Equations, discharge rate models

Fundamental Equations. Discharge rate models are based on a mechanical energy balance. A typical form of this balance is... 

In PV applications, an empirical model for a LAB derived from Shepherd s treatment was adopted by Facinelli to indicate SOH [21]. The model includes the charge efficiency (a key issue in PV) and temperature effects on battery performance. Experiments were conducted on a single cell of a C D QP 75-5 battery, which has a nominal capacity of 161 Ah at a 10-h discharge rate. The equation relating m to / and r is a rearrangement of the four-parameter empirical formula of Shepherd [17] ... 

The reality of the situation is that the maximum discharge rate of gas occurs when the leak first occurs, with the discharge rate decreasing as a function of time as the pressure within the tank decreases. The complete dynamic solution to this problem is difficult, requiring a mass discharge model cross-coupled to a material balance on the contents of the tank. An equation of state (perhaps nonideal) is required to determine the tank pressure given the total mass. 

The screw rotation analysis leads to the model equation for the extruder discharge rate. There are now two screw-rotation-driven velocities, and and a pressure-driven velocity, Pp that affect the rate. and transport the polymer fluid at right angles to one another. In order to calculate the net flow from screw rotation It Is necessary to resolve the two screw-rotation-driven velocities into one velocity, Vpi, that can be used to calculate the screw rotation-driven flow down the screw parallel to the screw axis (or centerline) as discussed in Chapter 1 and as depicted in Fig. 7.14. The resolved velocity will then be integrated over the screw channel area normal to the axis of the screw. 

For two-phase flow through pipes, an overall dimensionless discharge coefficient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality choked flow. Leung [28] indicated that Equation 12-11 be multiplied by a factor of 0.9 to bring the value in line with the classic homogeneous equilibrium model (HEM). Equation 12-11 then becomes... 

The absence of measurable specific adsorption means that Cs/Co 1. Hence, factor (99), forming part of the kinetic equation, is a value roughly equal to, or less than, unity and, consequently, the varying activity coefficients and the if/i potential cannot explain, in terms of this model, the increase in the discharge rate by several orders of magnitude. 

Fumes and vapors discharged to the environment via a chimney form a plume, which is approximately cone shaped. Mathematical modeling of dispersal rates is possible. The Gaussian dispersion model is commonly used to calculate the concentration of pollutants at coordinate positions X, Y and Z. (The coordinates are measured from the plume centerline.) The equation used is ... 

The fluid model is a description of the RF discharge in terms of averaged quantities [268, 269]. Balance equations for particle, momentum, and/or energy density are solved consistently with the Poisson equation for the electric field. Fluxes described by drift and diffusion terms may replace the momentum balance. In most cases, for the electrons both the particle density and the energy are incorporated, whereas for the ions only the densities are calculated. If the balance equation for the averaged electron energy is incorporated, the electron transport coefficients and the ionization, attachment, and excitation rates can be handled as functions of the electron temperature instead of the local electric field. 

The Streeter-Phelps model allows the estimation of the DO sag in the stream as a function of distance. This equation may be developed by considering a stream, initially saturated with oxygen, which receives a wastewater discharge containing BOD. As the water moves downstream, the BOD is assumed to decay at a first-order rate, KBOD, typically on the order of 0.2/day ... 

U.W.M. and L.W.M. are the upper and lower water masses, or brine layers. Computation for a three-layer model assumes a hypothetical concentration of 100 grams/liter in the upper water mass at time t — 0. Three concentration-time curves computed for different values of the salt input by surface inflow Curve Cj for concentration and discharge as the present mean River Jordan, and curves for twice and four times the present rate of salt input. Equation... 

Usually, Nr -h 1 reactors will be required to absorb non-productive time (discharge, cleaning and filling of reactor). Solving the equation that represents enzyme inactivation under operation conditions (i.e. Eq. 5.76) and the equation that model conversion profiles within the biocatalyst bed in CPBR (Eq. 5.79), residual enzyme activity in each bioreactor after each time interval can be determined and feed flow-rate to each bioreactor during each interval calculated as ... 

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