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Buoyancy is a fundamental concept that explains why objects float or sink in fluids. When a hydrometer is immersed in a liquid, it experiences an upward force known as the buoyant force. This force is caused by the pressure differences at various depths in the liquid. The principle of buoyancy was first described by Archimedes, and it states that the buoyant force equals the weight of the fluid displaced by the object.
For a hydrometer, floating occurs when the buoyant force is equal to its weight. If the weight of the displaced liquid is less than the hydrometer's weight, it sinks until the equilibrium is achieved. This balance between weight and buoyant force is what determines how much of the hydrometer is submerged in the liquid.
Understanding buoyancy helps in determining which marks should be put on a hydrometer for different liquids, such as battery acid and antifreeze. The differing densities of these liquids mean the hydrometer will float at different levels.

Measuring density is the main function of a hydrometer. Density is defined as the mass per unit volume of a substance. It can provide critical information about the properties of a liquid. For example, knowing the density of battery acid or antifreeze helps in judging their quality and efficacy.
A hydrometer measures density by observing how deep it sinks in the liquid. The denser the liquid, the higher the buoyancy, causing the hydrometer to float at a shallower depth. Conversely, in less dense liquids, it will sink deeper.
This principle allows markings on the hydrometer to provide a direct reading of the liquid's density. When calibrated correctly, one can easily measure the density of the liquid by looking at how much of the hydrometer is submerged.

Liquid displacement is the process that occurs when an object, like a hydrometer, enters a liquid. It pushes aside some of the liquid to make space for itself, which leads to displacement. The amount of liquid displaced is directly related to the volume of the submerged part of the object.
In the case of a hydrometer, the displaced liquid's weight equals the hydrometer's weight for it to float. By calculating the volume of the liquid displaced, we can determine the density of the liquid by knowing the weight and volume relationship.
This is why precise measurement of the volume of liquid displaced is essential. It allows us to understand not just the density, but also how different liquids will interact with the hydrometer.

Fluid mechanics is the study of fluids and how forces affect their motion. This understanding is crucial when using a hydrometer, as it involves principles like buoyancy and liquid displacement. These are both governed by the basic laws of fluid mechanics.
In fluid mechanics, we often deal with equations that relate to the viscosity, flow, pressure, and density of fluids. For a hydrometer to work, these factors must be considered to ensure accurate readings. The weight, cross-sectional area, and density all play a role in determining the hydrometer's behavior in a liquid.
By understanding fluid mechanics, one can also predict how a hydrometer will react in different liquids under varying conditions. This includes varying temperatures and pressures, which can alter fluid density and, consequently, the hydrometer's readings.