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 } = 0.813 c 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 r _ { g } , then in addition , a steady shock will form at r _ { sh } \sim 7.5 r _ { g } 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 .