Volume V

Figure 2.1: Fluid point written as:

Dc dc dc dx dc dy dc dz Dt dt dx dt dy dt dz dt in which dx, ddt and df are the components of the velocity of the boat. Now if we turn off the engne of the boat and float along counting fish (the lagrangian viewpoint), the velocity of the boat would be simply the velocity of the streams. The change of fish concentration in this case is called substantial time derivative and is written as follows:

— = ~ + vx^r- + vy— + vz — dx dy dz in which vx vyand vz are the components of the local fluid velocity v.

Figure 2.2: a)Lagrangian viewpoint b)Eulerian viewpoint

Figure 2.2: a)Lagrangian viewpoint b)Eulerian viewpoint

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