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5 January, 02:52

Two parallel plates, one moving at 4 m/s and the other stationary, are separated by a 5mm thick layer of oil with specific gravity of 0.80 and kinematic viscosity 1.25E-4 m2/s. What is the average shear stress in the oil? Show your work.

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  1. 5 January, 03:06
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    Average shear stress; τ = 80 Pa

    Explanation:

    We are given;

    Thickness; t = 5mm = 0.005 m

    Velocity; u = 4 m/s

    Specific Gravity; Sg = 0.8

    Kinematic viscosity; ν = 1.25 * 10^ (-4) m²/s

    We are not given density of the oil, but given specific gravity of 0.8. we know that formula for specific gravity of an object = Density of object/Density of water

    Density of water = 1000 kg/m³

    Thus;

    0.8 = density of oil/1000

    Density of oil = 800 kg/m³

    Now, let's calculate dynamic viscosity of the oil. It's given by the formula;

    μ = ρν

    Where;

    μ is dynamic viscosity

    ρ is density of oil

    ν is kinematic viscosity

    So,

    μ = 800 * 1.25 * 10^ (-4)

    μ = 0.1 kg/m. s

    Now, formula for the average shear stress is given as;

    τ = μ * u/t

    Plugging in the relevant values, we have;

    τ = 0.1 * 4/0.005

    τ = 80 Pa
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