  The pressure spectrum and structure function in homogeneous steady turbulence
of an incompressible fluid is studied using direct numerical simulation. The
resolution of the simulation is up to $1024^3$ and the Taylor microscale
Reynolds number $\Rl$ is between 38 and 478. The energy spectrum is found to
have a small but finite inertial range followed by a bump at large wavenumbers.
The Kolmogorov constant $K$ is found to be $1.66\pm 0.08$. The pressure
spectrum also has a small but finite inertial range of
$P(k)=B_p\eb^{4/3}k^{-7/3}$ followed by a bump of nearly $k^{-5/3}$ range at
higher wavenumbers. Both scaling ranges match at a crossover wavenumber, $k_p$,
which is a characteristic wavenumber for the pressure gradient. The constant
$B_p$ is found to be about $8.34\pm 0.15$ for $\Rl=460$. Its non-universality
is discussed. The second order pressure structure function, computed in terms
of the fourth order velocity structure functions, agrees well with that
obtained by the direct measurement over separations ranging between the
inertial and dissipation scales.
