Fluid Mechanics Reference Center

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

Engineering reference

Fluid Mechanics Reference: theory, method, and sources

This fluid mechanics workspace publishes 7 governing equations, 4 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

A browsable reference organized into six areas: fluid properties, dimensionless numbers, core equations, flow devices, measurement, and modeling and safety.

Each entry states what the relationship is used for, the range over which it is valid, and the conditions that invalidate it, so the correlation can be checked against the situation before it is applied.

Calculators and topics covered

reference
properties
equations
measurement
fluid properties
dimensionless numbers
flow meters
CFD
engineering safety

Core equations

\text{continuity:}\quad Q = A_{1} V_{1} = A_{2} V_{2}

\text{Bernoulli:}\quad \frac{p}{\rho g} \frac{+ V^{2}}{2 g} + z = \text{constant}

\text{Reynolds number:}\quad \mathrm{Re} = \frac{\rho VD}{\mu }

\text{Darcy–Weisbach:}\quad h_{f} = \frac{f \left(\frac{L}{D}\right) V^{2}}{2 g}

\text{Manning:}\quad V = \left(\frac{1}{n}\right) R^{\frac{2}{3}} S^{\frac{1}{2}}

\text{Froude number:}\quad \mathrm{Fr} = \frac{V}{\sqrt{gL}}

\text{Mach number:}\quad M = \frac{V}{\sqrt{\gamma RT}}

Method and assumptions

Assumptions

Property values are representative for water and air at standard conditions and vary with temperature and pressure.
Correlations are empirical and valid only within the Reynolds number and roughness ranges stated in each entry.
Bernoulli-based entries assume steady, incompressible, inviscid flow along a streamline.
Discharge coefficients depend on device geometry and approach conditions and should be taken from calibration data where accuracy matters.

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