Fluid Flow Dimensional Numbers Calculator

Calculate key dimensionless numbers in fluid mechanics for your engineering applications. Enter the required parameters below.

Fluid Density (ρ) [kg/m³]

Flow Velocity (v) [m/s]

Characteristic Length (L) [m]

Dynamic Viscosity (μ) [Pa·s]

Gravity (g) [m/s²]

Surface Tension (σ) [N/m]

Speed of Sound (c) [m/s]

Dimensionless Numbers Results

Reynolds Number (Re)

–

Ratio of inertial to viscous forces. Predicts flow regime (laminar/turbulent).

Froude Number (Fr)

–

Ratio of flow inertia to external field. Important in open channel flow.

Weber Number (We)

–

Ratio of inertial to surface tension forces. Important in multiphase flows.

Mach Number (Ma)

–

Ratio of flow velocity to speed of sound. Determines compressibility effects.

Interpretation Guide

Re < 2300: Laminar flow
2300 < Re < 4000: Transitional flow
Re > 4000: Turbulent flow
Fr < 1: Subcritical flow
Fr > 1: Supercritical flow
Ma < 0.3: Incompressible flow
Ma > 0.3: Compressibility significant

About Fluid Flow Dimensionless Numbers

Dimensionless numbers are crucial in fluid mechanics as they allow engineers to compare different flow situations and scale up laboratory results to real-world applications. These numbers help characterize flow regimes without needing to consider absolute system size.

Formulas Used:

Reynolds Number: Re = (ρ × v × L) / μ

Froude Number: Fr = v / √(g × L)

Weber Number: We = (ρ × v² × L) / σ

Mach Number: Ma = v / c

Applications:

Pipe flow design and analysis
Aerodynamics and aircraft design
Hydraulic engineering and open channel flow
Microfluidics and droplet formation
Chemical process engineering