Mass flow measurement coefficients

Mann, D.B., et al, Gas Orifice Meter Discharge Coefficients as Determined by Mass Flow Measurement, NBSIR 83-1685, August 1983. 

The discharge coefficient is in general determined experimentally by the valve manufacturer for a fixed nominal lift. It corresponds to the average value of the ratio from mass flows measured and calculated with the nozzle flow model [1]. At least... 

Wall-to-bed heat-transfer coefficients were also measured by Viswanathan et al. (V6). The bed diameter was 2 in. and the media used were air, water, and quartz particles of 0.649- and 0.928-mm mean diameter. All experiments were carried out with constant bed height, whereas the amount of solid particles as well as the gas and liquid flow rates were varied. The results are presented in that paper as plots of heat-transfer coefficient versus the ratio between mass flow rate of gas and mass flow rate of liquid. The heat-transfer coefficient increased sharply to a maximum value, which was reached for relatively low gas-liquid ratios, and further increase of the ratio led to a reduction of the heat-transfer coefficient. It was also observed that the maximum value of the heat-transfer coefficient depends on the amount of solid particles in the column. Thus, for 0.928-mm particles, the maximum value of the heat-transfer coefficient obtained in experiments with 750-gm solids was approximately 40% higher than those obtained in experiments with 250- and 1250-gm solids. 

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

Dengler and Addoms 8 measured heat transfer to water boiling in a 6 m tube and found that the heat flux increased steadily up the tube as the percentage of vapour increased, as shown in Figure 14.4. Where convection was predominant, the data were correlated using the ratio of the observed two-phase heat transfer coefficient (htp) to that which would be obtained had the same total mass flow been all liquid (hi) as the ordinate. As discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt, the parameter for two-phase turbulent flow developed by Lockhart and Martinelli(9). The liquid coefficient hL is given by ... 

For the ball-probe measurement of charge current in a dilute gas-solid suspension, prove that, for a given type of particle and a given mass flow ratio, the current measured is independent ofthe particle size for db 3> dp. It is assumed that the charge transfer coefficient is constant. 

The measured volumetric flow rate of ethane at 10.0 atm absolute and 35 C is 1.00 x 10 L/h. Using an estimated value of the second virial coefficient in the truncated virial equation (Equation 5.3-4), (a) calculate V (L/mol) (b) estimate the compressibility factor,and (c) determine the mass flow rate of ethane in kg/h. 

SOLUTION During an experiment involving an automotive radiator, the inlet and exit temperatures of water and air and the mass flow rate of water are measured. The overall heat transfer coefficient based on the inner surface area is to be determined. 

In this section the general trends of the measurements will be presented. Electrical power, refrigerant mass flow rate, in and outward fluid temperatures and wall temperatures were measured. From these data physical parameters of interest were computed as a function of tube length heat flux g (z), fluid temperature f h (z). vapour quality x(z) and heat transfer coefficient a(z). Table 3 presents uncertainties on some calculated parameters. 

Garimella and Bandhauer [32] conducted heat transfer experiments using the same test sections that were used for the pressure drop experiments of Garimella et al. [24, 25, 27, 28] described above. The high heat transfer coefficients and low mass flow rates in microchannels necessitate modifications to the test facility and test procedures described above. For the small zlx required in the test section, the heat duties at the mass fluxes of interest are relatively small. Calculating this heat duty from the test section inlet and outlet quality measurements would result in considerable... 

In many cases the shape of the body over which the fluid is flowing and with that the flow pattern are so involved that the functional relationship between the quantities can only be found experimentally. This requires the measurement of the heat and mass flows transferred at the body or a geometrically similar model and also the associated temperature and concentration differences. This then allows the calculation of the heat and mass transfer coefficients as... 

Flow-through relief valves have traditionally been analyzed by treating the valve as a convergent noz-2ie [i 29.30] discharge coefficient (kactual mass flow rate to the theoretical ideal mass flow rate through a one-dimensional convergent nozzle of exit area equal to the nominal bore of the tested valve. Measured discharge coefficients are derated by 10% (Aidr) to specify valve capacity. 

In typical applications, pure solid naphthalene is melted and poured into a mold so it will have the desired shape such as a flat plate [127], a circular cylinder [128], or a turbine blade [129]. For average mass transfer measurements on a test surface, the section coated with naphthalene can be weighed before and after exposure to air flow to determine the mass transfer rate. Local mass transfer coefficients can be determined from the sublimation depth, which is the difference in surface profiles, measured using a profilometer, before and after each test run. Once the vapor density of naphthalene is known, the local mass transfer coefficient hD can be evaluated from the following expression ... 

In order to calculate the recombination rate coefficient, it is necessary to know several flame region parameters. Flame temperature, average gas density, mass flow rate and various diffusion coefficients are among the quantities that have to be measured, calculated, or estimated. 

A rotameter is used to measure the flow rate of air at 25 °C and 1 bara. A 2 mm sapphire bead rises to a point in which the tube diameter is equal to 6 mm. Calculate the mass flow rate and the volumetric flow rate if the drag coefficient equals 0.1. M. Lessard... 

If the medium in the measuring space is allowed to flow, the measurement will be lowered since the coefficient of evaporation increases. However, care must be taken during measurement to maintain the mass flow of the flowing air at a constant value. 

The parameters measured include flow rate of the solids feed, mass flow rate of air, solids temperature at entry and exit, and the humidity of the drying air entering and leaving the dryer. The volumetric heat transfer coefficient can then be calculated from the definition... 

The complete description of a flame requires the specification of the pressure, the mass flow rate or burning velocity, the initial gas composition, and the appropriate transport coefficients and thermodynamic data. The remaining information is contained in a set of one-dimensional profiles of composition, temperature, and gas velocity as a function of distance (Fig. 2). Other independent variables than distance could have been used, e.g., temperature or time, but distance is common in experimental studies. Not all of these profiles are independent since there are a number of relations between the variables such as the equation of state, conservation of mass, etc. As an example, gas velocity can be obtained both by direct measurement and from temperature measurements using geometrical and continuity considerations. In the example given the indirect determinations of velocity are the more reliable and were used in the analysis. It is general practice to measure as many variables as convenient because the redundant profiles provide a check on the reliability of the measurements. 

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