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15 August, 22:55

For two 0.3-m-long rotating concentric cylinders, the velocity distribution is given by u (r) = 0.4/r-1000r m/s. If the diameters of the cylinders are 2cm and 4cm, respectively, calculate the fluid viscosity when the inner cylinder rotates at 500 rpm at 1W.

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  1. 15 August, 23:17
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    viscosity = 0.051725 N/m-s

    Explanation:

    Given data

    diameter = 0.3 m

    u (r) = 0.4/r - 1000r m/s

    diameter d1 = 2 cm = 0.02 m

    diameter d2 = 4 cm = 0.04 m

    rotation = 500 rpm

    power = 1 w

    to find out

    fluid viscosity

    solution

    we have given

    u (r) = 0.4/r - 1000r m/s

    du/dr = - 0.4/r² + 1000

    here r = 0.3 / 2 = 0.01 m

    du / dr = - 0.4 / (0.01) ² + 1000

    du/dr = 5000

    and

    so velocity is

    force = viscosity (2π*r*L) du/dr

    0.026 / 0.02 = viscosity (2π * 0.02*0.04) 5000

    viscosity = 0.051725 N/m-s
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