Question

Class Test A civil engineering student working in a fluid mechanics laboratory wants to measure the viscosity of a fluid by a viscometer constructed of two 90-cm-long concentric cylinders. The inner diameter of the outer cylinder is 16 cm, and the gap between the two cylinders is 0.12 cm. The inner cylinder is rotated at 200 rpm, and the torque is measured to be 2.0 N-m. What is the viscosity of the fluid? 200 rpm 0.12 cm Fluid Stationary cylinder

Answer 1

Given N = 200 rpm L = 90 cm d_i = 16 cm = > r = 16/2 = 8 cm = 0.08 m h = 0.12 cm = 0.12/100 = 1.2 times 10^-3 m Q_0 = Q_i + 0.12 times 2 = 16.24 cm T = 2N-m Area(A) = pi times d_0 times L = pi times 16.24 times 90 degree = 4.59175 times 10^3 cm^2 Force (F) = T times A = [mu times (v/h)] times A = mu times {w times r/n} times A w = 2 pi N/60 = 2 pi times 200/60 = 20.943 rad/sec \r\n Torque (T) = F times r = mu times w times r/h times A times r = mu w r^2/h times A 2 = mu times 20.943 times (0.08)62 times 4.59175 times 10^3 times 10^-4/1.2 times 10^-3 mu = 0.0389 N-S/M^2 = 0.0389 pa.sec