  Context. The structure and heating of coronal loops are investigated since
decades. Established scaling laws relate fundamental quantities like the loop
apex temperature, pressure, length, and the coronal heating. Aims. We test such
scaling laws against a large-scale 3D MHD model of the Solar corona, which
became feasible with nowadays high-performance computing. Methods. We drive an
active region simulation a with photospheric observations and found strong
similarities to the observed coronal loops in X-rays and EUV wavelength. A 3D
reconstruction of stereoscopic observations showed that our model loops have a
realistic spatial structure. We compare scaling laws to our model data
extracted along an ensemble of field lines. Finally, we fit a new scaling law
that represents well hot loops and also cooler structures, which was not
possible before only based on observations. Results. Our model data gives some
support for scaling laws that were established for hot and EUV-emissive coronal
loops. For the RTV scaling law we find an offset to our model data, which can
be explained by 1D considerations of a static loop with a constant heat input
and conduction. With a fit to our model data we set up a new scaling law for
the coronal heat input along magnetic field lines. Conclusions. RTV-like
scaling laws were fitted to hot loops and therefore do not predict well the
coronal heat input for cooler structures that are hardly observable. The basic
differences between 1D and self-consistent 3D modeling account for deviations
between our and earlier scaling laws. We also conclude that a heating mechanism
by MHD-turbulent dissipation within a braided flux tube would heat the corona
stronger than consistent with our model corona.
