•    In this method, observer concentrates on the fixed-point particles.

•    Observer remains stationary ad observes changes in the fluid parameters at the particular point only.

•    Let x, y, z be the space co-ordinates at time t, then the component of the velocity vector are functions of space co-ordinates and times.

u  =  f₁ ( x, y, z, t )
v   =  f₂ ( x, y, z, t )
w  =  f₃ ( x, y, z, t )

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

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

Resultant acceleration      V  =  √u² + v² + w²

Velocity vector                      V  =  ui + vj + wk

•    As the velocity of a fluid particle is a function of both position and time, the acceleration is given by the total rate of change of velocity.

d_u  =  ∂_u / ∂_x  d_x / d_t + ∂_u / ∂_y  d_y / d_t + ∂_u / ∂_z  d_z / d_t + ∂_u / ∂_t  =  u  ∂_u / ∂_x + v  ∂_u / ∂_y + w  ∂_u / ∂_z + ∂_u / ∂_t

•    Acceleration components are,

a_x  =  d_u / d_y = u  ∂_u / ∂_x + v  ∂_u / ∂_y + w  ∂_u / ∂_z + ∂_u / ∂_t

a_y  =  d_v / d_t  =  u  ∂_v / ∂_x + ∂_v / ∂_y + w  ∂_v / ∂_z + ∂_v / ∂_t

a_z  =  d_w / d_t = u  ∂_w / ∂_x + v   ∂_w / ∂_y + w  ∂_w / ∂_z + ∂_w / ∂_t

Resultant acceleration  a  = √a2x + a2y + a2z

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

This method is simple and is very commonly adopted to understand the fluid motion.

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