Both Lagrangian Method and Eulerian Method determine the motion of fluid particles. To get the relationship between Lagrangian equation and Eulerian equation, we consider the equations-
S ⃗ = S (S ⃗0 , t) (From Lagrangian Method)
V ⃗ = V (S ⃗, t) (From Eulerian Method)
If we integrate the equations, we get the scalar components of x, y and z coordinates as observed for Lagrangian method. It can be written as-
For x-direction,
x = x (x0, y0, z0, k)
Similarly,
y = y (x0, y0, z0, k) (For y-direction)
z = z (x0, y0, z0, k) (For z-direction)
This is only the scalar components of directions.
Note:
If we consider deriving the equation to get simultaneous differential equation, it is not easy to reach to the exact point. This is the reason Eulerian method is primarily preferred for the calculation of different factors for the motion of fluid particles.
Links of Previous Main Topic:-
- Vapour compression refrigeration cycle introduction
- Basic fluid mechanics and properties of fluids introduction
- Fluid statics introduction
- Manometers measurement pressure
- Fluid kinematics
- Lagrangian method for describing fluid method
Links of Next Mechanical Engineering Topics:-
- Steady and unsteady flows
- Uniform and non uniform flows
- Stream line
- Path lines
- Streak lines
- Acceleration of a fluid particle
- Continuity equation
- Continuity equation in three dimensions in differential form
- Continuity equation in a cylindrical polar coordinate system
- Bernoullis equation
- Basics and statics of particles introduction
- Equilibrium of rigid bodies introduction
