The viscosity of a fluid is to be measured by a viscometer constructed of two 80-cm-long concentric cylinders. The outer diameter of the inn

Question

The viscosity of a fluid is to be measured by a viscometer constructed of two 80-cm-long concentric cylinders. The outer diameter of the inner cylinder is 15 cm, and the gap between the two cylinders is 1 mm. The inner cylinder is rotated at 300 rpm, and the torque is measured to be 0.8 N·m. Determine the viscosity of the fluid.

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Linh Đan 4 years 2021-08-27T19:40:02+00:00 1 Answers 20 views 0

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  1. Thunguyet
    0
    2021-08-27T19:41:03+00:00
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    Answer:

    The viscosity of the fluid is 0.012 kg m⁻¹ s⁻¹

    Explanation:

    Given :

    Length of concentric cylinders, L = 80 cm = 0.8 m

    Outer diameter of inner cylinder, D = 15 cm = 0.15 m

    Gap between two cylinders = 1 mm = 0.001 m

    Rotation of inner cylinder = 300 rpm

    Torque, τ = 0.8 Nm

    The relation to determine area is:

    A = πDL

    A = π x 0.15 x 0.8 = 0.38 m²

    The relation to determine velocity is:

    v=\frac{\pi DN }{60}

    Here N is number of rotation per second.

    v=\frac{\pi\times0.15\times300 }{60}

    v = 2.36 m/s

    The relation to determine force between the two layers:

    F=\frac{\tau}{r}

    F=\frac{0.8}{0.075}

    F = 10.67 N

    Using Law of viscosity,

    \eta=\frac{F/A}{\Delta v/\Delta y }

    \eta=\frac{10.67/0.38}{2.36/0.001}

    η = 0.012 kg m⁻¹ s⁻¹

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