Mass Flow Rate Calculator Formula

Understand the math behind the mass flow rate calculator. Each variable explained with a worked example.

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Formulas Used

Mass Flow Rate

mass_flow = density * velocity * area

Mass Flow Rate

mass_flow_hr = density * velocity * area * 3600

Volumetric Flow Rate

vol_flow = velocity * area * 1000

Variables

VariableDescriptionDefault
densityFluid Density (rho)(kg/m³)1000
velocityFluid Velocity (V)(m/s)2
diameterPipe Inner Diameter (D)(mm)100
d_mDerived value= diameter / 1000calculated
areaDerived value= pi * pow(d_m, 2) / 4calculated

How It Works

Mass Flow Rate

Mass flow rate is the mass of fluid passing through a cross-section per unit time. It is a fundamental quantity in fluid mechanics, thermodynamics, and process engineering.

Formula

m_dot = rho × V × A

where rho is the fluid density, V is the average velocity, and A is the cross-sectional area. For a circular pipe, A = pi × D² / 4. Mass flow is conserved through a system (continuity equation).

Worked Example

Water (1000 kg/m³) flowing at 2 m/s through a 100 mm pipe.

density = 1000velocity = 2diameter = 100
  1. 01D = 100 mm = 0.1 m
  2. 02A = pi × 0.1² / 4 = 0.007854 m²
  3. 03m_dot = 1000 × 2 × 0.007854 = 15.708 kg/s
  4. 04Volume flow = 2 × 0.007854 × 1000 = 15.708 L/s

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