Question

fluids Question : please only do it if you're sure

4. (20 pts) One type of viscometer works by measuring the torque (T) needed to rotate a solid cylinder at an angular velocity (W) when the space between the tank and cylinder is filled with a liquid of interest. This torque is a function of the liquid viscosity (u), the angular velocity (w), the cylinder height (H), the cylinder radius (R), the liquid film thickness below the cylinder (h), and the liquid film thickness on the cylinder sides (t). Determine: a. The dimensionless Pi terms for this problem. (12 points) b. If the liquid and w remain the same but the cylinder height H increases by 2 times, how does the torque change? All other conditions (R, h and t) also remain constant. (8 points) CT Liquid Recall that (T) has dimensions of Force Length and w has dimensions of 1/time.

Answer 1

Page La Tusque T M1²T ? angular velocity wat vincity us milft height H L Radios RL holt here, mat & n=3 Total no. of IT terms=m-n=7-3=64 Consider H. W and u as Repeating -- rasiables, _ N.. Does In = 49Wb el T MOLOT (L)" (+ 2 b (M2 2+2 ° (M2²-2) Imouto = mcth, a-c+2 t-b-e-2 . ct1.co (=-1 a-c+2=0 a +1+2=0 a=-3 (b=-1 -b-c-2 0 -b + 1-2=0 T = Hawt u T = H² when I

ععا لیتا here becao & a = -2 f (I, 2 Tz, ITA) =0

Page constone w2 u ) constant h a h -H₂ = 2y = H2 = 34 Use Tg = I u wiß I - Tg = 27 Ig - T = 265 New Torque Tz to increases 26 times