problem 1: A 6 cm diameter rubber ball weighing 5 g is employed to plug a 4 cm hole in the base of a tank. The tank is in use and is gradually emptying. At around what depth will the ball plug fail by floating up and out of the hole?
problem 2: Rooms in the lower level of a cruise ship have 30 cm diameter circular windows termed as portholes. In rough weather the lower portholes can be momentarily submerged up to 4 m by waves. Find out the instantaneous hydrostatic force in terms of magnitude and position at one of such moments.
problem 3: A 2 x 2 m square gate opens clockwise on a horizontal hinge situated at point A, which is 100 mm beneath the centroid of the gate. The gate sits against solid rubber blocks which make an effective pressure seal. The gate is designed to open from the top when the water surpasses a certain depth. To what depth h can the water rise devid of the gate opening at C?
problem 4: Navy divers are called to rescue a group of office workers trapped in a basement beneath floodwater in Leeds, UK. The only access to the basement is via a 1.5 x 1.5 m horizontal hatch that is currently beneath 1.8 m of water. The hatch is hinged on one edge, with a solidly built brass ring handle at the other end. The divers try to pull it open, and soon realise they will require a crane. What minimum lifting load should they ask for? What mistake are they making?
problem 5: A long cylinder of radius 2 m hinged at point A is employed as an automatic gate. When the water level reaches 15 m the gate automatically opens. Find out the magnitude of the net hydrostatic moment on the cylinder at the moment the gate opens. Find out the mass per unit length of the cylinder?
problem 6: A 1.2 m diameter steel pipe carries oil of relative density 0.822 under a head of 70 m of oil. What minimum thickness of 120 MPa (yield stress) steel would be needed for a safety factor of 1.5?