Formula Sheet: Laws of Floatation
Basic Laws of Floatation
1. Upthrust (Buoyant Force)
U = Weight of fluid displaced
The upward force exerted by a fluid on a submerged object is equal to the weight of the fluid displaced by the object.
2. Condition for Floating
Weight of object = Upthrust
An object floats if its weight is exactly balanced by the buoyant force (upthrust) from the fluid.
3. Partially Submerged Object
Vs / V = ρobject / ρfluid
The ratio of the submerged volume (Vs) to the total volume (V) equals the ratio of the density of the object (ρobject) to the density of the fluid (ρfluid).
Derived and Related Formulas
Weight of fluid displaced
Weight = V × ρfluid × g
Weight of the displaced fluid equals its volume (V) times density (ρ) times gravitational acceleration (g).
Relative Density
Relative Density (R.D.) = ρobject / ρwater
Ratio of the density of the object to the density of water (or another reference fluid).
Condition for Sinking
Weight of object > Upthrust
An object sinks if its weight exceeds the buoyant force exerted by the fluid.
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