External Flow & Boundary Layers Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

External Flow & Boundary Layers: theory, method, and sources

This fluid mechanics workspace publishes 11 governing equations, 5 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Ten modules cover drag and lift force, flat-plate boundary layers in both laminar and turbulent regimes, sphere drag correlations, terminal and Stokes settling velocity, dimensionless group summaries, and model-scale similitude.

The similitude module solves the model velocity required for either Froude or Reynolds matching, which makes the classic conflict between the two scaling criteria explicit.

Calculators and topics covered

drag
lift
boundary layers
similarity
skin friction
terminal velocity
Stokes settling
Reynolds number
Weber number

Core equations

\text{drag force:}\quad F_{D} = \frac{1}{2} \rho V^{2} A \cdot C_{D}

\text{lift force:}\quad F_{L} = \frac{1}{2} \rho V^{2} A \cdot C_{L}

\text{plate Reynolds number:}\quad \mathrm{Re}_{x} = \frac{\rho Vx}{\mu }

\text{laminar skin friction:}\quad C_{f} = \frac{1.328}{\sqrt{\mathrm{Re}}}

\text{turbulent skin friction:}\quad C_{f} = \frac{0.074}{\mathrm{Re}^{\frac{1}{5}}}

\text{laminar boundary layer:}\quad \delta = \frac{5 x}{\sqrt{\mathrm{Re}_{x}}}

\text{turbulent boundary layer:}\quad \delta = \frac{0.37 x}{\mathrm{Re}_{x}^{\frac{1}{5}}}

\text{Stokes drag regime:}\quad C_{D} = \frac{24}{\mathrm{Re}}\; for\; \mathrm{Re} < 1

\text{terminal velocity:}\quad v_{t} = \sqrt{\frac{4 gd \left(\rho _{p} - \rho _{f}\right)}{3 \rho _{f}\; C_{D}}}

\text{Stokes settling:}\quad v = \frac{gd^{2} \left(\rho _{p} - \rho _{f}\right)}{18 \mu }

\text{Froude and Weber numbers:}\quad \mathrm{Fr} = \frac{V}{\sqrt{gL}},\; \mathrm{We} = \frac{\rho V^{2} L}{\sigma }

Method and assumptions

Assumptions

Flat-plate correlations assume a smooth plate with a sharp leading edge and zero pressure gradient.
The laminar-to-turbulent transition is taken at a fixed Reynolds number rather than being computed from disturbance level or roughness.
Drag and lift coefficients are user-supplied and must correspond to the reference area and Reynolds number range being used.
Stokes settling is valid only at low particle Reynolds number and neglects wall effects and particle interaction.
Compressibility, free-surface effects, and three-dimensional flow are not modelled.

Limitations and design boundaries

Educational screening calculations only. Real systems require verified fluid properties, calibrated coefficients, uncertainty analysis, applicable codes and standards, and qualified engineering review.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Çengel and Cimbala, Fluid Mechanics: Fundamentals and Applications
Munson et al., Fundamentals of Fluid Mechanics