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Acceleration of a Fluid Particle

We know                                 u = u (x, y, z, t)

v = v(x y, z, t)

w= w(x y, z, t)

where                             u = dx / dt , u = dy / dt and w = dz / dt

Equations (4.11), (4.12), (4.13) indicate that acceleration can result from two things, one from terms

which are called “temporal or local acceleration; another from terms 

in which each terms represents convective acceleration.

The total accelerations ax , ay and a z are called material or substantial acceleration.