Question

Please help me in this question

Answer 1

Explanation:

The velocity field associated with a fluid flow given by 2 u 20y , v 20xy, w 0.    Find the

acceleration, the angular velocity and the vorticity vector at the point (1,-1,2).

The acceleration vector is given by

Dq q q q q a uvw

Dt t x y z

 

   

 

    

2

2 32

Thus, a 20y ( 20yj) 20xy(40yi 20xj) ˆ ˆˆ

ˆ ˆ = 800xy i 400(y x y)j.

  

 



Thus at (1,-1, 2), ˆ 2 a is given by a 800im / s   

The vorticityvector is given by

 

xyz ( , , )

wv uw vu = , , yz zx xy

= 0, 0, ( 20y 40y) =(0 ,0, 60y)

   

                             

 



Hence, at z (1, -1, 2), (0, 0, 60).  

Thus, the x and y component of vorticity vector vanish whilst the z-component of vorticity

vector is given by z

ˆ ˆ   k 60krad / s.  Thus, the angular velocity at

(1, 1, 2) is given by (0, 0, 30). 

Application of continuity equation

2. Water flows at a uniform speed of 5m / s into a nozzle whose diameter reduces from