Hydraulic analogy

Electricity (as well as heat) was originally understood to be a kind of fluid. This hydraulic analogy is still of some use in teaching, not only for the fact that the names of the quantities are often struck by analogy.

type	hydraulic	electric	thermal
quantity	volume $V$ [m³]	charge $q$ [C]	heat $Q$ [J]
potential	pressure $p$ [Pa=J/m³]	potential $φ$ [V=J/C]	temperature $T$ [K=J/ $k B$ ]
flux	current $Φ V$ [m³/s]	current $I$ [A=C/s]	heat transfer rate $\dot{Q}$ [J/s]
flux density	velocity $v$ [m/s]	current density $j$ [C/m²s]	heat flux $\dot{Q}''$ [J/m²s]
linear model	Poiseuille's law $\Phi_{V} = \frac{\pi r^{4}}{8 \eta} \frac{\Delta p^{\star}}{\ell}$	Ohm's law $j=-\sigma \nabla \phi$	Fourier's law $\dot{Q}''=\kappa \nabla T$

Categories: Fluid dynamics