Fundamental Principles and Equations

Fundamental Principles and Equations

1. Graphic Representation of the Motion of a Fluid Element

   • Steady Flow
     • Pathlines and Streamlines are in the same direction so they're identical
   • Unsteady Flow
     • Pathlines
       • Path of a fluid element when it pass certain point "x" which properties are changing with time
     • Streamlines
       • The stream pattern, curves whose tangents at any point are in the velocity vector direction

2. Quantities in a velocity field

   • As an infinitesimal fluid element moves in a flow field, it may also rotate so its shape may become distorted. These concepts depend on the velocity field
     • Angular Velocity
       • Quantification of the dependency between the rotation and the velocity field
     • Vorticity
       • Known as twice the angular velocity, describes the spinning motion or tendency to rotate of certain point in a velocity field
       • In addition, the vorticity is equal to the curl of the velocity
         • • If the expression is not equal to 0 at every point, the flow is rotational
           • If the expression is equal to 0 at every point, the flow is Irrotational

3. Equations

   • Stream Function
     • Simplification of a basic two-dimensional flow represented by a single variable
       • used for steady flow
       • used for Incompressible flow
   • Velocity Potential
     • For irrotational flow there is a scalar function "fi" to simplify the velocity into one equation (instead of using the velocity components)
   • Laplace's Equation
     • The sum of the second-order partial derivatives of "R" (R=Any Function) equals to zero

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