Fluid flow pressure loss through tubes

Everything a fluid flows through or by contributes resistance to the flow of that fluid in an additive fashion. The pressure losses due to flow on the fluid through the tubing, piping, etc., couple with the pressure loss through the filter to produce resistance. 

There are two major sources of pressure loss on the tube-side of a shell and tube exchanger the friction loss in the tubes and the losses due to the sudden contraction and expansion and flow reversals that the fluid experiences in flow through the tube arrangement. 

A low molecular weight polymer melt, which can be modelled as a power-law fluid with m = 5 kPa-s" and n = 0.25, is pumped through a 13 mm inside diameter tube over a distance of 10 m under laminar flow conditions. Another pipe is needed to pump the same material over a distance of 20 m at the same flow rate and with the same frictional pressure loss. Calculate the required diameter of the new pipe. 

Many concentrated suspensions follow non-Newtonian behavior and considerations ought to be made as the viscosity is not a constant anymore, and such fluids should be characterized properly to use their parameters of characterization instead of viscosity in calculations using some dimensionless groups. Most of the theory developed for non-Newtonian fluid flow through tubes, apply to laminar flow round smooth tubes. The most studied non-Newtonian fluids are the power-law fluids and there are some relationships available for pressure-loss-flow rate in purely viscous and viscoelastics flows principally. Relations for thixotropic and rheopectic systems appear not to be available. 

In the CFD modelling of membrane filtration process, membranes are usually modelled as a porous wall while the flow within a membrane is usually solved using both Navier-Stokes and Darqr equations (Ghidossi et al, 2006). A porous media model is widely used for determining the pressure loss during flow through packed beds, filter papers, perforated plates, flow distributors and tube banks (ANSYS, 2010). A momentum source term is added to the governing momentum equations, which creates a pressure drop that is proportional to the fluid velocity ... 

A flow of fluid through a smooth tube of circular cross-section remains laminar while Re=a(V)/v < 1500 [427], where a is the tube radius and (V) the mean flow rate velocity of the fluid. For higher Reynolds numbers, the loss of stability of the laminar flow is observed and an intermediate regime occurs. For Re > 2500, a fully developed regime of turbulent flow is established which is characterized by a chaotic variation of the velocity and pressure in time and space. 

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