Could someone please help me work out this problem?? Thanks! A viscometer consis

Question

Could someone please help me work out this problem?? Thanks!

A viscometer consists of two concentric cylinders, 10.2 cm and 10.6 cm in diameter. A particular liquid fills the space between them to a depth of 12.0 cm. The outer cylinder is fixed, and a torque of 0.024 N?m keeps the inner cylinder turning at a steady rotational speed of 62 rev/min. For this particular geometry, the area, A, is the average surface area of the two cylinders [the inner (rotating) and outside (fixed) cylinder]. What is the viscosity of the liquid?

Background::: To move the upper plate requires a force. It is found that the force is proportional to the area of fluid contact with the moving plate, A, and to the speed, v, and is inversely proportional to the separation, l, of the plates. For different fluids, the more viscous the fluid, the greater is the required force. Thus the proportionality constant for this relationship is defined as the coefficient of viscosity, ?: F = ?Av/l. The SI unit for ? is N?s/m2 = Pa?s (Pascal?second).

Explanation / Answer

Fl/Av = ?

F= (Torque/Radius) = 0.024/0.052= 0.46153 N

l=2*pi*r=0.32672m

A=0.039207m^2

v=62*2*pi*0.052/60=0.3376165m/s

Therefore, ?=11.39 Pa.s

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