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  3. 3 the device in fig below is called a semiconeplate...

Question: 3 the device in fig below is called a semiconeplate...

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3. The device in Fig. below is called a semi-cone-plate viscometer. The first section of the cone is parabolic-like with equation y-ax2, where a is a constant parameter. Also, the constant depth at horizontal region is h and the gap is filled with the test liquid. The total torque M to rotate the cone at a rate 2 is measured. Assuming a linear velocity profile in the fluid filnm a) Derive an expression for fluid the Torque Mi in curved region. b) Derive an expression for fluid the Torque M2 in horizontal region. c) Hence obtain viscosity u as a function of (M, ri, r2 2, a, h). Note: arc length: ds-Jax? + dy2 = 11 + ( -) dx 2

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