Friction factor for a rotating disk, a thin circular disk of radius R is immersed in a large body of fluid with density p and viscosity If a torque T z is required to make the disk rotate at an angular velocity 12, then a friction factor f may be defined analogously to Eq 6 1 1 as follows, T z R AK...

Friction factor for a rotating disk, a thin circular disk of radius R is immersed in a

Question:

Friction factor for a rotating disk, a thin circular disk of radius R is immersed in a large body of fluid with density p and viscosity µ. If a torque T_z is required to make the disk rotate at an angular velocity 12, then a friction factor f may be defined analogously to Eq. 6.1-1 as follows, T_z/R = AKf where reasonable definitions for K and A are K = ½ p(ΩR)² and A = 2(πR²). An appropriate choice for the Reynolds number for the system is Re = R²Ωp/µ. For laminar flow an exact boundary layer development gives T_z = 0.616πpR⁴√µΩ³/p for laminar flow for turbulent flow, an approximate boundary layer treatment based on the 1/7 power velocity distribution leads to T = 0.073pΩ²R⁵ ⁵√µ/R²Ωp express these results as relations between f and Re.

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