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المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني
05/10/2012 11:36:53
VISCOSITY All fluids offer resistance to any force tending to cause one layer to move over another. Viscosity is the fluid property responsible for this resistance. Since relative motion between layers requires the application of shearing forces, that is, forces parallel to the surfaces over which they act, the resisting forces must be in exactly the opposite direction to the applied shear forces and so they too are parallel to the surfaces. It is a matter of common experience that, under particular conditions, one fluid offers greater resistance to flow than another. Such liquids as tar, treacle and glycerin cannot be rapidly poured or easily stirred, and are commonly spoken of as thick; on the other hand, socalled thin liquids such as water, petrol and paraffin flow much more readily. (Lubricating oils with small viscosity are sometimes referred to as light, and those with large viscosity as heavy; but viscosity is not related to density.) Gases as well as liquids have viscosity, although the viscosity of gases is less evident in everyday life. Newton (1642–1727) postulated that, for the straight and parallel motion of a given fluid, the tangential stress between two adjoining layers is proportional to the velocity gradient in a direction perpendicular to the layers. That is …(1) ? = F/A ? ?u/?y
Fig. 1
? = ??u/?y …….(2)
where ? is a constant for a particular fluid at a particular temperature. This coefficient of proportionality ? is now known by a number of names. The preferred term is dynamic viscosity to distinguish it from kinematic viscosity but some writers use the alternative terms absolute viscosity or coefficient of viscosity. The symbols ? and ? are both widely used for dynamic viscosity; in this book ? will be used. The restriction of eqn 1 to straight and parallel flow is necessary because only in these circumstances does the increment of velocity ?u necessarily represent the rate at which one layer of fluid slides over another. Dynamic viscosity is defined as the ratio of a shear stress to a velocity gradient. Since stress is defined as the ratio of a force to the area over which it acts, its dimensional formula is [FL?2]. Velocity gradient is defined as the ratio of increase of velocity to the distance across which the increase occurs, thus giving the dimensional formula [L/T]/[L] ? [T?1]. Consequently the dimensional formula of dynamic viscosity is [FL?2]/[T?1] ? [FTL?2]. Since[F] ? [MLT?2], the expression is equivalent to [ML?1T?1]. The SI unit of dynamic viscosity is Pa • s, or kg •m?1 • s?1, but no special name for it has yet found international agreement. (The name poiseuille, abbreviated Pl, has been used in France but must be carefully distinguished from poise – see below. 1 Pl=10 poise.) Water at 20 ?C has a dynamic viscosity of almost exactly 10?3 Pa • s. (Data for dynamic viscosity are still commonly expressed in units from the c.g.s. system, namely the poise (abbreviated P) in honour of J. L. M. Poiseuille (1799–1869). Smaller units, the centipoise, cP, that is, 10?2 poise, the millipoise, mP (10?3 poise) and the micropoise, ?P(10?6 poise) are also used.)
Kinematic viscosity and its units In fluid dynamics, many problems involving viscosity are concerned with the magnitude of the viscous forces compared with the magnitude of the inertia forces, that is, those forces causing acceleration of particles of the fluid. Since the viscous forces are proportional to the dynamic viscosity ? and the inertia forces are proportional to the density, the ratio ?/? is frequently involved. The ratio of dynamic viscosity to density is known as the kinematic viscosity and is denoted by the symbol ? so that
? = ?/? …………(3)
(Care should be taken in writing the symbol ?: it is easily confused with ?.) The dimensional formula for ? is given by [ML?1T?1]/[ML?3] ? [L2T?1]. It will be noticed that [M] cancels and so ? is independent of the units of mass. Only magnitudes of length and time are involved. Kinematics is defined as the study of motion without regard to the causes of the motion, and so involves the dimensions of length and time only, but not mass. That is why the name kinematic viscosity, now in universal use, has been given to the ratio ?/ ?. The SI unit for kinematic
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
