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Unformatted text preview: M O M E N T U M A N A LY S I S O F F L O W S Y S T E M S W hen dealing with engineering problems, it is desirable to obtain fast and accurate solutions at minimal cost. Most engineering problems, including those associated with fluid flow, can be analyzed using one of three basic approaches: differential, experimental, and control volume. In differential approaches , the problem is formulated accurately using differ-ential quantities, but the solution of the resulting differential equations is difficult, usually requiring the use of numerical methods with extensive computer codes. Experimental approaches complemented with dimensional analysis are highly accurate, but they are typically time-consuming and expensive. The finite control volume approach described in this chapter is remarkably fast and simple and usually gives answers that are sufficiently accurate for most engineering purposes. Therefore, despite the approxima-tions involved, the basic finite control volume analysis performed with paper and pencil has always been an indispensable tool for engineers. In Chap. 5, the control volume mass and energy analysis of fluid flow systems was presented. In this chapter, we present the finite control volume momentum analysis of fluid flow problems. First we give an overview of Newton’s laws and the conservation relations for linear and angular momen-tum. Then using the Reynolds transport theorem, we develop the linear momentum and angular momentum equations for control volumes and use them to determine the forces and torques associated with fluid flow. 167 CHAPTER 6 OBJECTIVES When you finish reading this chapter, you should be able to n Identify the various kinds of forces and moments acting on a control volume n Use control volume analysis to determine the forces associated with fluid flow n Use control volume analysis to determine the moments caused by fluid flow and the torque transmitted The design of many machines, such as this helicopter, requires use of the equations of conservation of mass and energy, and the linear momentum and angular momentum equations. Photograph by John M. Cimbala. 6–1 n NEWTON’S LAWS Newton’s laws are relations between motions of bodies and the forces act-ing on them. Newton’s first law states that a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the net force acting on it is zero . Therefore, a body tends to pre-serve its state of inertia. Newton’s second law states that the acceleration of a body is proportional to the net force acting on it and is inversely propor-tional to its mass. Newton’s third law states that when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first . Therefore, the direction of an exposed reaction force depends on the body taken as the system....
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- Fall '10