  We explore the possibility of formation of steady internal shocks in jets
around black holes. We consider a fluid described by a relativistic equation of
state, flowing about the axis of symmetry ($\theta=0$) in a Schwarzschild
metric. We use two models for the jet geometry, (i) a conical geometry and (ii)
a geometry with non-conical cross-section. Jet with conical geometry is smooth
flow. While the jet with non-conical cross section undergoes multiple sonic
point and even standing shock. The jet shock becomes stronger, as the shock
location is situated further from the central black hole. Jets with very high
energy and very low energy do not harbour shocks, but jets with intermediate
energies do harbour shocks. One advantage of these shocks, as opposed to shocks
mediated by external medium is that, these shocks have no effect on the jet
terminal speed, but may act as possible sites for particle acceleration.
Typically, a jet with energy $1.8~c^2$, will achieve a terminal speed of
$v_\infty=0.813c$ for jet with any geometry. But for a jet of non-conical
cross-section for which the length scale of the inner torus of the accretion
disc is $40\rg$, then in addition, a steady shock will form at $\rsh \sim
7.5\rg$ and compression ratio of $R\sim 2.7$. Moreover, electron-proton jet
seems to harbour the strongest shock. We discuss possible consequences of such
a scenario.
