Reference no: EM131016788
The concentric cylinder device of the type shown in Fig. P13.15 is commonly used to measure the viscosity, µ, of liquids by relating the angle of twist, θ, of the inner cylinder to the angular velocity, ω , of the outer cylinder. Assume that
θ = f(ω, µ, K, D1, D2, l)
where K depends on the suspending wire properties and has the dimensions FL. The following data were obtained in a series of tests for which µ = 0.01 lbf s/ft2, K = 10 lbf ft, µ = 1 ft, and D1 and D2 were constant.
| θ(rad) |
ω(rad/s) |
| 0.89 |
0.3 |
| 1.5 |
0.5 |
| 2.51 |
0.82 |
| 3.05 |
1.05 |
| 4.28 |
1.43 |
| 5.52 |
1.86 |
| 6.4 |
2.14 |
Determine from these data, with the aid of dimensional analysis, the relationship between θ, 0, and ω for this particular apparatus. Hint: Plot the data using appropriate dimensionless parameters, and determine the equation of the resulting curve using a standard curve-fitting technique. The equation should satisfy the condition that θ = 0 for ω 0.
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