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18 January, 02:58

Find the total friction loss in 100 mm diameter G. I. pipe discharging 4 L/s ina total length of 300 m. Assume pipe roughness, ε = 0.20 m. (hint: use the nomogram, use the head loss equation (darcy-weisbach equation) to calculate, hf and moody's diagram to estimate friction factor, f and compare the result.)

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  1. 18 January, 04:02
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    friction factor, f = 0.025, hf = 0.9903 m

    Explanation:

    We are given the following:

    Diameter, D = 100 mm = 0.1 m

    Rate of discharge, Q = 4 L/s = 0.004 m³/s

    Length of pipe, L = 300 m

    pipe roughness, ε = 0.2 mm

    velocity of pipe, v = ?

    From rate of discharge = velocity * area, hence

    0.004 = v * (π * (0.1/2) ²) where area = π * (D/2) ²

    solving the above expression, we have

    v = 0.509 m/s

    from Reynold's number = velocity * diameter / dynamic viscosity

    i. e Re = V * D / μ

    where μ = 10⁻⁶

    hence, substituting the values, we have

    Re = 0.509 * 0.1 / 10⁻⁶

    Re = 50900 and ε/d = 0.2 / 100 = 0.002

    from the moody diagram

    friction factor, f = 0.025 and I = 300

    total friction loss hf = flV² / (2gD)

    hf = (0.025 * 300 * 0.509²) / (2 * 9.81 * 0.1)

    This evaluates to

    hf = 0.9903 m
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