Hydrostatic scales: creation history, components, methods of use

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

Historical reference

The question of measuring the volume and density of bodies, mankind has been interested in since ancient times. According to preserved historical evidence, Archimedes first solved the problem with success when he dealt with the instructions given to him to determine whether the golden crown is fake.

Archimedes lived in the III century BC. After its discovery, it took humanity nearly 2000 years to create an invention that uses the physical principle formulated by the Greek in its work. This is a hydrostatic balance. Galileo invented them in 1586. These scales have long remained the main way to accurately measure the density of various liquids and solid materials. A photo of the hydrostatic balance of Galileo is shown below.

Subsequently, a variety of them appeared - the Mora-Westphal scale. 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 equilibrium. Mora Westphale Scales are shown below.

Currently, hydrostatic scales are rarely seen in scientific laboratories. They have been replaced by more accurate and easy-to-use instruments, such as a pycnometer or electronic scales.

Components of the Galileo Scales

This device has two levers of the same length, which can freely rotate around a central horizontal axis. A cup is hung at 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 to it.

In addition to weights, a set of hydrostatic scales 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 device in question is used to demonstrate the law of Archimedes and to determine the density of liquids and solid materials.

Demonstration of the law of Archimedes

Archimedes found 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 show how, using a hydrostatic balance, this law can be verified.

We first hang a hollow metal cylinder to the left bowl of the device, and then a full one. On the right side of the scale we put weights to balance the device. Now fill the glass cylinder with water and place the full metal weight of the left bowl in it so that it is completely submerged. You can observe that the weight of the right bowl is greater, and the balance of the device is disturbed.

Then we collect water into the hollow upper cylinder. We will observe how the balance restores its balance again. Since the volumes of the metal cylinders are equal, it turns out that the weight of the water displaced by the full cylinder will be equal to the force pushing it out of the liquid.

The figure below illustrates the described experience.

Solid Density Measurement

This is one of the main tasks of a hydrostatic weighing scale. The experiment is performed in the form of the following steps:

• The body weight 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 corresponding mass are placed on the second bowl. Denote the value of the cargo mass found in this way by the 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 .
• The density ρ _{s of the} solid is calculated by the following formula:

ρ _s = ρ _l * m ₁ / (m ₁ - m ₂ )

Here ρ _l = 1 g / cm ³ is the density of distilled water.

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

Determination of fluid density

The principle of Archimedes, which is the basis of the hydrostatic balance, allows you to measure the density of any liquid using the device in question. We describe how this is done:

• An arbitrary load is taken. It can be a solid metal cylinder or any other body of arbitrary shape. Then, the load is immersed in a liquid with a known density ρ _l1 and the mass of the load m _{1 is} measured.
• The same load is completely immersed in a liquid with an unknown density ρ _l2 . The value of its mass is recorded 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 _l1 * m ₂ / m ₁

Distilled water (ρ _l1 = 1 g / cm ³ ) is often used as a liquid with a known density.

Thus, the hydrostatic balance of Galileo is quite simple to use to determine the density of substances and materials. The accuracy of the results measured by them lies within 1%.