In fluid mechanics it is assumed, that the normal components of the stress tensor are all the same and identical to the pressure p: $\sigma_{xx}= \sigma_{yy}=\sigma_{zz} = p$

Where does this come from? In solid materials it is not the case in general, but why in fluids? In all my texts on fluid mechanics this assumption is not justified. What particular property of the state "fluid" is responsible for the assertion

$\sigma_{xy}= p \delta_{i,j}+\tau_{i,j}$ where $\tau$ is the viscous stress tensor.