By James N. Tilton
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Read or Download Perry's Chemical Engineers' Handbook 8 E Section 6:Fluid and Particle Dynamics PDF
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Additional info for Perry's Chemical Engineers' Handbook 8 E Section 6:Fluid and Particle Dynamics
In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU ρ/μ where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs.
6-22) and (6-24) leads to the Navier-Stokes equations, whose three Cartesian components are In vector notation, The pressure and gravity terms may be combined by replacing the pressure p by the equivalent pressure P = p + ρ gz. The left-hand side terms of the Navier-Stokes equations are the inertial terms, while the terms including viscosity μ are the viscous terms. Limiting cases under which the Navier-Stokes equations may be simplified include creeping flows in which the inertial terms are neglected, potential flows (inviscid or irrotational flows) in which the viscous terms are neglected, and boundary layer and lubrication flows in which certain terms are neglected based on scaling arguments.
6-1. Complete definitions require extension to multidimensional flow. For more information, several good references are available, including Bird, Armstrong, and Hassager (Dynamics of Polymeric Liquids, vol. 1: Fluid Mechanics, Wiley, New York, 1977); Metzner ("Flow of Non-Newtonian Fluids" in Streeter, Handbook of Fluid Dynamics, McGraw-Hill, New York, 1971); and Skelland (Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). FIG. 6-1 Deformation of a fluid subjected to a shear stress.