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Velocity of a fluid along any direction can be defined as the rate of change of displacement of the fluid along that direction. Acceleration of a fluid element along any direction can be defined as the rate of change of velocity of the fluid along that direction.

*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

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**,

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 *a _{x}*

*a _{x} = du/ dt.*

But ** u
= f (x, y, z, t)** and hence by chain rule, we can write,

_{ax}* *_{=}* *?*u dx *_{+}* *?*u dy *_{+}* *?*u dz *_{+}* *?*u *?*x dt *?*y dt *?*z dt *?*t*

Similarly

Tags : Civil - Mechanics Of Fluids - Fluid Kinematics And Dynamics

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