Pressure Drop in Laminar Pipe Flow

The sixth reactor design criterion requires that the pressure drop at the minimum residence time be less than 100 psi. For a small diameter channel, the flow through that channel wiU be laminar for all flow rates of interest for this particular applicahon. Neglecting end effects, the solutions to the equations of continuity and of motion for steady-state laminar flow of an incompressible Newtonian fluid are well-known, yielding a parabolic velocity distribution and the Hagen-Poiseuille equahon for pressure drop, as given in Eqs. (9) and (10)  

For the case considered earlier (7 s residence time in a 0.18 mm, or 0.007-inch, diameter by 1-m long tube), using the viscosity of water at ambient temperature, the predicted pressure drop across the reactor channel is 23 psi. 

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