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 <math>V<math> [m3] | charge <math>q<math> [C] | heat <math>Q<math> [J] |
| potential | pressure <math>p<math> [Pa=J/m3] | potential <math>\phi<math> [V=J/C] | temperature <math>T<math> [K=J/<math>k_B<math>] |
| flux | current <math>\Phi_{V}<math> [m3/s] | current <math>I<math> [A=C/s] | heat transfer rate <math>\dot{Q}<math> [J/s] |
| flux density | velocity <math>v<math> [m/s] | current density <math>j<math> [C/m2s] | heat flux <math>\dot{Q}''<math> [J/m2s] |
| linear model | Poiseuille's law <math> \Phi_{V} = \frac{\pi r^{4}}{8 \eta} \frac{\Delta p^{\star}}{\ell}<math> | Ohm's law <math>j=-\sigma \nabla \phi<math> | Fourier's law <math>\dot{Q}''=\kappa \nabla T<math> |
Categories: Fluid dynamics