Irregular solids, measuring volume

Measuring To calculate density, you need to know both the mass and volume of an object. You can find the volume of an irregular solid by displacing water. 

Volume Volume is the space occupied by an object. The derived unit for volume is the cubic meter, which is represented by a cube whose sides are all one meter in length. For measurements that you are likely to make, the more useful derived unit for volume is the cubic centimeter (cm ). The cubic centimeter works well for solid objects with regular dimensions, but not as well for liquids or for solids with irregular shapes. In the miniLAB on the next page, you will learn how to determine the volume of irregular solids. 

To Illustrate this method, we will consider the determination of the density of an Irregularly shaped solid. In this determination we make three measurements. First, we measure the mass of the object on a balance. Next, we must obtain the volume of the solid. The easiest method for doing this Is to partially fill a graduated cylinder with a liquid and record the volume. Then we add the solid and record the volume again. The difference In the measured volumes Is the volume of the solid. We can then calculate the density of the solid from the equation... 

Needing some relaxation, he decided to bathe at the public baths. As he stepped into the full tub and saw the water overflow, he realized that the volume of his body that was submerged was equal to the volume of water that overflowed. He had his answer for measuring the volume of the crown. He got so excited that he ran home naked through the streets, yelling Eureka, eureka G ve found it ) And this method of determining the volume of an irregular solid is still used today. (By the way, the crown was an alloy, and the dishonest jeweler received swift justice.)... 

With an irregular solid, like a rock, you can measure the volume by using the Archimedes principle. The Archimedes principle states that the volume of a solid is equal to the volume of water it displaces. Simply read the volume of water in a container, submerge the solid object, and read the volume level again. The difference is the volume of the object. 

Method B of ASTM D 792 uses a gas pycnometer to measure the volume of a powder or a granulated or irregular solid. The displacement of gas, usually helium, from a vessel of known volume is measured by sensitive differential pressure indicators. Suitable laboratory equipment is manufactured by Quantochrome (UltraFoam Pycnometer), Micromeiitics (Accu Pyc 1330), and others. This is also a convenient route to foam density. In troubleshooting production problems, SpG should always be checked, because of its sensitivity to misformulation. 

The density of an irregularly shaped solid is usually determined by measuring the mass and then measuring the volume of liquid that it displaces. The volume of liquid in a graduated cylinder is measured before the object is submerged and then measured again with the object submerged. The difference in the volume equals the volume of the object. 

Relatively little appears to be known about the influence of shape on the behaviour of particulate solids and it is notoriously difficult to measure. Whilst a sphere may be characterised uniquely by its diameter and a cube by the length of a side, few natural or manufactured food particles are truly spherical or cubic. For irregular particles, or for regular but non-spherical particles, an equivalent spherical diameter de can be defined as the diameter of a sphere with the same volume V as the original particle. Thus... 

When a solid is irregular in shape, it seldom is convenient or possible to find its volume by measurement of its dimensions. A convenient procedure is to immerse the object in a liquid, and then to determine its volume by measuring... 

Workers concerned with liquid/solid systems with exceptionally good wettability, such as some braze/metal workpiece systems, find that the drops do not preserve a perfectly circular area of contact because of the sensitivity of the liquid to changes in capillary attraction caused by minor variations in the surface texture of the workpiece. Because of such irregularity, some workers have used the contact area of a small volume of braze as a measure of wettability. Thus Feduska used area measurements to differentiate between the wetting of different stainless steels by a wide range of metals and alloys (Feduska 1959). 

In-situ density may also be determined from irregularly shaped field samples, by measuring the total volume by water displacement, then determining the specific gravity and volume of solids by standard test methods. To use this process, the grout in the soil voids must be eliminated. For the acrylics this is readily done by heating to the point where the gel vaporizes. 

Catalyst is being delivered by conveyor belt at a constant mass flow rate. The question we would like to be able to answer is How much catalyst mass is in the reactor vessel at any time The reason we care is that we will be paying for the catalyst on a per pound basis. If we look into the reactor at any time t, we may be able to measure the level to which the reactor is filled, and from that level measurement we could in principle compute the mass of catalyst if we had a density for the material. Remember though that this is solid and it packs irregularly into the reactor, as we can see from Figure 1. We can at best get an average value for tiie density and only after we have done an experiment in which the catalyst was carefully packed into a known volume and massed in order to find its so-called compacted bulk density. 

The volume of an irregularly shaped solid can be determined by measuring the amount of water it displaces. 

It is not possible to measure or define absolutely the size of an irregular particle, and perfectly regular crystalline solids are rarely, if ever, encountered. The terms length, breadth, thickness or diameter applied to irregular particles are meaningless unless accompanied by further definition, because so many different values of these quantities can be measured. The only meaningful properties that can be defined for a single solid particle are the volume and surface area, but even the... 

Equation (6.13) requires only the measurement of the dependence of the volume of the intruded mercury on the applied pressure, and can be used to investigate irregularities of the solids within the range of scales provided by mercury intrusion data. Application of the mercury porosimetry technique has been reported in several papers studying soils [14, 17, 33, 37 5]. 

The volume of an irregularly shaped solid can be determined by immersing the solid in a liquid and measuring the volume of liquid displaced. Find the volume and density of the following ... 

When submerged in a liquid, an irregularly shaped solid displaces a volume of liquid equal to its own volume. The necessary data can be obtained by two mass measurements of the type illustrated here the required calculations are like those in Example 1-3. 

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