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γ w is the unit weight of water; G s is the specific gravity of the solid; e is the void ratio [3] Submerged unit weight The difference between the saturated unit weight and the unit weight of water. [4] It is often used in the calculation of the effective stress in a soil. The formula for submerged unit weight is: ′ = where
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]
Submerged specific gravity is equal to the specific gravity given by the ratio of the weight of the object to the weight of the fluid) minus one. That is, the object and fluid have the same density when the specific gravity equals one, and the submerged specific gravity equals zero.
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.
Example 2: Consider a larger block of the same stone material as in Example 1 but with a 1-liter cavity inside of the same amount of stone. The block would still weigh 3 kilograms on dry land (ignoring the weight of air in the cavity) but it would now displace 2 liters of water so its immersed weight would be only 1 kilogram (at 4 °C).
γ′ is the effective unit weight when saturated or the total unit weight when not fully saturated. B is the width or the diameter of the foundation. φ′ is the effective internal angle of friction. K pγ is obtained graphically. Simplifications have been made to eliminate the need for K pγ. One such was done by Coduto, given below, and it ...
Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of ± 0.005 RD units.
For level ground conditions, the total vertical stress at a point, , on average, is the weight of everything above that point per unit area. The vertical stress beneath a uniform surface layer with density ρ {\displaystyle \rho } , and thickness H {\displaystyle H} is for example: