Thermal expansion factor

The experimentally determined densities of these mixtures at numerous elevated pressures and temperatures were adjusted to atmospheric psia and 60°F using suitable compressibility and thermal expansion factors. Then the mass and volume contributed by the heavier components were subtracted. This left the contribution due to iqethane or ethane, i.e., their apparent liquid densities. 

For convenience, the compressibility and thermal expansion factors have been put in graphical form.3,4 These correlations are given as Figures 11-3 and 11-4. Fortunately, the coefficient of thermal expansion of hydrocarbon liquids is not affected greatly by pressure so that Figure 11-4 can be used regardless of the pressure involved. 

The factor 1.7 arises from the viscosity dependence of 0.7 and the thermal expansion factor of 1.0. With constant inlet and outlet pressures, pjp is constant, and the outlet flow rate then changes with the 1.7 power of the temperature ... 

Figure 5-1 shows the locations and names of the orifice taps. The true mass flow rate for both liquids and gases is obtained by multiplying the theoretical mass flow equation by the discharge coefficient, the gas expansion factor, and the thermal-expansion factor. This is expressed as ... 

The thermal expansion factor F The material of primary element and pipe expands or contracts with temperature. The pipe and bore diameters are measured at room temperature, but will be larger or smaller when used at other temperatures. is introduced to correct for these differences. 

F3 = area thermal-expansion factor. Takes into account the expansion of the orifice with temperature changes h = full-scale orifice pressure differential, in. H2O at 68°F k = specific heat ratio (constant pressure to constant volume Cp/C ) P = upstream pressure, psia AP = full-scale orifice pressure-differential, psi Q = full-scale flow rate at upstream conditions, fp/min = ti ue full-scale flow rate, Ib/s Y = expansion factor... 

AREA THERMAL-EXPANSION FACTOR. ACCOUNTS FOR THE EXPANSION OF THE ORIFICE WITH TEMPERATURE CHANGES. FULL-SCALE ORIFICE PRESSURE-DIFFERENTIAL. INCH-H20 AT 68oF. 

In this equation Ap is the compressibility factor difference (P =PV) and Aa the difference of the thermal expansion factor (a =aV) of the denatured and native states of proteins. An important assumption in the derivation of this equation is the temperature and pressure independence of Aa, AP and ACp. The AG=0 curve is an ellipse on the P-T plane and it describes the equilibrium border between the native and denatured state of the protein. This curve is known as the phase or stability diagram. This is visualized in Fig. 2. The diagram illustrates the interconnection between the cold, heat and pressure unfolding of proteins. 

Introducing both the thermal expansion factor for the sweeping gas and the desorption expansion factor 8 in equation 5.62, we have... 

For applications where the fluid temperature is very high or low, it is important to include another correction factor. Pipe and orifice plate bore diameters are typically provided by the manufacturer and are based on room temperature. As the temperature of the orifice plate and pipe vary from room temperature, they expand and contract. To correct for the expansion and contraction of the material, a thermal-expansion factor is applied to the dimensions these new dimensions are then used in the calculation. The thermal-expansion correction factor for a temperature relative to 68°F is... 

In general, functions 0 and F are not known. To determine these functions one may use as the input values such experimental data as lattice parameters, elastic constants, energy of the vacancy formation, sublimation energy, and the stacking fault energy. Thermal expansion factors, heat of solution, phonon frequencies, surface energy, and energy of the vacancy diffusion can also be included in quantities used for determination of the functions 0 and F. 

Hall s Factors. For calculating the thermal expansion of a glass see THERMAL EXPANSION FACTORS FOR GLASS. 

Thermal Expansion Factors for Glass. Factors that have been proposed from time to time for the calculation of the coefficient of linear thermal expansion of a glass on the assumption that this is an additive property. The factors are inserted in the equation X,(= lO AI/lAT)... 

The thermal expansion factor depends on the meter material, tiie pipe material, and the temperature of the process fluid. The following equation is used to calculate the thermal expansion factor ... 

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