The density of gold, for example, is about 2. Density also reveals something about the phase of the matter and its substructure. Notice that the densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. The densities of gases are much less than those of liquids and solids, because the atoms in gases are separated by large amounts of empty space.
A reservoir has a surface area of What mass of water is held behind the dam? Then the mass m can be found from the definition of density. The volume V of the reservoir is its surface area A times its average depth h :. A large reservoir contains a very large mass of water. It is reasonable to ask whether the dam must supply a force equal to this tremendous weight. The answer is no. As we shall see in the following sections, the force the dam must supply can be much smaller than the weight of the water it holds back.
Figure 2. Three Gorges Dam in central China. The concrete dam is m high and 2. The reservoir made by this dam is km long. Over 1 million people were displaced by the creation of the reservoir. Give an example in which density is used to identify the substance composing an object.
Would information in addition to average density be needed to identify the substances in an object composed of more than one material?
Figure 3 shows a glass of ice water filled to the brim. Will the water overflow when the ice melts? Explain your answer. Mercury is commonly supplied in flasks containing What is the volume in liters of this much mercury? This is accomplished by the construction of a mathematical model of the charge density in a crystal and then by fitting the parameters of such a model to the experimental pattern of diffracted X-rays.
Each pseudoatom density consists of terms representing the core density, the spherical part of the valence density and the deviation of the valence density from sphericity. The continuous electron density in the crystal is then modelled as a sum of atom-centred charge distributions. Once the experimental electron density has been established, the "atoms in molecules" theory of Bader provides tools for the interpretation of the density distribution in terms of its topological properties.
Ref: Bader, R. Atoms in molecules: a quantum theory. When different elements move with different velocities, each element tries to drag its neighbouring elements along with it. Thus, shear stress occurs between fluid elements of different velocities. The relationship between the shear stress and the velocity field was studied by Isaac Newton and he proposed that the shear stresses are directly proportional to the velocity gradient or we can say shear strain rate. Dimensionless parameters are used to simplify analysis, and describe the physical situation without referring to units.
A dimensionless quantity has no physical unit associated with it. They arose from dimensional analysis techniques. These numbers have many applications in fluid mechanics as well as in related subjects like aerodynamics and convective heat transfer. Reynolds number after Osborne Reynolds, — is used in the study of fluid flows.
It compares the relative strength of inertial and viscous effects. Low Re indicates creeping flow, medium Re is laminar flow, and high Re indicates turbulent flow.
Reynolds number can also be transformed to take account of different flow conditions.
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