But any acceleration could be used for example if it is required to analyze the

# But any acceleration could be used for example if it

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is usually gravitational acceleration. But any acceleration could be used; for example, if it is required to analyze the behavior of propellants in orbiting spacecraft tanks during station-keeping maneuvers the factor g would be replaced by local acceleration induced by small thrusters of the spacecraft. Also note that ρ is mass per unit volume; hence, γ must be a force per unit volume leading to the generalized dimension of specific weight, γ F L 3 . We also remark that Bernoulli’s equation, to be studied later, is sometimes written in terms of specific weight. In addition, we note that the notation γ is often used in fluid dynamics for a very different quantity, the ratio of specific heats, c p /c v , usually denoted by k in thermodynamics texts. Nevertheless, the context of these symbols is usually clear, and no confusion should result. Definition 2.5 The specific gravity , SG , of a substance is the ratio of its weight to that of an equal volume of water at a specified temperature, usually 4 C . Because SG is a ratio of weights, it is a dimensionless quantity and thus has no dimension or units. Pressure and Surface Tension In general, fluids exert both normal and tangential forces on surfaces with which they are in contact ( e.g. , surfaces of containers and “surfaces” of adjacent fluid elements). We have already seen in our discussions of viscosity that tangential forces arise from shear stresses, which in turn are caused by relative motion of “layers of fluid.” Pressure is the name given normal forces per unit area; i.e. , Definition 2.6 Pressure is a normal force per unit area in a fluid. As we have done with other fluid properties, we can define average pressure acting over a finite area ∆ A as ¯ p = F n A , where ∆ F n is the normal component of the force ∆ F . Then the pressure at a point is given as p = lim A 0 F n A , (2.7) where, as usual, the limit process is viewed within the confines of the continuum hypothesis. It is clear from the definition that the dimensions of pressure must be p F L 2 . In Fig. 2.10 we display a qualitative summary of pressure and shear stress indicating their actions on the surface of a body submerged in a fluid flow. Moreover, as we will later see, there is yet another contribution to normal force that is present only in moving fluids. We note, however, that although the sketch is for flow over a surface, and specifically shows pressure and shear stress
26 CHAPTER 2. SOME BACKGROUND: BASIC PHYSICS OF FLUIDS U A τ F ~ ~ τ F p n F Figure 2.10: Pressure and shear stress. at a surface, these same quantities are present everywhere in a fluid flow because they apply also to surfaces of fluid elements which can be defined at any point of a fluid. On molecular scales pressure arises from collisions of molecules with each other or with the walls of a container. From an engineering viewpoint we have seen in elementary physics classes that pressure results from the weight of fluid in a static situation (hydrostatics), but we will later see that fluid motion also leads to pressure—which should not be surprising since fluid motion is also required to produce shear stresses.

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