Transport Process

Problem From the given illustration below, calculate the steady-state shear stress ?yx and the shear rate dvx/dy when the distance between the plates is 0.500 cm and the viscosity of the fluid in-between is 1.77 cp. Assumption No-slip condition between the plates and the fluid Fluid properties are constant all throughout Plate and fluid motion is unidirectional only No other external forces acting on the fluid Both plates have the same uniform surface area Solution Viscosity of Fluids As a fluid moves, shear stress develops. Recall Physics 71 definition “No-Slip” condition The layer of fluid adjacent to the boundary surface has zero velocity relative to that surface. Movement of a Fluid What if the surface is stationary? What if it is moving? Movement of a Fluid Velocity at wall should be zero But we know that there is flow, i.e. nonzero velocity Movement of a Fluid LAMINAR FLOW Movement of a Fluid Viscosity of a Fluid Viscosity of a Fluid Viscosity (dynamic, µ) Constant of proportionality Resistance to flow Gives rise to viscous forces that resist the relative movement of adjacent layers in the fluid Viscosity of a Fluid Newtonian Fluids A linear relationship exists between the shear stress ? and the velocity gradient dv/dy. GASES Increases with increasing temperature Independent of pressure (up to 1000 kPa) At > 1000 kPa, viscosity increases with increasing pressure LIQUIDS Decreases with increasing temperature Independent of pressure Viscosity of Fluids Outline Molecular Transport Equations Viscosity of Fluids Fluid Flow Fluid Flow Fluid Flow LAMINAR Low velocity No lateral mixing TURBULENT High velocity Formation of eddies Fluid Flow Viscous forces are dominant Occur at low velocities Layers of fluid seem to slide by one another without eddies or swirls No lateral mixing in the fluid Fluid travels smoothly and in regular paths Laminar Flow Inertial forces are dominant Fluid travels in random, chaotic paths Heavy and lateral mixing occurs Turbulent Flow Ratio of inertial forces (?v2) on a fluid to the viscous forces (?v/D) acting on it. Used to characterize different flow regimes NRe < 2100 : laminar 2100 < NRe < 4000 : transition NRe > 4000 : turbulent Reynolds Number