Fluid Flow - Equation of Continuity

Calculator for the Equation of Continuity based on conservation of mass in steady flow processes. Calculates output velocity for fluids with uniform density through pipes and ducts using the formula: vout = vin × Ain / Aout

Calculator

Inputs

Results

Output Velocity (vout)-- m/s
Input Flow Rate (q)-- m³/s
Output Flow Rate (q)-- m³/s
ScenarioInput Velocity (m/s)Input Area (m²)Output Area (m²)Output Velocity (m/s)
100mm to 80mm pipe0.350.007850.005030.55
Pipe expansion2.00.0050.0101.0
Pipe reduction1.00.0100.0052.0
Large diameter change0.50.0200.0052.0

Equation of Continuity

The Equation of Continuity states that for a steady flow process with uniform density:

vin × Ain = vout × Aout

Or rearranged:

vout = vin × Ain / Aout

Where:

  • vin = input velocity (m/s)
  • Ain = input area (m²)
  • vout = output velocity (m/s)
  • Aout = output area (m²)

This principle applies to incompressible fluids like water, oil, and other liquids flowing through pipes, tubes, and ducts. When a fluid flows from a larger diameter pipe to a smaller one, the velocity increases to maintain constant flow rate.

Fluid Flow - Equation of Continuity | MEPKit Engineering Tools | MEPKit