Answer to Question #202708 in Mechanical Engineering for Lihle

Question #202708

Determine the minimum diameter to maintain stable conditions for a warming bouy. The centre of gravity is 750 mm above the base. It has a height of 2,75 m and a relative density of 0,55. It should float with its longitudinal axis in the vertical plane in seawater with a density of 1025kg/m^3.


1
Expert's answer
2021-06-07T05:49:53-0400

density of buoy = 0.55 × 1025kg/m³ = 563.75kg/m³

"\u2206\\rho = 1025 - 563.75 = 461.25kg\/m\u00b3"


"V_{up}= (2.75 -0.75)\u00d7 \\pi (\\dfrac{d\u00b2}4) =1.571 d^2"

"V_{down}= (0.75)\u00d7 \\pi (\\dfrac{d\u00b2}4) =\n0.589 d^2"


"1.571d\u00b2- 0.589d\u00b2 = 1\\\\ 0.982 d^2 =1\\\\\nd\u00b2 = \\dfrac1{0.982}"


"d = \\sqrt{\\dfrac{1}{0.982}} = 1.009m"

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