2-13 - CHAP 2 Uniaxial Bar and Truss Elements 103 13 The...

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CHAP 2 Uniaxial Bar and Truss Elements 103 13. The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: () i i j j j i q K P P q K P P  where q i and q j are fluid flow at nodes i and j , respectively; P i and P j are fluid pressure at nodes i and j , respectively; and K is 4 128 D K L where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9 10 -4 Pa s. (a) Write the element matrix equation for the flow in the pipe element. (b) The net flow rates into nodes 1 and 2 are 10 and 15 m 3 /s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero.
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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2-13 - CHAP 2 Uniaxial Bar and Truss Elements 103 13 The...

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