Excluded-volume explanation of Archie's law

Archimedes' principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to the weight of the fluid displaced by it. To understand how much buoyant force is needed to make an object float, let us think about what happens when a submerged object is removed from a fluid. If the object were not in the fluid, the space occupied by the object would be filled by the fluid having a weight wfl. This weight is supported by the surrounding...

When a lump of clay is dropped into water, it sinks. But if the same lump of clay is molded into the shape of a boat, it starts to float. Because of its shape, the clay boat displaces more water than the lump and experiences a greater buoyant force, even though its mass is the same. The same holds true for steel ships. The average density of an object majorly determines if the object will float. If an object's average density is less than that of the surrounding fluid, it will float. The reason...

Unsoundness in aggregates due to volume changes is primarily caused by the physical alterations aggregates undergo, such as freezing and thawing, thermal changes, and wetting and drying. Unsound aggregates, when subjected to these changes, result in volume change upon disintegration. This, in turn, contributes to the deterioration of concrete, including scaling, pop-outs, and cracking. Particular types of aggregates, such as porous flints, cherts, and those containing clay minerals, are...

Archimedes' principle is fundamental in analyzing the buoyant force and stability of floating bodies. In this example, a wooden block with a rectangular section floats in seawater. Based on the block's dimensions, its specific gravity and the specific weight of seawater are used to find the volume of water displaced and the center of buoyancy.
The volume of seawater displaced by the block is determined by first calculating the block's weight. This is done by multiplying the block's volume by...

Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...