Question

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

Answer 1

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.