Verify the below velocity distribution describes a fluid in a state of pure rotation. What is the angular Velocity? (a)-Vx = -1/2bx (b)-Vy = -1/2by (c)-Vz = bz

Question

asked Feb 28, 2020 178k views

1 Answer

David Gras · Answer 1 · 2020-03-04T15:39:21+0000

Answer:

Angular velocity of fluid is zero.

Step-by-step explanation:

Given that

V_x=(1)/(2)bx

V_y=(1)/(2)by

V_z=-bz

The angular velocity in Z direction

$\omega _z=0.5*\left ((\partial V_y)/(\partial x)-(\partial V_x)/(\partial y) \right )$

V_x=(1)/(2)bx

$(\partial V_y)/(\partial x)=0$

V_y=(1)/(2)by

$(\partial V_x)/(\partial y)=0$

So

$\omega _z=0$

Similarly

$\omega _y=0.5*\left ((\partial V_z)/(\partial x)-(\partial V_x)/(\partial z) \right )$

$\omega _x=0.5*\left ((\partial V_z)/(\partial y)-(\partial V_y)/(\partial z) \right )$

$\omega _y=0$

$\omega _x=0$

$\omega =\omega_xi+\omega_yj+\omega_zk$

ω = 0

So the angular velocity of fluid is zero.