important concepts in fuid dynamics

important concepts in fuid dynamics

1. pathlines

   • Pathlines are the trajectories that individual fluid particles follow.

2. streamline

   • a streamline is a curve whose tangent at any point is in the direction of the velocity vector at that point
     • if the flow is unsteady, the velocity vectors are fluctuating with the time in both magnitude and direction

3. are identical, however in a steady flow there is no distinction between pathalines and streamlines

4. angular velocity

   • Angular velocity is a pseudovector, with its magnitude measuring the angular speed, the rate at which an object rotates or revolves,
     • equation

5. vorticity

   • is a vector field that gives a microscopic measure of the rotation at any point in the fluid.
     • is defined by
     • in a velocity field, the curl of the velocity is equal to the vorticity
     • exist the rotational an irrotational flow, it depends of the conditions of velocity

6. circulation

   • the circulation si simply the negative of the line integral of velocity around a closed curve in the flow
     • circulation is related to vorticity as follows

7. stream function

   • Stream functions are defined for two-dimensional flow and for three-dimensional axial symmetric flow. The stream function can be used to plot the streamlines of the flow and find the velocity.
     • the equation for a stream line can be derived as

8. velocity potential

   • the scalar quantity whose negative gradient equals the velocity in the case of irrotational flow of a fluid
     • equation

9. Laplace's equation.

   • The Laplace equation is a mixed boundary problem which involves a boundary condition for the applied voltage on the electrode surface and a zero-flux condition in the direction normal to the electrode plane.

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