# Design equation

For a given duty and overall heat transfer coefficient, the 1-1 design offers the lowest requirement for surface area. Many flow arrangements other than the 1-1 design exist, the most common of which is the 1-2 design (1 shell pass, 2 tube passes), as illustrated in Fig. 7.76. Because the flow arrangement involves part countercurrent and part cocurrent flow, the effective temperature difference for heat exchange is reduced compared with a pure counter-current device. This is accounted for in design by introduction of the Ft factor into the basic heat exchanger design equation [c.222]

Pressure Swing. Design equations have been developed to predict temperature rise, minimum bed length to retain the heat front, minimum purge rate, and effluent composition (135). A nonequihbrium, nonisothermal simulation program with a Freundhch isotherm equation was found to agree with data for drying with sihca gel (136). A somewhat simpler isothermal model using an isotherm approximated by two straight lines successhiUy calculated the volumetric purge-to-feed ratio needed to achieve varying product dryness using sUica gel (137). An adiabatic equihbrium model with a Langmuir isotherm was used to study the blowdown step of a cycle removing CO2 on activated carbon and 5A zeohte (138). Changing to an isothermal assumption introduced significant errors into the results. The countercurrent pressurization step was investigated with an isothermal equihbrium model using a Langmuir isotherm for O2 production from air with 5A zeohte (139). The model predicted the dependence of O2 concentration on countercurrent pressure and was used to study other parameters. An isothermal model with linear isotherms and component-specific pore diffusivity was used and compared to data for the kinetic-limited separation of air by RS-10 zeohte (140). The simulations agreed well with the experimental parametric studies of time and pressure of feed, blowdown, purge, and pressurization. An equihbrium model was formulated to simulate RPSA using a Freundhch isotherm for separation of N2 and CH (141). Pressure responses, flow rates, and compositions compared favorably as a function of feed pressure, cycle frequency, and product rate. A nonequihbrium, nonisothermal model for RPSA was developed using a linear isotherm and Darcy s law for pressure drop (142). The model predicted performance in agreement with previous data (57) for air separation on 5A zeohte. [c.287]

Cyclone Efficiency. Most cyclone manufacturers provide grade-efficiency curves to predict overall collection efficiency of a dust stream in a particular cyclone. Many investigators have attempted to develop a generalized grade-efficiency curve for cyclones, eg, see (159). One problem is that a cyclone s efficiency is affected by its geometric design. Equation 15 was proposed to calculate the smallest particle size collectable in a cyclone with 100% efficiency (157). [c.395]

For the air—water system, the Lewis relation shows that r = 1. Under these conditions, the two parenthetical terms on the right-hand side of equation 33 ate enthalpies, and equation 33 becomes the design equation for humidification operations [c.100]

The simplification of equation 33 to equation 34 is possible only if r = 1 that is, foi simple monoatomic and diatomic gases. Foi other systems the design equation can be obtained by a direct rearrangement of equation 33. [c.100]

Fig. 6. Integration of the design equation (eq. 35). |

This equation shows that for 5 percent maldistribution, the pressure drop across the holes shoiild be about 10 times the pressure drop over the length of the pipe. For discharge manifolds with K = 0.5 in Eq. (6-147), and with 4/E/3D 1, the pressure drop across the holes should be 10 times the inlet velocity head, pV V2 for 5 percent maldistribution. This leads to a simple design equation. [c.658]

Overall Heat-Transfer Coeffieient The basic design equation for a heat exchanger is [c.1034]

Thermal Design If the controUing resistance for heat and mass transfer in the vapor is sensible-heat removal from the cooling vapor, the following design equation is obtained [c.1042]

Thermal design concerns itself with sizing the equipment to effect the heat transfer necessaiy to cany on the process. The design equation is the familiar one basic to all modes of heat transfer, namely, [c.1054]

By rearrangement, this can be made into a design equation as follows [c.1060]

Numerical values for for use in the general design equation may be calculated from experimental data by [c.1060]

Approximate design equations apphcable only to the case of pure physical desorption are developed later in this sec tion for both packed and plate stripping towers. A more rigorous approach using distiUation concepts may oe found in Sec. 13. A brief discussion of desorption with chemical reac tion is given in the subsec tion Absorption with Chemical Reaction. [c.1352]

The number of transfer units can be calculated from the adiabatic design equation, Eq. (14-46) [c.1361]

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as [c.1368]

When one of these three conditions is apphcable, the appropriate design equation can be obtained by substitution into Eq. (14-71), followed by integration of the resulting relationship. [c.1368]

This, then, is our final design equation. It shows how the survival probability depends on both the stress (rand the volume V of the component. In using it, the first step is to fix on an acceptable failure probability, Pp 0.3 for chalk, 10 for the cutting tool, 10 for the vacuum-chamber window. The survival probability is then given by P = 1 -. [c.189]

