  Velocity distribution functions link the micro- and macro-level theories of
fluid flow through porous media. Here we study them for the fluid absolute
velocity and its longitudinal and lateral components relative to the
macroscopic flow direction in a model of a random porous medium. We claim that
all distributions follow the power exponential law controlled by an exponent
$\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on
the porosity. We find that $\gamma$ has a universal value $1/2$ at the
percolation threshold and grows with the porosity, but never exceeds 2.
