| | | You will find the volume expansion coefficients of several liquids in the appendix of this booklet. Other Formulas for Calculating the Density of Liquids The densities of supercooled liquids and overheated gasses, hydrocarbons, and mixtures of materials are frequently calculated by using the model equations of Lee and Kessler (Lee, B.I. and M.G. Kessler: AICHE J.21 (1975) pg.510). The calculation model is described in detail in the VDI-Warmeatlas (Association of Engineers Thermal Atlas). You will find extensive tables with calculation constants necessary for many different types of media in the same reference source. Calculating the Density of Steam and Water The IAPWS Equation is used for the exact calculation of the density (and other state variables) of water and water steam. (IAPWS is the International Assosiation for the Properties of Water and Steam: www.iapws.org.) The IAPWS Equation requires a considerable amount of numerical and mathematical process. The precise definition has been documented in an extensive publication (W. Wagner and A. Pruss, "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use," J. Phys. Chem. Ref. Data, 31, 387-535 (2002)). Various pre-programmed source codes or libraries are available for purchase (see www.ruhr-uni-bochum.de/thermo/Forschung/ Seiten/Zustandsgln/IAPWS-95.htm ). If the operational position is not too far from the design point, the density of water can be roughly calculated by using a constant volume expansion coefficient (see description above). The density of overheated steam can be calculated by using the ideal gas equation (see description below) at small distances from the design point. It is simple matter to calculate density by using tables (refer to the Water/Steam Table in the Appendix). Interpolating beyond the boiling point, however, could result in large discrepancies and is not recommended. Calculating the Density of Gasses | | If no tables are available, or if the medium in question is a mixture of gasses, then various calculation equations are available, among them van der Waals, Redlich Kwong, and many others. Various calculation models are described in detail in the VDI-Warmeatlas. You will also find extensive tables with necessary calculation constants for many different types of media in the same reference source. The ideal gas equation is a very simple equation which often provides sufficient accuracy when calculating density within short distances from the design point. | | |
| | | The more operational pressure and temperature deviate from the design point, the more unreliable the calculation. This is especially true when the operational level approaches the boiling point of the gas. When this happens, the pressure increases and the temperature decreases. At greater distances from the boiling point, the ideal gas equation generally provides fairly accurate calculations. The ideal gas equation can also be used for overheated steam. The same conditions apply as for other gasses. Example: | | |
| | | 2 15•554 15 pB = 8.330kg/w32qq 54315 = 9A36kg/m3 According to the IAPWS 95, the actual density at 2.15 Mpa and 543.15K is 9.221 kg/m3. The error in density calculation, then, is 0.92%, and the resulting error in the flow measurement equals approximately 0.46%. Density Correction for Water-laden Gasses Gases can absorb water (humidity). Mixtures of gas and water have a different density than "pure," or dry, gasses. The amount of water a gas is able to absorb increases with the temperature of that gas. Very hot | | |