Entropy equation
Acoustics - Propagation in a fluid

In a fluid, stresses are essentially due to hydrostatic pressure p. The mechanical tension T exerted on each surface element is almost normal to it. A deviation from this law occurs with viscosity, which creates tangential stresses τ_ij. To separate the two effects, let's take the stress tensor as :

with δ_ij Kronecker symbol.

The viscous stresses τ_ij lead to the dissipation of part of the mechanical energy. The evolution of entropy results from the second principle of thermodynamics.

The infinitesimal amount of heat δq dissipated in the specific volume V = $\frac{1}{\rho }$