Answer:
Angular velocity of fluid is zero.
Explanation:
Given that
[tex]V_x=\dfrac{1}{2}bx[/tex]
[tex]V_y=\dfrac{1}{2}by[/tex]
[tex]V_z=-bz[/tex]
The angular velocity in Z direction
[tex]\omega _z=0.5\times\left (\dfrac{\partial V_y}{\partial x}-\dfrac{\partial V_x}{\partial y} \right )[/tex]
[tex]V_x=\dfrac{1}{2}bx[/tex]
[tex]\dfrac{\partial V_y}{\partial x}=0[/tex]
[tex]V_y=\dfrac{1}{2}by[/tex]
[tex]\dfrac{\partial V_x}{\partial y}=0[/tex]
So
[tex]\omega _z=0[/tex]
Similarly
[tex]\omega _y=0.5\times\left (\dfrac{\partial V_z}{\partial x}-\dfrac{\partial V_x}{\partial z} \right )[/tex]
[tex]\omega _x=0.5\times\left (\dfrac{\partial V_z}{\partial y}-\dfrac{\partial V_y}{\partial z} \right )[/tex]
[tex]\omega _y=0[/tex]
[tex]\omega _x=0[/tex]
[tex]\omega =\omega_xi+\omega_yj+\omega_zk[/tex]
ω = 0
So the angular velocity of fluid is zero.
