Eulerian method determines the behavior of fluid particles in fluid flow. It describes the velocity, acceleration, density, pressure, etc. of the fluid particles.

Consider S be the position vector of one particle from a fixed reference point. The particle can travel from initial spatial coordinates at time 0 to reach certain point in time t0.

Velocity, V of fluid particles can be given by-

V ⃗ = V (S ⃗, t)

Where,

S ⃗ = xi ̂ + yj ̂ + zk ̂

V ⃗ = u i ̂+ v j ̂ + w k ̂

Thus,

To identify the position of the particle, we can write-

u = u (x, y, z, t)                    (For scalar components)

v = v (x, y, z, t)                    (For scalar components)

w = w (x, y, z, t)                (For scalar components)

Similarly,

dx/dt = u (x, y, z, t)                (For scalar components)

dy/dt= v (x, y, z, t)                (For scalar components)

dz/dt = w (x, y, z, t)                (For scalar components)

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