Fluid Properties & Hydrostatics Workbench

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

Engineering reference

Fluid Properties & Hydrostatics: theory, method, and sources

This fluid mechanics workspace publishes 10 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 density and specific weight, hydrostatic pressure, manometry, hydrostatic force on submerged surfaces, buoyancy, barge stability, capillary rise, bulk compressibility, Couette flow, and viscosity relationships.

The stability module computes the metacentric height from the barge geometry, which determines whether a floating body returns upright after a small heel rather than capsizing.

Calculators and topics covered

density
pressure
buoyancy
viscosity
hydrostatic pressure
manometer
center of pressure
metacentric height
capillary rise

Core equations

\text{density relations:}\quad \rho = \frac{m}{V},\; v = \frac{1}{\rho },\; \gamma = \rho g

\text{pressure at depth:}\quad p_{\mathrm{gauge}} = \rho gh,\; p_{\mathrm{abs}} = p_{\mathrm{atm}} + \rho gh

\text{differential manometer:}\quad \Delta p = \left(\rho _{m} - \rho _{\mathrm{line}}\right) gh

\text{force on a vertical rectangle:}\quad F = \rho g \cdot \bar{h} \cdot A\; \text{with}\; \text{centre}\; of\; \text{pressure}\; y_{cp} = \bar{y} \frac{+ I}{\bar{y} A}

\text{buoyancy:}\quad F_{B} = \rho gV_{\mathrm{displaced}}

\text{metacentric height:}\quad GM = KB + BM - KG\; \text{with}\; BM = \frac{I}{V}

\text{capillary rise:}\quad h = \frac{4 \sigma cos\; \theta }{\rho gd}

\text{bulk modulus:}\quad \frac{\Delta V}{V} = \frac{- \Delta p}{K}

\text{Couette flow:}\quad \tau = \frac{\mu \cdot U}{h},\; F = \tau A

\text{kinematic viscosity:}\quad \nu = \frac{\mu }{\rho }

Method and assumptions

Assumptions

The fluid is at rest and incompressible for all hydrostatic modules, with constant density through the depth.
Gauge pressure is measured relative to a user-supplied surface pressure, taken as atmospheric by default.
Barge stability uses a rectangular waterplane and assumes small heel angles, so the metacentre is treated as fixed.
Capillary rise assumes a clean circular tube and a uniform contact angle.
Couette flow assumes a linear velocity profile between parallel plates in the laminar regime.

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