We are all in the same page in this case. From my previous experience in silencer stress analysis, there is no consideration for thrust force, maybe this is almost negligible from structural standpoint (almost steady).
Thanks Sigma for the info. I've read the thread and the silencer is connected to PSV at the outlet to atmosphere. In this case we can use formula from PSV's. The thread shows whether it will be considered open or close system.
How about a case where silencer is only present. No PSV's. I'm thinking to use the (back pressure-atmospheric pressure times the inside area of pipe at the outlet times impact factor). But if the silencer is open to atmosphere will there be a sudden pressure drop at the silencer/outlet pipe interface (abrupt increase in volume). But I'm also thinking this will be almost steady flow only (since the flow will not be restricted going to atmosphere) so there will be almost negligible reaction force.