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Lagrangian Method

•    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 / ∂ v  = ∂y / ∂   w  =  ∂z / ∂t

Resultant velocity    V  =  √u2 + v2 + w2

Velocity vector          V  =  ui + vj + wk

•    Acceleration component,

a =  ∂u / ∂ =  ∂2 x / ∂t2   a = ∂2 y / ∂t2     az  =  ∂2 z / ∂t2

Resultant acceleration      a  = √ax2 + ay2 + az2

Acceleration vector          ¯a  = ax i + ay j + az k

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

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