  Compact Riemannian solar twisted magnetic flux tube surfaces model are tested
against solar extreme ultraviolet (EUV) lines observations, allowing us to
compute the diameter and height of solar plasma loops. The relation between
magnetic and torsion energies is found for a nonplanar solar twisted
(torsioned) loop to be $10^{9}$, which shows that the contribution of torsion
energy to the solar loop is extremely weaker than the magnetic energy
contribution. In this case solar loops of up $5000 km$ in diameter can be
reached. The height of $220.000 km$ is used to obtain an estimate for torsion
based on the Riemannian flux tube surface, which yields ${\tau}_{0}=0.9{\times}
10^{-8} m^{-1}$ which coincides with one of the data of
$(0.9{\pm}0.4){\times}10^{-8}m^{-1}$ obtained by Lopez-Fuentes et al (2003).
This result tells us that the Riemannian flux tube model for plasma solar loops
is consistent with experimental results in solar physics. These results are
obtained for a homogeneous twisted solar loop. By making use of Moffatt-Ricca
theorem for the bounds on torsional energy of unknotted vortex filaments,
applied to magnetic topology, one places bounds on the lengths of EUV solar
loops. New results as the vorticity of the plasma flow along the tube is also
computed in terms of the flux tube twist.
