Question

UBT Civil Engineering Department Fluid Mechanics (CE 315) CE College of Engineering جامعة الأعمال و التكنولوجيا كلية الهندية UNIVERSITY OF BUSINESS ROTOROLOGY 06) (10 marks) Specific gravity For the shown figure below, a cube of wood of side length (L) is float in water. If the specific gravity of the wood is 0.88. Determine if this cube is stable or not 프 Water 71 Page

Answer 1

Solution : Given A cube of wood Specific Gravity of of side wood Tength - L To this cibe is stable not out you find Metacentric Height (GM) determine have to GMTO this say SO it we mean cube is BMX BG stable con Y- h L L Metacentric BM-BG Height (GM) and where Distance between meta centric point Distance between Centre centre of buoyancy centre of Guoyancy BG. anot ن Moment of Inertia about minor axis Volume of liquid displaced 4/12) (L XLXL) 12 h d by body 2 L BM

Centre and uiz Distance Distance between GIOVI BG) centre of of busyoney of Gravity (BG) 3G -4; b) Metacentric height (GM) L2 12h 2 L2 L 2 5 12 h 2 L2 GM + h 2 q 12. h * Let up assume it is Force atable equilbrium then Weight of = (0.88 X?!) x 23 cube Випурзу Yo XC6XLY) of wood 0.88L 2 put eqh on value in equation © L4 GM 0.882 7 L 2 12 X ORK 2 L 0.81 L 오 7 10.56 2 GMG_00346.4

It mean assumption BM> BG is correct Hence GAZO cube Oy can say this of loood S TABLE__equilbriune