Flow Rate Calculator Formula

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

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Formulas Used

Volumetric Flow Rate

vol_flow = area * velocity

Flow Rate (litres/s)

vol_flow_lps = area * velocity * 1000

Mass Flow Rate

mass_flow = area * velocity * density

Variables

VariableDescriptionDefault
diameterPipe Inner Diameter(mm)100
velocityAverage Flow Velocity(m/s)2
densityFluid Density(kg/m^3)1000
d_mDerived value= diameter / 1000calculated
areaDerived value= pi * pow(d_m, 2) / 4calculated

How It Works

Volumetric & Mass Flow Rate

Flow rate through a pipe depends on the cross-sectional area and the average fluid velocity.

Formulas

Q = A V = (pi D^2 / 4) V (volumetric flow)

m_dot = rho Q = rho A V (mass flow)

where D is the pipe diameter, V is the average velocity, and rho is the fluid density.

Worked Example

Water flowing at 2 m/s through a 100 mm diameter pipe.

diameter = 100velocity = 2density = 1000
  1. 01D = 100 mm = 0.1 m
  2. 02A = pi x 0.1^2 / 4 = 0.007854 m^2
  3. 03Q = 0.007854 x 2 = 0.01571 m^3/s = 15.71 L/s
  4. 04Mass flow = 1000 x 0.01571 = 15.71 kg/s

Frequently Asked Questions

What is the typical pipe flow velocity for water?

For water supply systems, design velocities are typically 1-3 m/s. Higher velocities increase friction losses and noise. Lower velocities may allow sediment to settle.

How do I convert between flow rate units?

1 m^3/s = 1000 L/s = 15,850 US gpm = 35.31 ft^3/s. For quick estimates, 1 L/s is roughly 15.85 US gallons per minute.

Does flow rate change along a pipe?

For incompressible fluids in a closed pipe system with no branches, volumetric flow rate is constant along the pipe (continuity equation). If the pipe diameter changes, velocity adjusts to maintain Q = A V.

Learn More

Guide

Understanding Fluid Mechanics Basics: A Practical Introduction

Master the fundamentals of fluid mechanics including pressure, viscosity, Bernoulli's equation, Reynolds number, and flow types. Essential knowledge for engineers working with pipes, pumps, and hydraulic systems.

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