•    In this method, the observer concentrates on the movement of single particle.
 
•    Observer has to move with the particle movement.

•    The path followed by the particle and changes in its velocity, acceleration, density etc, described. in this method, the observer moves with motion of fluid.

•    In Cartesian system, the position of the fluid particle in space (x, y, z) at any time t from its position (a, b, c) at time t = 0 shall be given as,

x  = f₁ (a, b, c, t)                  y  = f₂ (a, b, c, t)                        z  = f₃ (a, b, c, t)

•    The velocity component of flow field is represent by three component scalar equations.

u  = ∂_x / ∂_t  v  = ∂_y / ∂_t    w  =  ∂z / ∂_t

Resultant velocity    V  =  √u² + v² + w²

Velocity vector          V  =  ui + vj + wk

•    Acceleration component,

a_x  =  ∂_u / ∂_t  =  ∂² _x / ∂_t²   a_y  = ∂² _y / ∂_t²     a_z  =  ∂² _z / ∂_t²

Resultant acceleration      a  = √a_x² + a_y² + a_z²

Acceleration vector          ¯a  = a_{x ⁱ} + a_y ^j + a_z ^k

•    This method is cumbersome and complex. It is also difficult to understand the fluid motion.

For more help in Lagrangian Method click the button below to submit your homework assignment