Method for determining volume of solids

Abstract

FIELD: measuring technology.SUBSTANCE: devices for measuring density and temperature. The essence of the method is that first a solid body is placed rigidly on a mount, then a liquid capsule with a liquid of known density is installed on the scale. The initial mass is measured as the sum of the masses of the liquid capsule and the mass of the liquid contained in the liquid capsule. Then the solid body is immersed in a liquid of the same volume in a liquid capsule and held there in the absence of direct force contacts between the solid body and the walls of the liquid capsule. Next, the final mass is measured using scales, and then the volume of the solid is calculated as the ratio of the difference between the final and initial masses, recorded by the scales, to the density of the liquid. The volume of the part of the fastener located in the liquid is subtracted from the calculated volume of the solid.EFFECT: increasing the accuracy and simplicity of measuring the volume of a solid body.2 cl, 4 dwg

Description

[0001] The invention relates to methods for determining the properties of solid materials.

[0002] It is well known that volume is a quantitative characteristic of the space occupied by a body or substance. The volume of a body is determined by its shape and linear dimensions. The main property of volume is additivity, that is, the volume of any body is equal to the sum of the volumes of its (non-intersecting) parts (see Volume / / Mathematical Encyclopedia (in 5 volumes). - Moscow: Soviet Encyclopedia, 1982. - Vol. 3). The unit of volume in the SI is the cubic meter.

[0003] There are known methods for calculating the volume of solids:

[0004] A method based on the law of the ancient Greek scientist Archimedes: when a body is immersed in a liquid, the volume of the displaced liquid will be equal to the volume of the measured body.

[0005] Disadvantages of this method: 1) complex and careful preparation for the implementation of the method, because it is necessary to prepare a container for immersing the body with a certain volume of liquid (e.g. water), and then it is necessary to collect the poured liquid in a measuring container containing, for example, volume marks; 2) the method is not entirely accurate, since when implementing this method, some of the liquid may remain on the edge of the container, from which it is displaced by the solid body; to calculate the volume of poured liquid, they often resort to simply observing the level of the measuring container with marks; 3) the method is difficult to implement with an extremely small volume of a solid body.

[0006] The mathematical method involves calculating the volumes of simple solids using known mathematical formulas. For example, to find the volume of a cube, raise its edge length to the third power.

[0007] Disadvantages of this method: it is impossible to accurately determine the volume of a solid body if it has a complex, irregular shape.

[0008] Body density method - this is done by calculating body mass and then dividing the body mass by the average body density.

[0009] Disadvantages of this method: low accuracy due to the need to use several measuring devices, such as scales and a density meter; it is not always possible to accurately calculate the density of a liquid, especially when the ambient temperature changes.

[0010] A known invention is "Method for determining the volume of solids" (see Kopylov VB, Strakhov VM, Krupkin Yu.S., Method for determining the volume of solids, USSR Author's Certificate No. 1343246, IPC G01F 17 / 00, Published 07.10.1987, Bulletin No. 37), in which, to determine the volume of a solid, a measuring vessel with a test sample and a comparison vessel, having the same volumes, are evacuated, then connected to a gas inlet system through two independent flow pipelines, the dependence of the difference in pressure drop in the pipelines on time is recorded, and the volume of the sample is determined by the peak area on the measured dependence.

[0011] Disadvantages of this method: relatively complex implementation (the diagram contains at least 11 elements, the method itself is carried out in several stages); low efficiency when measuring the volume of large solids.

[0012] The closest in technical essence is the invention - "Hydrostatic press" (see Altunin K.V. Hydrostatic press. Russian Federation Patent IZ No. 2839217. IPC B30B 1 / 32, B30B 15 / 22. Bulletin No. 13 dated 04 / 28.2025), comprising a lower support with a frame fixed thereto, an upper support, a liquid capsule configured to supply liquid thereto by means of pipelines and valves; wherein the hydrostatic press is provided with springs fixed to the upper support, on which the liquid capsule is suspended, a float rigidly fixed to the upper support in a stationary position with the possibility of being surrounded from below and on the sides by liquid placed in the liquid capsule, and a bottom for pressing the body being pressed, installed on the bottom of the liquid capsule from the outside, wherein the pipelines and valves are configured to regulate the supply of liquid to the liquid capsule and the weight of the liquid capsule, and the frame is configured to accommodate the body being pressed on it; the float can also be provided with marks located on its surface to determine the required level of liquid in the liquid capsule.

