Density, Pressure, and Gravity as a Function

DENSITY, PRESSURE, AND GRAVITY AS A FUNCTION OF DEPTH WITHIN THE EARTH... 

Density, Pressure, and Gravity as a Function of Depth within the Earth.14-15... 

Density of Solvents as a Function of Temperature, 15-25 Density of Sulfuric Acid, 15-40 Density of Various Solids, 15-39 Density, Pressure, and Gravity as a Function of Depth within the Earth,... 

This table gives the density p, pressure p, and acceleration due to gravity as a function of depth below the earth s surface, as calculated from the model of the structure of the earth in Reference 1. The model assumes a radius of 6371 km for the earth. The boundary between the crust and mantle (the Mohorovicic discontinuity) is taken as 21 km, while in reality it varies considerable with location. 

The first term on the left-hand side describes the variation of the fluid momentum in time and the second term describes the transport of the momentum in the flow (convective transport). The first term on the right-hand side describes the effect of gradients in the pressure p the second term, the transport of momentum due to the molecular viscosity p (diffusive transport) the third term, the effect of gravity g and in the last term, F lumps together all the other forces acting on the fluid. Techniques for solving the set of four equations (one continuity and three momentum equations) are discussed in a later section of this entry. When the flow is compressible, it is usually necessary to close the system of equations listed above using a thermodynamic equation of state (such as the ideal gas law) that calculates the density as a function of temperature and pressure. 

The specific gravity (relative density) of the gas is required for calculating flow through pipes and orifices and to establish the relationship between the amounts of gas measured volumetrically to the corresponding mass or molar amounts. The relative density can be determined fi om a knowledge of the molar volumes of the component gases as a function of temperature and pressure and selected binary mixture properties. 

Gas density is controlled very strongly by gas pressure. Gas mixture density is characterized frequently by a specific gravity G. Specific gravity G is the ratio of the gas density to air density at 15.6 °C (60 °F) and atmospheric pressure. Figure 4.2 shows the density of methane as a function of temperature and pressure. 

The values for a single property of two compounds, A and B, are useless unless these values are compared at equal temperature or pressure. Then a deviation from some intermediate value can be determined. If this intermediate value is chosen to be the value of one particular substance, ie. A, the reference substance, both A and B can then be expressed as functions of the reference substance. One very simplistic example is specific gravity where the density of a compound is expressed as the actual density divided by the density of water at 4°C and water is the reference substance. 

---