Slabo stlačiv fluid.

Kod slabo stlačivog fluida je $\rho(u) = \rho_0\,(1+\alpha\,u),$ gdje je $\alpha$ recipročna vrijednost prostornog modula elastičnosti. Pri tom je $0<\alpha\ll 1.$ Tada je

$$\rho'(u) = \rho_0\,\alpha$$

$$\frac{\partial}{\partial x}\left(\frac{\kappa\,\rho(u)}{\mu}\,\f... ...c{\kappa}{\mu}\rho_0\,(1+\alpha\,u)\,\frac{\partial u(x,t)}{\partial x}\right)$$

$$= \frac{\partial}{\partial x}\left(\frac{\kappa}{\mu}\rho_0\,\fr... ...frac{\kappa}{\mu}\rho_0\,\alpha\,u\,\frac{\partial u(x,t)}{\partial x}\right).$$

Kad se radi o malim promjenama polja tlaka, $\frac{\partial u(x,t)}{\partial x}$ je mala veličina, pa se $\alpha\,u\,\frac{\partial u(x,t)}{\partial x}$ može zanemariti. Tako imamo jednadžbu

$$\gamma(x)\,\rho_0\,\alpha\,\frac{\partial u(x,t)}{\partial t} = ... ...frac{\kappa\,\rho_0}{\mu}\,\frac{\partial u(x,t)}{\partial x}\right) + f(x,t).$$