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The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV. The fluid displaced has a weight W = mg, where g is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as W = ρVg. The weight of an object or ...
The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force (F b) on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume (V) times the gravity (g) [1] [3]
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object —with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object ...
ρ f = Mass density of the fluid; V imm = Immersed volume of body in fluid; F b = Buoyant force; F g = Gravitational force; W app = Apparent weight of immersed body;
The ship's hydrostatic tables show the corresponding volume displaced. [4] To calculate the weight of the displaced water, it is necessary to know its density. Seawater (1,025 kg/m 3) is more dense than fresh water (1,000 kg/m 3); [5] so a ship will ride higher in salt water than in fresh. The density of water also varies with temperature.
Example 1: If a block of solid stone weighs 3 kilograms on dry land and 2 kilogram when immersed in a tub of water, then it has displaced 1 kilogram of water. Since 1 liter of water weighs 1 kilogram (at 4 °C), it follows that the volume of the block is 1 liter and the density (mass/volume) of the stone is 3 kilograms/liter.
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This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically, = where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of fluid directly above the curved surface. [8]