Variation of Flow Parameters in Time and Space
 

Hydrodynamic parameters like pressure and density along with flow velocity may vary from one point to another and also from one instant to another at a fixed point.

According to type of variations, categorizing the flow:

Steady and Unsteady Flow

• Steady Flow
  A steady flow is defined as a flow in which the various hydrodynamic parameters and fluid properties at any point do not change with time.

          In Eulerian approach, a steady flow is described as,

          and

        Implications:

1. Velocity and acceleration are functions of space coordinates only.
   
   
2. In a steady flow, the hydrodynamic parameters may vary with location, but the spatial distribution of these parameters remain invariant with time.

        In the Lagrangian approach,

1. Time is inherent in describing the trajectory of any particle.
   
   
2. In steady flow, the velocities of all particles passing through any fixed point at different times will be same.
   
   
3. Describing  velocity as a function of time for a given particle will show the velocities at different points through which the particle has passed providing the information of velocity as a function of spatial location as described by Eulerian method. Therefore, the Eulerian and Lagrangian approaches of describing fluid motion become identical under this situation.

• Unsteady Flow
  An unsteady Flow is defined as a flow in which the hydrodynamic parameters and fluid properties changes with time.