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Unformatted text preview: 530.327  Introduction to Fluid Mechanics  Su Applications of the momentum equation. Reading: Text, Â§ 4.4 (The following examples are discussed in F.M. White, Fluid Mechanics , 5th ed.). Example 1. Vector nature of Newtonâs second law. V 1 V 2 q 1 2 Figure 1: A streamtube embedded in a steady ïŹow. This example emphasizes that Newtonâs second law deals with vector quantities. Figure 1 depicts a streamtube in a steady ïŹow, where a streamtube is defined as followsâ âą Streamtube : a closed surface whose sides are everywhere parallel to the local velocity vector. For convenience, we will also say that the surfaces labeled 1 and 2 on the ends of the streamtube are perpendicular to the local velocity vector, and that density and velocity are uniform on those surfaces. What we want to know is, what force must act on the streamtube to cause the ïŹow to bend as shown? First, we will write the equation for conservation of mass for the system. (In general, even in problems where weâre concerned with forces and momenta, we need to start by ensuring that mass conservation is satisfied.) The general form of the conservation of mass is â ât Z CV Ï dV + Z CS Ï ( ââ V Â· ââ dA ) = 0 . (1) We will define the control volume here as being exactly the streamtube depicted in Fig. 1. In this case, the ïŹow is steady, so the first term in the above equation is zero. Also, the only mass inïŹow/outïŹow terms on the control surface are on surfaces 1 and 2, because the velocity is always...
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 Spring '08
 Su
 Fluid Dynamics, Force, Mass

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