Mass Flow Rate Calculator Formula

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

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

Frequently Asked Questions

Why use mass flow instead of volumetric flow?

Mass flow is independent of temperature and pressure changes. Volumetric flow varies with density (especially for gases). For energy and mass balance calculations, mass flow rate is preferred.

What is a typical pipe velocity for water?

For water in process piping: 1-3 m/s for pump suction, 2-4 m/s for pump discharge, 0.5-1 m/s for gravity flow. Too high a velocity causes erosion and excessive pressure drop.

How does the continuity equation work?

At steady state, mass flow in = mass flow out for any control volume. If a pipe changes diameter, rho1 × V1 × A1 = rho2 × V2 × A2. For incompressible flow, V1 × A1 = V2 × A2.

Ready to run the numbers?

Open Mass Flow Rate Calculator