How Do We Express Vector Fields in Fluid Mechanics?

[jordansas]

Hi,
I am experiencing a little bit of trouble grasping the concept of vector fields in fluid mechanics:

If the vector V = u i + v j + w k, where i,j,k are unit vectors in the x,y,z directions, then how can u,v,w be functions of x,y,z,t?

I.e. if say v is in the y direction, then how can it be expressed in terms of x and z as well?

Many thanks :)

 

[Chestermiller]

Hi,
I am experiencing a little bit of trouble grasping the concept of vector fields in fluid mechanics:

If the vector V = u i + v j + w k, where i,j,k are unit vectors in the x,y,z directions, then how can u,v,w be functions of x,y,z,t?

I.e. if say v is in the y direction, then how can it be expressed in terms of x and z as well?

Many thanks :)

Think of the wind blowing in the horizontal x direction, but the speed of the horizontal wind varies with height above the ground. Say, it is 1 ft/sec at the ground, but 2 ft/sec at a height of 10 ft.

 

[jordansas]

Ah ok, I get it now! Thanks for the help :)