Finite Volume Analysis:       Selection of Control Surface or Surfaces

 

 

                       Control Surface and Control Volume

             for conservation of Linear Momentum Application

 

                           

 

where   CS  is the control surface        CV is the control volume

              n1,  n2,   n3  are the unit outer normal vectors to the control surface

              A1, A2, A3  are the areas at stations 1, 2, and 3

              V1, V2 are the velocities of the fluid entering the control surface

              V3  is the velocity of the fluid leaving the control surface

              ρ  is the density of the fluid

              θ  is the angle at station 3

        P1A1, P2A2, P3A3 are the pressure forces acting on the CS at 1, 2, and 3

   Gravity, g, is taken to be into the paper so that the weight of the fluid in the

   CV does not contribute to the forces else it would need to be included.

 

Linear momentum flux out ˗ linear momentum flux in = ∑ F  (vector eq)

 

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