An Approach to the Mechanics of Fluids

by Frank C. Fung - 1st published in June, 2008.

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Section VI - { Flow Net } in Soil Mechanics

Summary for the Section :

• In this Section , we shall present the concept of { Flow Net } ,
  • a quasi-empirical method from { Soil Mechanics } .

• This then give rise to the notion of :
  • using the { General-Random-Type Six-Face Object } as the [ finite element ] in { Fluid Mechanics Analysis } .

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{ Flow Net } in Soil Mechanics :

• { Flow Net } is simply a quasi-empirical method used in { Soil Mechanics } :
  • Let us look , for a brief moment , at the seepage of water under a Dam , as per this diagram below :

    

• The { Flow Net } method is then as follows :
  • First , we draw-in , roughly what we think are the { Stream-Lines } for the flow :
    • as marked by the { blue-color lines } in the diagram below .

    

  • Next , we draw-in , lines that intersect the { Stream-Lines } at [ Right-Angles ] :
    • as marked by the { green-color lines } in the diagram below .

      ( Right-Angles ] are [ 90-degrees angles ] )

    

  • If the { intersection angles } do not look-like [ Right-Angles ] ,
    • we simply make adjustments to the { blue-color lines } and the { green-color lines } :
      • until the { intersection angles } do look-like [ Right-Angles ] .

• We shall not go into the full details of the { Flow-Net } method , but will simply note here :
  • that each { Finite Element } in the { Flow Net } is a { planar surface } with 4 [ nodal-points ] ,

    

    as marked in { orange-color } in the diagram above .

  ( see [ Soil Mechanics in Engineering Practice - Karl Terzaghi and Ralph B. Peck ] - ISBN 0-471-85273-2 for full details . )

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The { General-Random-Type Six-Face Object } as a [ Finite Element ] :

• We simply note here that with 4 { nodal-points } , we can always form :
  • a planar [ Finite Element ] with 4 [ straight-edges ] ,
    • which is essentially a { quadrangle } .

• When we extend this to { 3-D Space } , we can always use :
  • the { General-Random-Type Six-Face Object } as the [ Finite Element ] ,
    • which has 8 { nodal-points } and exactly 6 [ faces ] which are all [ planar surfaces ] .

  We then have a clear and distinct advantage here :

  • each [ face ] of the [ finite element ] here is always in { full contact } with the corresponding { face } of the adjacent [ finite element ] ,
    • so that there are no [ gaps ] in-between and unbroken { continuity } can always be achieved and maintained , if so desired .

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• Next , we shall look at the usage of this type of [ finite elements ] in a { steady flow } situation .

go to the next section : Section VII - A Steady Flow Situation

go to the last section : Section V - General Stress-Strain Relations

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original dated 2008-6-08