Hydrostatic balances: history of creation, components, methods of use

2024 Author: Aaron Duncan | [email protected]. Last modified: 2024-01-01 20:00

To determine the density of liquids and solids, you need to know their mass and volume. If there are no problems with measuring the mass, then the exact value of the volume of the body can be found if it has a known regular geometric shape, for example, the shape of a prism or pyramid. If the body has an arbitrary shape, it is impossible to accurately determine its volume by standard geometric means. However, the density value of a liquid or solid can be measured with high accuracy using a hydrostatic balance.

Historical background

Mankind has been interested in the issue of measuring the volume and density of bodies since ancient times. According to surviving historical evidence, the noted problem was first successfully solved by Archimedes when he coped with the assignment given to him to determine whether the golden crown was fake.

Archimedeslived in the III century BC. After its discovery, it took mankind almost 2000 years to create an invention that uses the physical principle formulated by the Greek in its work. This is a hydrostatic balance. Invented by Galileo in 1586. These balances have long been the main way to accurately measure the density of various liquids and solids. A photo of Galileo's hydrostatic balance is shown below.

Subsequently, their variety appeared - Mohr-Westphal scales. In them, instead of two identical levers, only one was used, on which the measured load was suspended, and along which loads of a known mass slid to obtain balance. Mohr-Westphal scales are shown below.

At present, hydrostatic balances are rarely seen in scientific laboratories. They have been replaced by more accurate and easier-to-use instruments such as the pycnometer or electronic scales.

Components of Galileo's scales

This appliance has two arms of the same length that can freely rotate around a central horizontal axis. A cup is suspended from the end of each lever. It is designed to hold weights of known mass. There is a hook at the bottom of the cups. You can hang different loads from it.

In addition to the weights, the hydrostatic balance includes two metal cylinders. They have the same volume, only one of them is made entirely of metal, and the second is hollow. Also included is a glass cylinder.which is filled with liquid during measurements.

The instrument in question is used to demonstrate the law of Archimedes and to determine the density of liquids and solids.

Demonstration of the law of Archimedes

Archimedes established that a body immersed in a liquid displaces it, and the weight of the displaced liquid is exactly equal to the buoyant force acting upward on the body. We will show how, using a hydrostatic balance, this law can be verified.

To the left bowl of the device we will first hang a hollow metal cylinder, and then a full one. We put weights on the right side of the scales to balance the device. Now let's fill the glass cylinder with water and place the full metal weight of the left bowl into it so that it is completely submerged. It can be observed that the weight of the right bowl will be greater, and the balance of the device will be disturbed.

Then we draw water into the hollow upper cylinder. Let's watch how the scales again restore their balance. Since the volumes of metal cylinders are equal, it turns out that the weight of water displaced by a full cylinder will be equal to the force pushing it out of the liquid.

The picture below illustrates the experience described.

Density measurement of solids

This is one of the main tasks of hydrostatic weighing scales. The experiment is carried out in the form of the following steps:

• The weight of the body is measured, the density of which should be found. To do this, it is suspended from the hook of one of the bowls, and weights of the appropriate mass are placed on the second bowl. Let's denote what we foundway the value of the weight of the load symbol m_1.
• The measured body is completely immersed in a glass cylinder filled with distilled water. In this position, the body is weighed again. Suppose the measured mass was m_2.
• Calculate the density value ρ_{s of a solid using the following formula:}

ρ_s=ρ_lm₁/(m ₁- m₂₎

Here ρ_l=1 g/cm^{3 is the density of distilled water.}

Thus, to determine the density of a solid body, it is necessary to measure its weight in air and in a liquid whose density is known.

Determining the density of liquids

The principle of Archimedes, which is the basis for the operation of hydrostatic balances, allows you to measure the density of any liquid using the device in question. Let's describe how it's done:

• An arbitrary load is taken. It can be a metal solid cylinder or any other body of arbitrary shape. Then, the load is immersed in a liquid with a known density ρ_l1 and the weight of the load is measured m_1.
• The same load is completely immersed in a liquid with an unknown density ρ_l2. Write down the value of its mass in this case (m_2).
• The measured values are substituted into the formula and determine the density of the liquid ρ_l2:

ρ_l2=ρ_l1m₂/m ₁

Bdistilled water is often used as a liquid with a known density (ρ_l1=1 g/cm^3).

Thus, Galileo's hydrostatic balance is easy enough to use to determine the density of substances and materials. The accuracy of their results is within 1%.