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30 May, 16:13

A ship tows a submerged cylinder, 1.5 m in diameter and 22 m long, at U = 5 m/s in fresh water at 20°C. Estimate the towing power in kW if the cylinder is (a) parallel, and (b) normal to the tow direction.

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  1. 30 May, 19:40
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    (a) 120 kW

    (b) 800 kW

    Explanation:

    Given:

    diameter: 1.5 m

    length = 22 m

    U = 5 m/s

    temperature = 20°C

    For water at 20°C, take ρ = 998 kg/m³ and µ = 0.001 kg/m⋅s

    To find:

    power in kW

    (a) if the cylinder is parallel

    Length / Diameter = L / D = 22 / 1.5 = 14.6 = 15

    Re (L) = ρ*U*L / µ = 998 * 5 * 22 / 0.001 = 109780000 = 1.1E8

    C (D. Frontal) ≈ 1.1

    Force = F = 1.1 * ρ/2 * U² * π / 4 * D

    = 1.1 (998 / 2) (5) ² (π / 4) (1.5) ²

    = 1.1 * 499 * 25 * 0.785 * 2.25

    = 24000 N

    Power = Force * Displacement / time

    = F * U

    = 24000 * 5

    = 120000

    Power = 120 kW

    b) if the cylinder is normal to the tow direction.

    Re (L) = ρ*U*D / µ = 998 * 5 * 1.5 / 0.001 = 7485000 = 7.5E6

    C (D. Frontal) ≈ 0.4

    Force = F = 0.4 * ρ/2 * U² * D * L

    = 0.4 (998 / 2) (5) ² (1.5) (22)

    = 164670 ≈ 165000

    Power = Force * Displacement / time

    = F * U

    = 165000 * 5 = 825000

    ≈ 800 kW

    Power = 800 kW
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