the fluid (kg/m³)
  • v: Flow velocity (m/s)
  • A: Cross-sectional area of the flow (m²)

Step-by-Step Calculation Example

Let's calculate the mass flow rate for water flowing through a standard pipe:

  1. Identify Fluid Density: For water at room temperature, ρ is approximately 1000 kg/m³.
  2. Determine Velocity: Assume the water is moving at 2 m/s.
  3. Calculate Area: If the pipe diameter is 100mm (0.1m), the radius is 0.05m.
    Area = π × (0.05)² ≈ 0.007854 m².
  4. Final Calculation: ṁ = 1000 × 2 × 0.007854 = 15.708 kg/s.

Why is Mass Flow Rate Important?

Unlike volumetric flow rate (m³/s), mass flow rate remains constant throughout a steady-state system even if temperature or pressure changes cause the fluid to expand or contract (Law of Conservation of Mass). This makes it the preferred metric for thermal calculations, such as calculating the heat transfer rate (Q = ṁ × Cp × ΔT).

Common Fluid Densities (Reference)

Fluid Density (kg/m³)
Fresh Water 1,000
Sea Water 1,025
Air (at Sea Level) 1.225
Engine Oil 885

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