In this paper inviscid flows in the three-dimensional space are studied. A PDE system (the Euler system) describing such flows is considered. We also formulate this system in special coordinates corresponding to a model of a pipe. The Lie algebra of symmetries of this system is described. Then we give an algebra of differential invariants, in particular, in coordinate-free form. Finally, we present the Euler system describing flows along a circular helix, discuss its symmetries and invariants.