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Fluid Kinematics And Dynamics: Velocity, Acceleration

   Posted On :  26.07.2016 06:32 pm

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 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,

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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