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Eulerian Method

•    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 / ∂    v  =  ∂y / ∂t       w  =  ∂z / ∂

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.

du  =  ∂u / ∂x  dx / dt + ∂u / ∂y  dy / dt + ∂u / ∂z  dz / dt + ∂u / ∂t  =  u  ∂u / ∂x + v  ∂u / ∂y + w  ∂u / ∂z + ∂u / ∂t

•    Acceleration components are,

ax  =  du / dy = u  ∂u / ∂x + v  ∂u / ∂y + w  ∂u / ∂z + ∂u / ∂t

a =  dv / dt  =  u  ∂v / ∂x + ∂v / ∂y + w  ∂v / ∂z + ∂v / ∂t

a=  dw / dt = 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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