Question

At a given flow parameter, we would like to increase G' from 0.1 to 0.2. Check which of the following will result.

A. The effect on pressure drop cannot be determined.

B. The pressure drop will decrease.

C. The pressure drop will increase.

D. The pressure drop will remain the same.

Answer 1

The pressure drop through a pipe depends on the fluid properties as well as the velocity of the flow.SImilarly the pressure drop for a packed bed is dependent on the porosity of bed,diameter of particle,its sphericity and other fluid properties like its density,viscosity,etc.Now if all of these properties remains fixed then we have only velocity term which is going to be varied.Also this velocity of fluid is dependent on the mass or molar flux.Area being constant,an increase in mass or molar flux(G) means mass rate or molar flow rate is increased and thus volumetric flow rate.This increase in volumetric flow rate means their is an increase in velocity.

In every pressure drop equation,for a fluid flowing through pipe given by Hagen-Poiseulli equation or flow through packed bed given by Ergun equation ,pressure drop is always proportional to velocity and velocity may be linear or any higher order term and hence an increase in velocity means their is an increase in pressure drop.

Hagen Poiseulli equation: Δp= 32μVL/D^2 where Δp is pressure drop across length of the pipe of L and diameter D.

here, Δp is directly proportional to velocity.Similarly in ergun equation velocity is linear in nature for low reynolds number and parabolic for high reynolds number i.e. turbulent flow and whole equation is their will be an increase in pressure drop if mass or molar flux will be increased because of an increase in velocity,other parameters being constant either pipe area or its fluid properties.

Hence,option (c) is correct.