Answer to Question #202708 in Mechanical Engineering for Lihle

Question

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.

Answer 1

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

$∆\rho = 1025 - 563.75 = 461.25kg/m³$

$V_{up}= (2.75 -0.75)× \pi (\dfrac{d²}4) =1.571 d^2$

$V_{down}= (0.75)× \pi (\dfrac{d²}4) = 0.589 d^2$

$1.571d²- 0.589d² = 1\\ 0.982 d^2 =1\\ d² = \dfrac1{0.982}$

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