The tubular reactor with laminar flow

In Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

The average velocity of fluid in the reactor tube = (total flow)/(cross-section of the tube), i.e. 

at any radial position, the time of passage, t, of a fluid element is given by 

Substituting eqns. (112)—(114) in eqn. (107) gives the volumetric flow rate through an annulus 

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