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f06_fall

# f06_fall - Fluids Lecture 6 Notes 1 Control Volumes 2 Mass...

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Fluids – Lecture 6 Notes 1. Control Volumes 2. Mass Conservation 3. Control Volume Applications Reading: Anderson 2.3, 2.4 Control Volumes In developing the equations of aerodynamics we will invoke the firmly established and time- tested physical laws: Conservation of Mass Conservation of Momentum Conservation of Energy Because we are not dealing with isolated point masses, but rather a continuous deformable medium, we will require new conceptual and mathematical techniques to apply these laws correctly. One concept is the control volume , which can be either finite or infinitesimal. Two types of control volumes can be employed: 1) Volume is fixed in space (Eulerian type). Fluid can freely pass through the volume’s boundary. 2) Volume is attached to the ﬂuid (Lagrangian type). Volume is freely carried along with the ﬂuid, and no ﬂuid passes through its boundary. This is essentially the same as the free-body concept employed in solid mechanics. V V Eulerian Control Volume Lagrangian Control Volume fixed in space moving with fluid Both approaches are valid. Here we will focus on the fixed control volume. Mass Conservation Mass ﬂow Consider a small patch of the surface of the fixed, permeable control volume. The patch has 1

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��� �� ��� area A , and normal unit vector ˆ n . The plane of ﬂuid particles which are on the surface
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f06_fall - Fluids Lecture 6 Notes 1 Control Volumes 2 Mass...

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