All power supply engineers follow a general pattern of steps in the design of power supplies. If the pattern is followed, each step actually sets the foundation for subsequent design steps and will guide the designer through a path of least resistance to the desired result. This text presents an approach that consists of two facets first it breaks the power supply into distinct blocks that can be designed in a modular fashion secondly, it prescribes the order in which the blocks are to be designed in order to ease their pasting together. The reader is further helped by the inclusion of typical industry design approaches for each block of various applications used by power supply designers in the field. Each block includes the associated design equations from which the component values can be quickly calculated. The result is a coherent, logical design flow in which the unknowns are minimized. The approach is organized such that the typical inexperienced designer can produce a professional grade power supply schematic in under 8 working hours, which is about 40 percent of the entire design process. The physical design, such as breadboarding techniques, low-noise printed circuit board (PCB) layouts, transformer winding techniques, etc., are shown through example. The physical factors always present a problem, not only to the inexperienced designer, but to the experienced designer as well. It is hoped that these practical examples will keep the problems to a minimum. All power supplies, regardless of whether they are linear or switching, follow a general design flow. The linear power supplies, though, because of the maturity of the technology and the level of integration offered by the semiconductor manufacturers, will be presented mainly via examples. The design flow of the switching power supplies, which are much more complicated, will be covered in more detail in the respective chapters dealing with the selected power supply technology. The generalized approach is as follows. [c.8]

There are several generalized switching power supply design software packages available primarily from circuit simulator companies. Caution should be practiced in reviewing all software-based switching power supply design tools. Designers should compare the results from the software to those obtained manually by executing the appropriate design equations. Such a comparison will enable designers to determine whether the programmer and his or her company really understands the issues surrounding switching power supply design. Remember, most of the digital world thinks that designing switching power supplies is just a matter of copying schematics. [c.9]

D. Caleulate the eomponent values and ratings from the design equations using your partieular set of operating eonditions. [c.269]

Application of the Design Equations to Packed Liquid Chromatography Columns and Open Tubular Gas Chromatography Columns [c.395]

At the end of this chapter you will find three annexes. The first of these is a list of nomenclature used in the chapter. There are quite a few design equations that are summarized in the foregoing sections and, hence, you will need to refer to this [c.157]

Modeling of Chemioal Kinetios and Reaotor Design Equation 3-42 is resolved into partial fraetions as [c.122]

For the ideal reactors considered, the design equations are based on the mass conservation equations. With this in mind, a suitable component is chosen (i.e., reactant or product). Consider an element of volume, 6V, and the changes occurring between time t and t + 6t (Figure 5-2) [c.263]

The design problem is next formulated as a mathematical problem with design equations and design variables. The design equations are the modeling equations of the units and their specification constraints. Design variables are of two types. The first t3qje of design variables describe the operation of each unit (flow rate, composition, temperature, and pressure), its size (volume, heat transfer area, etc.), as well as the costs or profits associated with the units. Since [c.9]

Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). [c.489]

In every process plant, heat exchangers are used for process—process-stream heat transfer, and heaters or coolers are used for process-utiUty heat transfer. More sophisticated process design led to more focus on optimizing heat exchanger size as part of the process energy flow. Initial optimizations usually involved only a process—process heat exchanger and a cooler. Economic credit was taken for reduction in operating costs but it was expected that capital equipment cost could only increase. Later it was realized that greater saving could be achieved if whole networks of exchangers could be optimized. Graphical techniques were subsequently developed to visualize the flow of energy through the process. However, most attempts involved the mathematical optimization of equation sets centered on assumed cost functions plus appropriate energy balance and exchanger design equations. Early in the 1970s, a firm thermodynamic foundation was laid for the minimum required energy flow in a process plant. At the same time it was demonstrated that costs for operating and capital savings might both be expected if the pairing and sequencing of process streams for heat exchange was carefully considered. [c.517]

M. V. Arastoopour, M. V. Modi, D. V. Punwani, and A. T. Talwalker,M Keview of Design Equations for Dilute Phase Gas-Solids Hori ntal Conveying Systems for Coal and Belated Material, Powder and Bulk SoHds Conference, Philadelphia, 1979. [c.164]

Liquid metals constitute a class of heat-transfer media having Prandtl numbers generally below 0.01. Heat-transfer coefficients for hquid metals cannot be predicted by the usual design equations applicable to gases, water, and more viscous fluids with Prandtl numbers greater than 0.6. Relationships for predicting heat-transfer coefficients for liquid metals have been derived from solution of Eqs. (5-38 ) and (5-2>8b). By the momentum-transfer-heat-transfer analogy, the eddy conductivity of heat is /cNpt(E / l) = k for small Np,. Thus in the solution of Eqs. (5-38 ) and (5-2>Sb) the knowledge of the thickness of various layers of flow is not critical. In fact, assumption of slug flow and constant conductivity (=/c) across the duct gives reasonable values of heat-transfer coefficients for liquid metals. [c.565]

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows [c.603]

The function of the decouplers is to compensate for the undesirable process interactions represented by Gpi9 and Gp9i. Suppose that the process transfer functions are all known. Then the ide design equations are [c.737]

