Archimedes’ Principle: body immersed in a fluid experiences a buoyant force equal to weight of fluid it displaces.
Which fluid is denser? A or B
Buoyant force FB
FB = weight of displaced fluid
= g x (submerged volume of body)
used to measure S.G of a fluid is based on principle of buoyancy
What is stability?
A body subjected to small angular displacement will try to get back to original.
Or, moments that try to rotate body get it back to where it was before.
· Two moments try to restore body.
· FBxa and Wxa
· Lesser of the two is called “Righting Moment”
Righting moment = Wxa , if W<FB
= FB xa, if W>FB
CRITERION FOR STABILITY OF A FULLY SUBMERGED BODY IS THAT CENTER OF BUOYANCY MUST BE ABOVE CENTER OF GRAVITY.
· Body will rise until W=FB
· At equilibrium, W and FB
are equal and opposite and lie in the same vertical line
· Recall, for a fully
submerged body center of buoyancy (B)and center of gravity (G)are fixed and the
criterion for stability is that B is above G
· For a floating body, B can
move relative to G, depending on how much fluid is displaced.
· Stability of floating body depends on its shape.