That is, ©Fx p1 1gage2 A1 p2 1gage2 A2 Where ( p1 patm) and ( p2 patm) are recognized as the gage pressures at (1) and (2), respectively. 12.1a can be written in terms of gage pressures as ©Fx 1 p1 patm 2 A1 1 p2 patm 2A2 Where p1, p2, and patm are absolute pressures. The net pressure force acting axially is ©Fx p1A1 p2A2 patm 1A1 A2 2 Also, as shown in the figure, the atmospheric pressure patm acts on the washer-shaped area (A1 A2), producing a surface force patm(A1 A2) acting opposite to the flow direction. Surface forces acting on the control volume include the force p1A1 acting in the direction of flow and the oppositely directed force p2A2. Figure 12.1 shows a control volume enclosing a horizontal contraction consisting of a smaller diameter pipe following one having a larger diameter. We conclude the present discussion of surface forces by considering the role that gage pressure can play when evaluating the forces acting on a control volume. The shear force concept is studied in the next section together with the property viscosity. The Momentum and Mechanical Energy Equationsįigure 12.1 Pressure forces acting on a sudden In fact, the definition of a fluid is that it is a material in which the application of any shear stress (no matter how small) will cause motion.Ĭhapter 12. Although it is possible to generate a shear stress in a stationary solid (e.g., apply a horizontal force to a table top), it is impossible to generate a shear stress in a fluid without the fluid being in motion. Similarly, the tangential component of force is Ftangential :, where is the shear stress, the tangential force per unit area. 11, the normal component of force is Fnormal pA, where p is the pressure. Surface forces can be written in terms of components normal and tangential to the surface. ▲ Surface forces are exerted on the contents of the control volume by material just outside the control volume in contact with material just inside the control volume. Similarly, the weight of a fluid may affect its motion. when a ball is thrown, its weight is one of the forces that clearly alters the motion of the ball and affects its trajectory.
We experience this body force as weight, w. The only body force we consider is that associated with the action of gravity. These concepts include body and surface forces, viscosity, and the incompressible flow model.ġ2.1.1 Body and Surface Forces In fluid mechanics, the resultant force on the contents of a control volume is commonly represented as the sum of all the surface and body forces acting. 12.8–12.10).ġ2.1 Fluid Flow Preliminaries In this section we introduce some important concepts relating to fluid flow that support not only the discussions of the present chapter but also those of Chaps.
A discussion of compressible flow is also provided on the accompanying CD-ROM (Secs.
Thus, the objective of this chapter is to show the use of these equations in thermal systems engineering. These equations deal with a flowing fluid, unlike the equations in the previous chapter that involved stationary fluids. In this chapter we consider three equations that are mathematical representations of these laws-the momentum equation, the Bernoulli equation, and the mechanical energy equation. The application of laws such as the conservation of mass, Newton’s laws of motion, and the laws of thermodynamics form the foundation of fluid mechanics analyses. Introduction… A fluid’s behavior is governed by a set of fundamental physical laws expressed by an appropriate set of equations. THE MOMENTUM AND MECHANICAL ENERGY EQUATIONS
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