Energy balance mechanisms

Economic lot size, 350 Effective interest, 218-222, 224, 241 Efficiency, packing, 702-706 plate, 661-667 pump, 517-518, 520 Ejectors, cost of, 528 Electrical installation, cost of, 174, 807 Electricity, cost of, 815 Electromotive series of metals, 433 Emissivity of surfaces, 582-585 Energy balance, mechanical, 479-480 for reactor design, 715-716 total, 479-480... 

The impact response of composite panels can also be understood from the point of view of energy balance mechanisms. As discovered in previous experimental and theoretieal analyses [72-74,77], the impact energy dissipation can be generally divided into three major components ... 

Microscopic Balance Equations Partial differential balance equations express the conservation principles at a point in space. Equations for mass, momentum, totaf energy, and mechanical energy may be found in Whitaker (ibid.). Bird, Stewart, and Lightfoot (Transport Phenomena, Wiley, New York, 1960), and Slattery (Momentum, Heat and Mass Transfer in Continua, 2d ed., Krieger, Huntington, N.Y., 1981), for example. These references also present the equations in other useful coordinate systems besides the cartesian system. The coordinate systems are fixed in inertial reference frames. The two most used equations, for mass and momentum, are presented here. 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can he solved using the mechanical energy balance. In a well-made venturi, viscous losses are neghgihle, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

Mechanical Energy Balance The mechanical energy balance, Eq. (6-16), for fully developed incompressible flow in a straight circular pipe of constant diameter D reduces to... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

In the present section, attention will focus on the size of fragments created in a violent fragmentation event. The objective will be to explore some theoretical ideas which appear important to the dynamic fragmentation process. The two underlying phenomena that have dominated theoretical efforts in this area of dynamic fracture mechanics are the presence of an inherent flaw structure, and energy balance in the fracture process. 

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

This paper presents the physical mechanism and the structure of a comprehensive dynamic Emulsion Polymerization Model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles, the monomer conversions, the copolymer composition, and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations. 

EPM has been developed to simulate as a function of time all the phases, species, and the detailed )tinetic mechanism of the previous section. The structure of EPM consists of material balances, the particle number concentration balance, an energy balance, and the calculation of important secondary variables. 

If specific heat capacities can be assumed constant and the mechanical energy input by the stirrer, Wagit, is significant, the energy balance equation simplifies... 

Electrical, and the mechanical forms of energy, are included in the work term in an energy balance. Electrical energy will only be significant in energy balances on electrochemical processes. 

If one wants to model a process unit that has significant flow variation, and possibly some concentration distributions as well, one can consider using computational fluid dynamics (CFD) to do so. These calculations are very time-consuming, though, so that they are often left until the mechanical design of the unit. The exception would occur when the flow variation and concentration distribution had a significant effect on the output of the unit so that mass and energy balances couldn t be made without it. 

The preceding calculation of the thermal energy balance of a planet neglected any absorption of radiation by molecules within the atmosphere. Radiation trapping in the infrared by molecules such as CO2 and H20 provides an additional mechanism for raising the surface temperature - the greenhouse effect. The local temperature of a planet can then be enhanced over its black body temperature by the atmosphere. 

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