Plug Flow Reactor PFR Design Equation and Turbulent Flow

I use the general mole balance equation to derive the design equation for a plug flow reactor (also sometimes referred to as a tubular reactor) by making use of the definition of derivative and a control volume. I also discuss the flow profile and radial well mixed and steady state assumptions required in this derivation.

[@paulsalama6421]

Hey man I am trying to design a PFR with multiple reactions and am running into some issues, if you could help me out, I would highly appreciate it. Thank you.