Due to the unchanged volume of the hydrometer, the displaced water volume remains the same. However, it becomes heavier due to the additional water content. When gravity exceeds buoyancy, the hydrometer sinks. Since the hydrometer's weight is less than the gravitational force of an equivalent volume of water, it floats back up.
When immersed in different liquids, the volume remains unchanged while the reading varies. The iron sand or lead shot at the bottom of the hydrometer is used to maintain balance.
Gravity pulls objects towards the Earth's surface, but if an object is placed in a liquid, buoyancy will exert an opposite force. The magnitude of buoyancy is equal to the weight of the liquid displaced by the object.
A hydrometer rises or sinks based on changes in the balance of gravity and buoyancy. A fully functional hydrometer can only float, so the upward force of buoyancy must be slightly greater than the downward force of gravity. However, at equilibrium, the gravity it experiences is equal to the buoyancy.
Expanded Information
Application:
For Density Timing: Can measure the specific gravity of various fluids and semi-solids. Examples include: cement slurry, mortar, mineral slurry, pulp, and random specific gravity in the process of chemical products.
For concentration timing: It can determine the percentage concentration (or ratio) of solutions. For example, concentrations of various solutions, slurry, mud, mortar, beverage flotation agents, etc. With a flowmeter, it can conveniently calculate the instantaneous mass flow rate and cumulative amount of dry minerals.
This is primarily due to the structure of the hydrometer.
We know that the bottom of the hydrometer is irregular and contains lead balls, while the top is regular (in the shape of a cylinder).
The lower volume of the hydrometer is Vo, the upper cross-sectional area is S, and the total weight of the hydrometer is G.
The hydrometer was respectively immersed in three liquids with densities of ρ1, ρ2, and ρ3 (with the cylindrical section immersed to depths of h1, h2, and h3, respectively, where h1 > h2 > h3, and h1 indicates the density value of ρ1), and ρ3 - ρ2 = ρ2 - ρ1 > 0.
Clearly, when a hydrometer is immersed in a liquid with a density of ρ1, there is:
(Vo + h1 * S) * ρ1 * g = G (That is, F buoy = G)
Solve for h1: h1 = G / (ρ1 * g * S) - Vo / S
Similarly, (Vo + h2 * S) * ρ2 * g = G
h2=G/(ρ2*g*S)-Vo/S
(Vo+h3*S)*ρ3*g=G
h3=G/(ρ3*g*S)-Vo/S
Here, h1-h2 = [G/(ρ1*g*S) - Vo/S] - [G/(ρ2*g*S) - Vo/S]
=[G/(g*S)]*[(ρ2-ρ1)/(ρ1*ρ2)]
Similarly, h2-h1 = [G/(g*S)] * [(ρ3-ρ2)/(ρ3*ρ2)]
Clearly, due to ρ3 - ρ2 = ρ2 - ρ1
However, ρ3 > ρ2.
So, h1-h2 > h2-h3
Therefore, the density gauge has wider spacing on its scale from h1 to h2 and narrower spacing from h2 to h3.
