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12 November, 23:27

Compute the mean and maximum velocities for a liquid with a flow rate of 20 L/min in a 1.5-in nominal diameter sanitary pipeline. The liquid has a density of 1030 kg/m3 and viscosity of 50 cP. Is the flow laminar or turbulent?

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  1. 13 November, 00:37
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    Mean velocity = 0.292 m/s

    Maximum velocity = 0.584 m/s

    The flow is laminar as Re = 229.2

    Explanation:

    D = 1.5 inches = 0.0381 m

    Q = volumetric flow rate = 20 L/min = 0.000333 m³/s

    Q = A * v

    A = Cross sectional Area = πD²/4 = π (0.0381) ²/4 = 0.00114 m²

    v = average velocity

    v = Q/A = 0.000333/0.00114 = 0.292 m/s

    For flow in circular pipes, maximum velocity = 2 * average velocity = 2 * 0.292 = 0.584 m/s

    To check if the flow is laminar or turbulent, we need its Reynolds number

    Re = (ρvD) / μ

    ρ = 1030 kg/m

    v = 0.292 m/s

    D = 1.5 inches = 0.0381 m

    μ = 50 cP = 0.5 poise = 0.05 Pa. s

    Re = (1030 * 0.292 * 0.0381) / 0.05 = 229.2

    For laminar flow, Re < 2100

    For turbulent flow, Re > 4000

    And 229.2 < 2100, hence, this flow is laminar.
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