[0013] Possible disadvantages of this invention: the impossibility of determining the density of a liquid and the volume of a solid; the lack of accurate measuring devices, such as electronic scales.

[0014] The problem solved by the claimed invention is to increase the accuracy of determining the volume of a solid body of complex shape.

[0015] The technical result that the proposed invention is aimed at achieving consists in reducing the number of measuring elements, instruments, devices, and in reducing the number of stages in carrying out the method.

[0016] The technical result is achieved in that in the method for determining the volume of solids, which includes placing the solid on a mount, filling a liquid capsule with liquid to the liquid level, using scales on which the liquid capsule is installed, using the scales to measure the initial mass as the sum of the mass of the liquid capsule and the mass of the liquid in the liquid capsule, then completely immersing the solid in a liquid of the same volume in the liquid capsule and holding it there using a mount in the absence of direct force contacts of the solid with the walls of the liquid capsule, which leads to an increase in the weight of the liquid, using the scales to measure the final mass, which is greater than the initial mass, then calculating the volume of the solid as the ratio of the difference between the final mass and the initial mass, recorded by the scales, to the density of the liquid;Moreover, in order to increase accuracy, the volume of the part of the fastening immersed in the liquid is subtracted from the calculated volume of the solid body.

[0017] To explain the technical essence of the proposed invention, let us consider Fig. 1, 2, 3, 4, where: 1 - liquid; 2 - liquid capsule; 3 - float; 4 - support; 5 - scales, 6 - liquid level, 7 - fastening, 8 - solid body, 9 - part of the fastening immersed in the liquid.

[0018] Fig. 1 - Float on the surface of the liquid inside the liquid capsule installed on the scale;

[0019] Fig. 2 - A float immersed and held in a liquid inside a liquid capsule mounted on a scale;

[0020] Fig. 3 - Preparation for implementing the method;

[0021] Fig. 4 - Implementation of the method by immersing a solid body in a volume of liquid and holding it in this liquid.

[0022] From a physics course, we know that when a volume of a body is immersed in a liquid (for example, water), the Archimedes force arises, which pushes this volume of the body and at the same time is opposite to the force of gravity.

[0023] Consider Fig. 1. Here, liquid capsule 2 contains a volume of liquid 1 at a level HI from the bottom of this capsule. A float 3, rigidly connected to a support 4, is located on the surface of the liquid. We assume that the weight of float 3 together with support 4, as well as the weight of liquid capsule 2 (without liquid) are negligible compared to the weight of the volume of liquid 1, and they can be neglected. Let the hermetically sealed housing of float 3 contain air. The gravitational force of the volume of liquid 1 is equal to F т1 . Now we begin to press down on support 4, thereby achieving the immersion of float 3 into the liquid; we stop the movement when float 3 is completely immersed in the liquid, and the liquid level rises to the H2 mark (Fig. 2), then in this case the Archimedes force F arises a2, which balances the force F2, i.e. F a2 =F2, while scales 5 will show a different, namely greater weight: F тс =F т1 +F a2 or F тс =F т1 +F2.

[0024] If you fix the support 4 with the body of the liquid capsule 2, for example, this can be done with the help of a rope, chain, etc. (not shown in the description and in the figure), i.e. if you destroy the force F2, which balances the force F a2 , then scales 5 will again show weight F т1 and F тс =F т1 , despite the fact that float 3 will be in liquid 1.

[0025] Experiments were conducted using the diagrams in Figs. 1 and 2, with float 3 containing various substances, including air, fresh water, and vegetable oil. It was found that when float 3 was completely immersed (with the substance inside) in a liquid (fresh water) by the same amount, the scales showed the same mass. Thus, a fundamental conclusion can be drawn: when any body that is not rigidly attached to the body of the liquid capsule is immersed in liquid and held there, an additional weight force is generated, equal to and opposite to the Archimedes force acting on the body.

[0026] Based on the theoretical and experimental studies conducted, it can be stated: “The weight of the volume of liquid in a liquid capsule is equal to the sum of the gravity of the liquid itself and the Archimedes force acting on a body immersed in this liquid, if the immersed body is not rigidly fixed to the body of the liquid capsule.”

