such as density and pressure both of which might also be viewed as

Such as density and pressure both of which might also

This preview shows page 21 - 23 out of 164 pages.

such as density and pressure, both of which might also be viewed as thermodynamic properties, especially in the context of fluids. Finally, we will briefly consider surface tension. 2.3.1 Viscosity Our intuitive notion of viscosity should correspond to something like “internal friction.” Viscous fluids tend to be gooey or sticky, indicating that fluid parcels do not slide past one another, or past
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16 CHAPTER 2. SOME BACKGROUND: BASIC PHYSICS OF FLUIDS solid surfaces, very readily (but in a fluid they do always slide). This can be an indication of some degree of internal molecular order, or possibly other effects on molecular scales; but in any case it implies a resistance to shear stresses. These observations lead us to the following definition. Definition 2.2 Viscosity is that fluid property by virtue of which a fluid offers resistance to shear stresses. At first glance this may seem to conflict with the earlier definition of a fluid (a substance that cannot resist deformation due to shear stresses), but resistance to shear stress, per se , simply implies that the rate of deformation may be limited—it does not mean that there is no deforma- tion. In particular, we intuitively expect that water would deform more readily than honey if both were subjected to the same shear stress under similar physical conditions, especially temperature. Furthermore, our intuition would dictate that water and air would likely have relatively low vis- cosities while molasses and tar would possess rather large viscosity—at least if all were at standard temperature. Observations of this sort can be more precisely formulated in the following way. Newton’s Law of Viscosity . For a given rate of angular deformation of a fluid, shear stress is directly proportional to viscosity. We remark that in some fluid mechanics texts this is stated as the definition of viscosity, but we will see later that there are fluids (termed “non-Newtonian”) whose shear stress does not behave in this way. However, they do, of course, possess the physical property viscosity. Hence, Def. 2.2 should always be used. The statement of Newton’s law of viscosity may at first seem somewhat convoluted and difficult to relate to physical understanding of any of the quantities mentioned in it. We will attempt to remedy this by considering a specific physical situation that will permit a clear definition of “angular deformation rate” and physical intuition into how it is related to the other two quantities (shear stress and viscosity) of this statement. Flow Between Two Horizontal Plates with One in Motion We consider flow between two horizontal parallel flat plates spaced a distance h apart, as depicted in Fig. 2.4. We apply a tangential force F to the upper plate sufficient to move it at constant velocity U in the x direction, and study the resulting fluid motion between the plates.
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