These decoupler design equations are very similar to the ones for feedforward control in an earlier section. In fact, decoupling can be interpreted as a type of feedforward control where the input signal is the output of a feedback controller rather than a measured load variable. [c.737]

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. [c.737]

For example, the packed-tower design equation for a dilute system in which gas-phase reaciant A is being absorbed and reacted with liquid-phase reagent B is [c.1366]

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. [c.1633]

The term P is not constant for some important separations. Even worse, it can exhibit maxima that make analytic treatment difficult. Operating diagrams are often used for prehminaiy design rather than equations. Because of the veiy complex behavior in the membrane as concentrations change, all design begins with an experiment. For water removal applications, design equations often mispredict the rate constants as the water content of the feed approaches zero. The estimates tend to be lower than the experimental values, which would lead to overdesign. Therefore it is necessary to obtain experimental data over the entire range of water concentrations encountered in the separation. Once the Idnetic data are available, heat transfer and heat capacity are the problem. It is general prac tice to pilot the separation on a prototype module to measure the changes due to thermal effects. This is particularly true for water as the permeant, given its high latent heat. [c.2055]

Although identical results are not obtained for other reactor configurations, the design equations yield similar patterns. The dominant parameters in determining system performance are again the BSRT and the pseudo constants. The latter are not under the control of the design engineer as they are functions of the waste and the microorganisms that developed in the system. The BSRT is the major design parameter under the control of the design engineer. This parameter has been defined as the ratio of the biomass in the reactor to the biomass produced from the waste each day. At steady state, the level of biomass in the system is constant thus, the biomass produced must equal the biomass wasted. The minimum BSRT that can be utilized is that which will produce the degree of treatment required. Generally, [c.2217]

This book is organized so that the massive proeess of designing a eustom switehing power supply is broken down into smaller, more understandable pieees. Eaeh pieee is then explained in non-power engineer terms, and eom-monly aeeepted design approaehes are illustrated with the relevant design equations. The intent is for the reader to read the seetion, ehoose the best design approaeh to meet his or her needs, use his or her partieular system parameters, and produee a subeireuit that ean be inserted into a larger power supply design. The design order is the way that seasoned power engineers use to approaeh their designs, and has proven to provide answers before the questions have arisen. [c.21]

Onee the topology is seleeted, the design path is determined and the design may proeeed. By proeeeding through the bloek diagram in Figure 3-7, in the order indieated by the design flow in Figure 3-6, the design will progress relatively quiekly. The first-time designer may be able to produee a very good paper design (or sehematie) within 8 working hours, if he or she has a good library of data books. Eaeh funetional bloek in Figure 3-7 will have a ehoiee of typieal design approaehes for that bloek. The designer determines from his or her requirements whieh approaeh is most appropriate for the needs of the supply. Then, by exeeuting the design equations and using the parameters supplied by the design speeifieation, the bloek ean be designed within a matter of minutes. [c.26]

The greatly expanded 8th Edition of the Standards of the Tubular Exchanger Manufacturers Association retains the useful data and features, found in the Seventh Edition, plus many clarifications and innovations. All sections have been reviewed to incorporate new data, which were not available at the time of the 1988 printing, including suggestions, which resulted from the extensive use of the Standards by both manufacturers and users of shell and tube heat exchangers. Many helpful recommendations were also received through the cooperation of the American Petroleum Institute (API) and the American Society of Mechanical Engineers (ASME). Some noteworthy features of the Eighth Edition include (a) Metrification has been included where feasible and appropriate (b) Methods for calculating several types of floating head backing rings have been added (c) A method for incorporating pass partition rib area into flange design has been incorporated (d) The vibration section has been expanded and vibration amplitude for vortex shedding and acoustic resonance have been added (e) Nozzle flange pressure/temperature rating tables from ASME Standard B16.5-1996 w/ 1998 addenda are included (f) New materials have been included in coefficient of thermal expansion, modulus of elasticity, and thermal conductivity tables (g) Design equations for double tubesheets have been added (h) A method for calculating the mean metal temperature for tubesheets has been added (i) Stress multipliers have been added to account for the stiffness of [c.26]

The type of optimum reaetor that will proeess 200 m /hr is a eon-tinuous flow stirred tank reaetor (CFSTR). This eonfiguration operates at the maximum reaetion rate. The volume V[ of the reaetor ean be determined from the design equation [c.201]

Related ealeulation proeedures ean be made with different stoiehio-metry, whieh strongly influenees tlie final form of the design expression. Also, different rate expressions often result in different relationships between time and eonversion. In eomplex reaetions, analytieal integration of die design equation may be eumbersome and tedious, and perhaps impossible to solve. In sueh eases, die designer should resort to numerieal integradon mediods sueh as die Euler Simpson s mediod or graphieal evaluation of jg f(X)dX by plotting f(X) versus X and determining die area beneadi die eurve. [c.275]

See pages that mention the term

**Design equation**:

**[c.11] [c.2213] [c.526] [c.657] [c.1429] [c.1570]**

Modeling of chemical kinetics and reactor design (2001) -- [ c.0 ]