In an ideal plug flow tubular reactor (no radial gradients), what is the axial velocity profile across any given cross-section?

Introduction / Context:
The plug flow reactor (PFR) idealization assumes that all fluid elements move with the same axial velocity and that there is no axial mixing. This simplifies reaction engineering analysis and forms a reference case against which real tubular reactors are compared.

Given Data / Assumptions:

• No radial gradients (uniform properties over the cross-section).
• No axial dispersion (no backmixing).
• Steady flow conditions.

Concept / Approach:
Under the PFR idealization, the cross-sectional velocity profile is flat: each fluid “plug” advances at the same speed. Real laminar flow in pipes has a parabolic profile; turbulence can flatten it, and static mixers or design choices further approach the plug assumption.

Step-by-Step Solution:

Verification / Alternative check:
Residence-time distribution for a PFR is delta-like; deviations (broadening) indicate non-plug behavior linked to non-uniform velocity.

Why Other Options Are Wrong:

• Varying with time or power function of time: describes unsteady flow, not the ideal cross-sectional profile.
• Non-linear/parabolic: typical of laminar flow but contradicts the plug idealization.
• Randomly oscillatory: not a design assumption.

Common Pitfalls:
Confusing real hydrodynamic profiles with the idealized model used for reaction calculations.

Final Answer:
Constant (flat profile across the cross-section)