Question

The torque τ required to rotate a disk of diameter D with angular velocity w in a fluid is a function of the density ρ and the viscosity μ of the fluid (torque has units of work) (a) Find a nondimensional relationship between these quantities. (b) Calculate the angular velocity and the torque required to drive a 750 mm diameter disc rotating in air if it requires a torque of 1.2 Nm to rotate a similar disc of 230 mm diameter in water at a corresponding speed of 1500 rpm Assume the temperature is 15° C

Answer 1

a)The torque is, The dimensions are Disk diameter D-L Angular velocity-ω-Ti Density= ρ=MI Viscosity: μ-MTT Consider Equating the powers gth-1 e-3g -h-2 =2+3(1-h)th 5-2h f-5-2h Sub e,f, and g values in equ1 b) The angular velocity is, 60 Ет (1500) 60 157.07 rad/s For air viscosity-μ 1.798 10-5 kgm /s For water viscosity= μ' = 8.9 x 10-4 kgm/s

For dynamic similarity (1.2)(a)(0.75) (1000 157.07)(0.23) 1.79x10 8.9x104 ω = 10.95 rad/s 10.95 60 (10.95)(60) 27) 104.56 rpm (1.2)(1.2) (10.95) (0.75 (1000) (157.07) (0.23) 0.00258 Nm