Airflow equation

The airflow equations presented above are based on the assumption that the soil is a spatially homogeneous porous medium with constant intrinsic permeability. However, in most sites, the vadose zone is heterogeneous. For this reason, design calculations are rarely based on previous hydraulic conductivity measurements. One of the objectives of preliminary field testing is to collect data for the reliable estimation of permeability in the contaminated zone. The field tests include measurements of air flow rates at the extraction well, which are combined with the vacuum monitoring data at several distances to obtain a more accurate estimation of air permeability at the particular site. 

For heat transfer directly to solids, predictive equations give directly the volume V or the heat-transfer area A, as determined by heat balance and airflow rate. For devices with gas flow normal to a fluidized-solids bed,... 

This is the state equation of an ideal gas, where p is pressure, v is specific volume, p is density, R is the gas constant, and T is absolute temperature. In an airflow there is a transfer of heat from one layer to another. This change of... 

It is important to emphasize that, especially in process measurements, radiation can have an essential influence on the wet bulb temperature, and therefore generally the wet bulb temperature is dependent on the mea,surement device and the method of measurement. If the airflow is very low, the radiation can have a remarkable contribution in addition to the convective heat transfer. Basically, an equation analogous to Eq. (4.138) can be empirically determined for each wet bulb temperature and method of measurement. 

Theories of hood performance with nonbuoyant pollution sources are based on the equation of turbulent diffusion. The following equation allows the engineer to determine the contaminant concentration decay in the uniform airflow upstream from the contaminant source ... 

Equations for airflow rate computation in compact, linear, and radial jets are presented in Table 7.13. 

Similar studies were conducted by Troyanovsky, who concluded that to maintain the airflow pattern in rooms with heated or cooled air supply as in isothermal conditions, it is necessary that the rise of horizontally supplied jet does not exceed Ay = 0.1 BH at the distance from the outlet X = 0.15K BH) -. From this assumption the following equation for the maximum air temperature difference was derived ... 

Thermal plumes above point (Fig. 7.60) and line (Fig. 7.61) sources have been studied for many years. Among the earliest publications are those from Zeldovich and Schmidt. Analytical equations to calculate velocities, temperatures, and airflow rates in thermal plumes over point and line heat sources with given heat loads were derived based on the momentum and energy conservation equations, assuming Gaussian velocity and excessive temperature distribution in... 

For a nonenclosing hood with a nonbuoyant contaminant source, the characteristic airflow can be calculated using the following equation ... 

Comparison of the relative velocity change in the airflow created by a hood with a finite face area and by a point source is graphically illustrated in Fig. 7.85. At a distance greater than X/R = 1, the velocities induced by a realistic hood and by a point source are practically equal. This means that in some cases airflow in front of realistic hoods can be described using the simplified point source equations. 

The airflow rate infiltrating and exfiltrating through each air leakage pass, Q , due to the combined effect of wind, stack, and mechanical ventilation system perfotmance can be calculated ftom the mass balance equation... 

The mass balance equation for the airflow through the gate can be described as... 

Airflow through an opening used for natural building ventilation is approximately turbulent. In this case the flow rate, Q (m /s), can be calculated from an equation similar to Eq. (7.237) ... 

By assuming a steady state and since the sum of the supply and return flow rates is equal to the total flow rate through the room, it is possible to manipulate this equation to get the following, where is the supply airflow... 

To design an air recirculation system it is necessary to know the performances of fans, air cleaners, and exhaust hoods included in the current system. The equations described here include the source generation rate and the total airflow rate through the room, which could be difficult to measure. The ratio between source rate and flow rate has the unit of concentration and should in fact be equal to the concentration without recirculation. The equations could thus be transformed to include the contaminant concentration without recirculation instead of this ratio. In this way a direct comparison between concentration without and with recirculation is possible. By using the described equations it is then possible to design an air recirculation system to result in the demanded concentration in a workroom. 

The aim of this section is to provide a basic introduction to the methods by which air may enter a space and be distributed and to consider tlie governing equation for the determination of the air quantity and temperature. The governing equation relating to airflow patterns in a space is not covered in this section, as it is discussed elsewhere in the guides. 

Equation (9.102) gives = C2a- The axial component does not change, but when C2 > then C2 > Cj. Thus, the axial fan increases the absolute velocity of airflow. 

The solution to the above equations will result in a value for the airflow set in motion by the heated source. The actual airflow through the hood, must be larger than to ensure complete contaminant capture. Heinsohn recommends that... 

Outside the jet and away from the boundaries of the workbench the flow will behave as if it is inviscid and hence potential flow is appropriate. Further, in the central region of the workbench we expect the airflow to be approximately two-dimensional, which has been confirmed by the above experimental investigations. In practice it is expected that the worker will be releasing contaminant in this region and hence the assumption of two-dimensional flow" appears to be sound. Under these assumptions the nondimensional stream function F satisfies Laplace s equation, i.e.. 

Equation (10.133) is more useful than Eq. (10.134), where the escaped airflow is difficult to measure. 

Considered are mass conservation of air and species (contaminants and humidity). Momentum equations are not considered on a global scale but have been used in some cases for the definition of the airflow-pressure relation of the individual links. Heat fluxes and thus energy conservation equations are not considered. 

The highest level of integration would be to establish one large set of equations and to apply one solution process to both thermal and airflow-related variables. Nevertheless, a very sparse matrix must be solved, and one cannot use the reliable and well-proven solvers of the present codes anymore. Therefore, a separate solution process for thermal and airflow parameters respectively remains the most promising approach. This seems to be appropriate also for the coupling of computational fluid dynamics (CFD) with a thermal model. ... 

The integration of the ventilation model into the thermal building model can be realized on different levels, from simple stack-flow equations to a full integration of a multizone airflow and contaminant transport model. 

The movement of air in the subsurface during the application of SVE is caused by the pressure gradient that is applied in the extraction wells. The lower pressure inside the well, generated by a vacuum blower or pump, causes the soil air to move toward the well. Three basic equations are required to describe this airflow the mass balance of soil air, the flow equation due to the pressure gradient, and the Ideal Gas Law. 

Equation 14.11 introduces the notion of radius of influence, which is one of the important design parameters of S VE systems. Theoretically, the maximum radius of influence of a well is the distance at which the pressure becomes equal to the ambient atmospheric pressure, i.e., P = Patm. In practice, Pj is determined as the distance at which a sufficient level of vacuum still exists to induce airflow, e.g., 1% of the vacuum in the extraction well.912 The extraction wells are usually constructed using pipes with a standard radius, e.g., Pw = 5.1 cm (2 in.) or 10.2 cm (4 in.), and the vacuum applied in the wells typically ranges from 0.05 to 0.15 atm, i.e., Pw = 0.95-0.85 atm.9 12 If the vacuum required in the radius of influence is 1% of the vacuum in the extraction well, the... 

For nebulizers and MDIs, the external resistance (Re) is quite low. Different approaches have been made to describe the external airflow resistance of DPIs. Olsson and Asking [99] derived an empirical relationship between flow rate () and pressure drop (AR), AR = for a number of inhalers (such as Rotahaler , Spinhaler and Turbuhaler ) in which they define the proportionality coefficient (C) as the airflow resistance. This relationship differs only slightly from the general (theoretical) equation for orifice types of flow constrictions ... 

Choose locations, considering the airflow, criticality, and configuration distributions (determine on the area drawing). The number of sampling point locations shall be less than Aj derived from the following equation ... 

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