  The recent theory of 't Hooft [ Nucl. Phys. Suppl. {\bf 68}, 174 (1998)]
models the black hole as a system endowed with an envelope of matter that obeys
an equation of state in the form $ p=(\gamma -1)\rho$, and acts as a source in
Einstein's equations. The present paper generalizes the 't Hooft theory so as
to take into account a bulk viscosity $\zeta$ in the fluid. It is shown that
even a slight positive value of $\zeta$ will suffice to yield complete
agreement with the Hawking formula for the entropy of the black hole, if the
value of the constant $\gamma$ takes a value that is slightly less than 4/3.
The value $\gamma=4/3$ corresponds to a radiation fluid.
