= Linear homentropic acoustic equations
For perturbations $(\rho',p',\mathbf u)$ about a uniform fluid of density $\rho_0$, the linearized <continuity equation>, <Euler equations for an inviscid fluid>[momentum equation], and <homentropic pressure perturbation> relation are
$$
\rho'_t+\rho_0\nabla\mathbin\cdot\mathbf u=0,
\qquad
\rho_0\mathbf u_t=-\nabla p',
\qquad
p'=c_0^2\rho'.
$$
For <irrotational flow> $\mathbf u=\nabla\phi$, they imply $p'=-\rho_0\phi_t$ and $\phi_{tt}=c_0^2\nabla^2\phi$.
Back to article page
