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Unformatted text preview: Transport Properties: Momentum Transport, Viscosity 13th February 2011 1 Introduction Much as mass(material) is transported within fluids (gases and liquids), linear momentum is also associated with transport, in this case, due to gradients in velocity . See Figure 35.11 for a descriptive picture of a fluid flowing between 2 fixed plates (or within a tube, as one would expect process materials to flow in a manufacturing plant, or the plumbing in your house, blood flowing in arteries and veins, etc). Though this is discussed in the context of gases, such simple relations can hold in the liquid as well, and these connections have been borne out by experiments connected with specific solutions of the Navier-Stokes solutions. • There is a gradient in velocity orthogonal to the direction of flow (for flow in x-direction, gradient along z-direction) • We have gradient in linear momentum orthogonal to flow Following the derivation of diffusion from our previous discussion, the flux of x-direction linear momentum is given by: J net flux =- 1 3 h ν i ˜ Nλm dv x dz z =0 J net flux =- η dv x dz z =0 1 η is the coefficient of viscosity, or viscosity. Represents a conductance of linear momentum in a fluid. By multiplying both sides of the flux relation, we obtain the viscous drag force: F drag = ηA dv x dz z =0 (1) In this sense, the viscosity is a measure of a fluid’s resistance to flow gradi- ents (velocity gradients)....
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