Velocity
Velocity of a fluid along any direction can be defined as the rate of change of displacement of the fluid along that direction.
u = dx / dt
Where dx is the distance traveled by the fluid in time dt.
Velocity of a fluid element is a vector, which is a function of space and time.
Let V be the resultant velocity of a fluid along any direction and u, v and w be the velocity components in x, y and z directions respectively.
Mathematically the velocity components can be written as
u = f ( x, y, z, t )
v = f ( x, y, z, t )
w = f ( x, y, z, t )

Acceleration
Acceleration of a fluid element along any direction can be defined as the rate of change of velocity of the fluid along that direction.
If ax , ay and az are the components of acceleration along x, y and z directions respectively, they can be mathematically written as
ax = du/ dt.
But u = f (x, y, z, t) and hence by chain rule, we can write,
Similarly
