Chapter 3 (The Equations of Change for Isothermal Systems) - Chapter 3 The Equations of Change for Isothermal Systems ChE 771 Advanced Transport

Chapter 3 (The Equations of Change for Isothermal Systems)...

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Chapter 3 The Equations of Change for Isothermal Systems ChE 771: Advanced Transport Phenomena Dr Rami Jumah Department of Chemical Engineering Jordan University of Science and Technology
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Outline Perspectives of Fluid Motion Types of Time Derivatives The Equation of Continuity (The Mass Balance) The Equation of Motion (The Momentum Balance) Common Simplifications of the Equation of Motion The Equations of Change and Solving Steady-State Problems with One Independent Variable 2
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3 Introduction It is tedious to set up a shell balance for each problem that one encounters. The shell balance method cannot be applied to all flows, such as flows with curved streamlines. What we need is a general mass balance and a general momentum balance that can be applied to any problem. The two main equations that we derive are called the equation of continuity (for the mass balance ) and the equation of motion (for the momentum balance ). The term equation of change may be used to describe how any physical quantity changes with time and position.
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Perspectives of Fluid Motion Eulerian Perspective: the flow as seen at fixed locations in space, or over fixed volumes of space, the observer is fixed in space (the perspective of most analysis). In the Eulerian description of fluid flow, a finite volume called a flow domain or control volume is defined, through which fluid flows in and out. Lagrangian Perspective : the flow as seen by the fluid material, the observer moving with the particle with the same velocity as the fluid particle (the perspective of the laws of motion) Lagrangian analysis is analogous to the (closed) system analysis; namely, we follow a mass of fixed identity. 4 fixed observer measuring velocity of wind 10 km/h observer in a balloon 0 km/h
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