[0027] Mathematically it can be written:

[0028]

[0029] where F тж - gravity of the liquid, N; F A - Archimedes' force, N; m ƒ - mass of liquid, kg; g - acceleration of gravity, m / s 2 ; ρ ƒ - liquid density, kg / m3 3 ; V т - volume of the submerged body, m 3 ; P is the total weight of liquid in the liquid capsule, N.

[0030] Expression (2) can be rewritten in another form:

[0031]

[0032] where V ƒ - volume of liquid inside the liquid capsule, m 3 .

[0033] Implementation of the method for determining the volume of solids:

[0034] First, the solid body 8 is attached to the fastening 7 by any available means. Fig. 3 shows the preparation for implementing the method, where the solid body 8 of complex shape is rigidly attached to the fastening 7 and is located above the level of the liquid 6, while the liquid capsule 2 contains a sufficient amount of liquid 1, but the volume of liquid should not exceed the maximum possible so that liquid 1 does not spill out of the liquid capsule 2 when the solid body 8 is immersed. At this stage, using scales 5, the initial mass M1 is measured, equal to the sum of the mass of liquid 1 and the mass of liquid capsule 2.

[0035] Then the solid body 8 is completely immersed in the liquid 1 and held there in the absence of rigid contact between the solid body 8 and the walls of the liquid capsule 2, and the final mass M2 is measured using scales 5.

[0036] Calculate the volume of solid body 8 using the formula:

[0037]

[0038] where Vт - volume of a solid body, m 3 ; ρ ƒ - liquid density, kg / m3 3 ; M1 - mass of liquid and liquid capsule before immersion of solid body, kg; M2 - mass of liquid and liquid capsule after immersion of solid body, kg; ΔM - difference in masses, kgf.

[0039] However, when a solid body is immersed in a liquid, a situation may arise where part of the fastening element holding the solid body will be in the liquid, for example, as in Fig. 4. In this case, to improve the accuracy of the measurement, it is necessary to subtract the volume of the part of the fastening immersed in the liquid 9 V к from the volume previously found using formula (4):

[0040]

[0041] V value кcan be calculated in advance using some known method or one can resort to this proposed method and, using formula (4), accurately calculate the volume of the part of the fastening immersed in liquid 9 (i.e., it is necessary to immerse the part of the fastening to the same depth without the solid body 8).

[0042] Thus, no matter what the density of a submerged solid body of the same volume is, the scale will show the same value for the increased mass if the body's volume remains unchanged (Fig. 4). This is the fundamental versatility of the proposed method.

[0043] In this case, to improve the accuracy of determining the volume of solids, it is necessary to use more accurate scales, for example, modern electronic scales with a low accuracy class and high accuracy.

[0044] Advantages of the proposed method for determining the volume of solids:

[0045] - easy to implement: only one measuring instrument in the form of scales is required, there is no need to accurately measure the volume of liquid; the method can be carried out at home;

[0046] - sufficient accuracy: only one measuring device in the form of a scale can be used; no liquid loss at the edge of the container;

[0047] - practicality: minimal number of implementation steps; the method can be used with different liquids, not just water;

[0048] - versatility: it is possible to measure the volumes of solid bodies of different densities, sizes, dimensions, and shapes.

[0049] Thus, the method for determining the volume of solids is universal, accurate and reliable, and can be used to measure the volume of solids of any shape in both domestic and industrial conditions.

Claims

1. A method for determining the volume of solids, which includes placing the solid on a fixture, filling a liquid capsule with liquid to the liquid level, characterized in that a scale is used on which the liquid capsule is mounted, the scale is used to measure the initial mass as the sum of the mass of the liquid capsule and the mass of the liquid in the liquid capsule, then the solid is completely immersed in a liquid of the same volume in the liquid capsule and held there by a fixture in the absence of direct force contacts of the solid with the walls of the liquid capsule, which leads to an increase in the weight of the liquid, the scale is used to measure the final mass, which is greater than the initial mass, then the volume of the solid is calculated as the ratio of the difference between the final mass and the initial mass, recorded by the scale, to the density of the liquid.

2. A method for determining the volume of solids according to paragraph 1, characterized in that, in order to increase accuracy, the volume of the part of the fastener immersed in the liquid is subtracted from the calculated volume of the solid.

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