Buoyancy

Buoyancy arises from the fact that fluid pressure increases with depth and from the fact that the increased pressure is exerted in all directions (Pascal's principle) so that there is an unbalanced upward force on the bottom of a submerged object.

Since the "water ball" at left is exactly supported by the difference in pressure and the solid object at right experiences exactly the same pressure environment, it follows that the buoyant force on the solid object is equal to the weight of the water displaced (Archimedes' principle). 由于左边的“水球”恰好由压力差支撑，而右边的固体物体所处的压力环境完全相同，因此可以推断固体物体所受的浮力等于被排开的水的重量（阿基米德原理）。 浮力的产生源于两个事实：其一，流体的压强随深度增加而增大；其二，这种增大的压强在所有方向上都作用（帕斯卡原理），因此浸在流体中的物体底部会受到一个向上的不平衡力。

Objects of equal volume experience equal buoyant forces.

Applications of buoyancy.

Equal Volumes Feel Equal Buoyant Forces

Each would displace 10 grams of water, yielding apparent masses of -8 (the cork would accelerate upward), 17 and 103 grams respectively.

The behavior of the three balls would certainly be different upon release from rest in the water. The cork would bob up, the aluminum would sink, and the lead would sink more rapidly. But the buoyant force on each is the same because of identical pressure environments and equal water displacement. The difference in behavior comes from the comparison of that buoyant force with the weight of the object.

Archimedes' Principle

Hmm! The crown seems lighter under water!

The buoyant force on a submerged object is equal to the weight of the liquid displaced by the object. For water, with a density of one gram per cubic centimeter, this provides a convenient way to determine the volume of an irregularly shaped object and then to determine its density. 浸在液体中的物体所受的浮力等于物体排开的液体的重量。对于密度为1克每立方厘米的水来说，这提供了一种方便的方法来确定不规则形状物体的体积，进而确定其密度。

What is it's density?

它的密度是多少？

Archimedes' Principle

Hmm! The crown seems lighter under water!

The buoyant force on a submerged object is equal to the weight of the liquid displaced by the object. For water, with a density of one gram per cubic centimeter, this provides a convenient way to determine the volume of an irregularly shaped object and then to determine its density. 浸在液体中的物体所受的浮力等于物体排开的液体的重量。对于密度为1克每立方厘米的水来说，这提供了一种方便的方法来确定不规则形状物体的体积，进而确定其密度。

Archimedes' Principle

The buoyant force on a submerged object is equal to the weight of the fluid displaced. This principle is useful for determining the volume and therefore the density of an irregularly shaped object by measuring its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter). This effective mass under water will be its actual mass minus the mass of the fluid displaced. The difference between the real and effective mass therefore gives the mass of water displaced and allows the calculation of the volume of the irregularly shaped object (like the king's crown in the Archimedes story). The mass divided by the volume thus determined gives a measure of the average density of the object. Archimedes found that the density of the king's supposedly gold crown was actually much less than the density of gold -- implying that it was either hollow or filled with a less dense substance.

Examination of the nature of buoyancy shows that the buoyant force on a volume of water and a submerged object of the same volume is the same. Since it exactly supports the volume of water, it follows that the buoyant force on any submerged object is equal to the weight of the water displaced. This is the essence of Archimedes principle.