Friction Factor Fluid flowing through pipes experiences resistance due to viscosity, turbulence and roughness of the pipe surface. The Darcy-Weisbach Equation (1) is commonly used for the analysis of steady-state, Newtonian-fluid flow inside pipes. It summarizes the relations between frictional…
Laminar Pipe Flow For steady flow in a pipe (whether laminar or turbulent), a momentum balance on the fluid gives the shear stress at any distance from the pipe centerline. In Equation (1), Φ = P + ρ gz. The…
Biodiesel can be produced from vegetable oils by three types of reactions: base catalyzed transesterification of the oil; direct acid-catalyzed transesterification of the oil; and conversion of the oil to its fatty acids, and then to biodiesel. Biodiesel is typically…
Crystallization is a method of solid-fluid separation in which pure chemical crystals are formed. Crystallization kinetics consists of three major phenomena: nucleation (the birth of a crystal), transfer of the solute from the supersaturated solution to the crystal surface, and…
Packed Columns [1] A packed column is a vertical, cylindrical pressure vessel containing one or more sections of a packing material over whose surface the liquid flows downward by gravity, as a film or as droplets, between packing elements. Vapor…
Separation by a membrane is achieved by creating a boundary between different bulk gas or liquid mixtures. As different solvents and solutes flow through a membrane at different rates, separation is achieved. Here, we will focus on three filtration techniques:…