Question

Struggling with this question, please help with questions underlined or bracketed in yellow, help will be greatly appreciated!

From Acheson: Elementary Fluid Dynamics

7.2. A rigid sphere of radius a is immersed in an infinite expanse of viscous fluid. The sphere rotates with constant angular velocity Ω. The Reynolds number R-Ωα2/v is small, so that the slow flow equations apply (r, θ, φ) with θ=0 as the rotation axis, show that a purely rotary flow u us(r, θ)ee is possible provided that Using spherical polar coordinates (Ho sin θ)-0.

Hint from the Book answer to the amount of torque needed at end of question:

Answer 1