The 12 Mg helicopter is hovering over a lake as the suspended bucket collects 5 m3 of water used to extinguish a fire. Determine the power r

Question

The 12 Mg helicopter is hovering over a lake as the suspended bucket collects 5 m3 of water used to extinguish a fire. Determine the power required by the engine to hold the filled water bucket over the lake. The horizontal blade has a diameter of 14 m. Use rhow = 1000 kg/m3 and rhoa = 1.23 kg/m3

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Sigridomena 2 months 2021-08-06T05:31:16+00:00 1 Answers 0 views 0

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    2021-08-06T05:32:23+00:00

    Answer:

    7 MW

    Explanation:

    mass of helicopter, m = 12 Mg = 12000  

    volume of water in bucket, V = 5 m³

    diameter of blade, D = 14 m

    density of water, d = 1000 kg/m³

    density of air, d’ = 1.23 kg/m³

    The weight of water and the helicopter is balanced by the thrust produced by the rotor blade of the helicopter.

    So, force

    F = m x g  + V x d x g

    F = 12000 x 9.8 + 5 x 1000 x 9.8

    F = 166600 N

    Let initially the velocity of blade is v

    F = \frac{d' \times 3.14\times R^{2}}{2}v^{2}

    166600 = \frac{1.23 \times 3.14\times 7^{2}}{2}v^{2}

    v = 41.96 m/

    Power of the helicopter, P = Force x velocity

    P = 166600 x 41.96

    P = 7 x 10^6 Watt

    P = 7 MW

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