Applied mechanics?

Here's a shot:

power P = τ * ω

420e3 W = τ * (180*2π/60 rad/s)

torque τ = 2.23e4 N·m

but also τ = J*G*Θ / ℓ

where J is the torsion constant, = πd⁴ / 32 for a circular section

But this section is hollow. I'm going to have to guess that for this shaft

J = (π/32)[(1.6d)⁴ - d⁴] = (d⁴π/32)(1.6⁴ - 1) ≈ 0.545d⁴ ← corrected math error!

and so

2.23e4 N·m = 0.545d⁴ * 85e9Pa * π/180 / 40d = 2.02e7Pa * d³

d³ = 1.10e-3 m³

d = 0.103 m = 10.3 cm ← inner

1.6d = 0.165 m = 16.5 cm ← outer

if my assumption about calculating J is correct.

Hope this helps!