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8 - Ideal Fluids 8 The biological world could not exist...

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I N T RO D U C T I O N 205 J. Newman, Physics of the Life Sciences , DOI: 10.1007/978-0-387-77259-2_8, © Springer Science+Business Media, LLC 2008 The biological world could not exist apart from fluids. Water is the primary constituent of our bodies and of all animals and plants and it is difficult to imagine life without water. All life on Earth is also bathed in fluids, namely air or water, and the exchange of gases (oxygen and carbon dioxide) is required for all life as well. In this and the next chapter we study fluid mechanics, composed of the subjects of hydrostatics and hydrodynamics. These are generalizations of the statics and dynamics we have already studied and we use many of the fundamental principles and methods that have been developed. The major difference here is that we treat the fluid as a smooth continuous medium that continually exerts forces on immersed objects over their entire contact surface. First pressure is introduced and we examine fluid flow of simple ideal fluids, those having no frictional losses of mechanical energy, showing how to apply the conserva- tion laws we have learned to fluid motion. We show the power of these conservation laws in the context of a variety of different problems dealing with fluid dynamics. Then we study hydrostatics as a special case of hydrodynamics, considering the properties of a fluid in equilibrium and its effects on an immersed object. The chapter ends with a discussion of how pressure can be measured. In the next chapter we study some more complex phenomena in fluids. These include a study of viscous fluids such as blood, in which there are frictional losses and complex behavior (we also discuss the human circulatory system from the perspective of fluid mechanics), as well as surface tension and capillarity of fluids. 1. INTRODUCTION A fluid is a gas or liquid that, unlike a solid, flows to assume the shape of the con- tainer in which it is placed. This occurs because a fluid responds to a shear stress, or a force per unit area directed along the face of a cube of fluid, by flowing, rather than by an elastic displacement as in a solid. A drop of water on a kitchen counter flows when a towel is drawn over the surface whereas a pencil eraser bends when it is rubbed along the surface of a paper and then returns to its original shape. The mole- cules in a fluid are randomly located whereas those in a solid have some higher degree of order; intermolecular forces in a fluid are both somewhat smaller and are of a shorter range than in a solid, so that no elasticity exists in an (ideal) fluid. Gases, under so-called ideal gas conditions, have molecules that move completely indepen- dently of each other, without any intermolecular forces. Spreading out to fill any volume in which it is placed, a gas can have its average number of molecules occu- pying a unit volume change dramatically. Gases are therefore said to be compress- ible and their mass density (or just density) , defined as (8.1) r m V , 8 Ideal Fluids
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206 I D E A L F L U I D S is quite variable. On the other hand, liquids are characterized by their incompressibil-
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