Chapter 1 Introduction to Fluid Flow
CHAPTER 1 INTRODUCTION TO FLUID FLOW 1.1 INTRODUCTION Fluid flows play a crucial role in a vast variety of natural phenomena and man- made systems. The life-cycles of stars, the creation of atmospheres, the sounds we hear, the vehicles we ride, the systems we build for flight, energy generation and propulsion all depend in an important way on the mechanics and thermody- namics of fluid flow. The purpose of this course is to introduce students in Aeronautics and Astronautics to the fundamental principles of fluid mechanics with emphasis on the development of the equations of motion as well as some of the analytical tools from calculus needed to solve practically important problems involving flows in channels along walls and over lifting bodies. 1.2 CONSERVATION OF MASS Mass is neither created nor destroyed. This basic principle of classical physics is one of the fundamental laws governing fluid motion and is a good departure point for our introductory discussion. Figure 1.1 below shows an infinitesimally small stationary, rectangular control volume 6x6y6z through which a fluid is assumed to be moving. A control vol- ume of this type with its surface fixed in space is called an Eulerian control volume. The fluid velocity vector has components UUVW= (),, in the xxyz= (),, directions and the fluid density is l . In a general, unsteady, com- pressible flow, all four flow variables may depend on position and time. The law of conservation of mass over this control volume is stated as bjc 1.1 3/26/13 Conservation of mass ¨¬Rate of mass ¨¬Rate of mass ¨¬Rate of mass «««««« ««accumulation ««flow «« flow ©= ©– ©(1.1) ««inside the control ««into the control ««out of the control «««««« ª®volume ª®volume ª®volume z lW z + 6z ()x +y6x,,+z6y + 6z W(x,y,z,t) lV y + 6y V(x,y,z,t) U U(x,y,z,t) lU x + 6x l()xyzt,,, lU x 6z y ()xyz,, lV lW y 6y z 6x x Figure 1.1 Fixed control volume in a moving fluid.
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