Balance problems

An important use of the triangular equiHbrium diagram is the graphical solution of material balance problems, such as the calculation of the relative amounts of equiHbrium phases obtained from a given overall mixture composition. As an example, consider a mixture where the overall composition is represented by point M on Figure 2a. If the A-rich phase is denoted by point R (raffinate) and the B-rich phase is denoted by point E (extract), it can be shown that points R, M, and E are coUinear, and also... 

The arrangement in Figure 5-14, generally called back to back," is normally considered useful in solving difficult thrust balance problems where the conventional thrust bearing and balance drum size are inade... 

See Figure 12-8. Pistons may be of aluminum, built-up carbon or graphite, cast iron, cast steel, fabricated and metaUzed steel, stainless steel, or forged carbon or stainless steel. The selection involves the corrosive nature of the gas plus the weight-balancing problem of the compressor manufacturer. 

This section provides information needed to understand and solve the majority of balancing problems using a vibration/balance analyzer, a portable device that detects the level of imbalance, misalignment, etc., in a rotating part based on the measurement of vibration signals. 

The amplitude of each point of imbalance must be known to resolve dynamic balance problems. Most dynamic balancing machines or in situ balancing instruments are able to isolate and define the specific amount of imbalance at each point on the rotor. 

No hard and fast rules can be given on the selection of suitable boundaries for all types of material balance problems. Selection of the best sub-division for any particular process is a matter of judgement, and depends on insight into the structure of the problem, which can only be gained by practice. The following general rules will serve as a guide ... 

Simple material-balance problems involving only a few streams and with a few unknowns can usually be solved by simple direct methods. The relationship between the unknown quantities and the information given can usually be clearly seen. For more complex problems, and for problems with several processing steps, a more formal algebraic approach can be used. The procedure is involved, and often tedious if the calculations have to be done manually, but should result in a solution to even the most intractable problems, providing sufficient information is known. 

Material-balance problems are particular examples of the general design problem discussed in Chapter 1. The unknowns are compositions or flows, and the relating equations arise from the conservation law and the stoichiometry of the reactions. For any problem to have a unique solution it must be possible to write the same number of independent equations as there are unknowns. 

Consider the general material balance problem where there are Ns streams each containing Nc independent components. Then the number of variables, N, is given by ... 

The solution of more complex material balance problems involving several recycle loops is discussed in Chapter 4. 

The radiation balance problem is not specific to our solar system and can be applied to all stellar planetary systems, although the number of planets outside our solar system - so-called extrasolar planets - is unknown. As noted earlier, the highest... 

A simpler and general discrete time scheduling formulation can also be derived by means of the Resource Task Network concept proposed by Pantelides [10], The major advantage of the RTN formulation over the STN counterpart arises in some problems involving many identical pieces of equipment. In these cases, the RTN formulation introduces a single binary variable instead of the multiple variables used by the STN model. The RTN-based model also covers all the features at the column on discrete time in Table 8.1. In order to deal with different types of resources in a uniform way, this approach requires only three different classes of constraints in terms ofthree types of variables defining the task allocation, the batch size, and the resource availability. Briefly, this model reduces the batch scheduling problem to a simple resource balance problem carried out in each predefined time period. 

Master-alloy production, 23 318-319 Masterbatching, 11 307-308 Master contracts, 24 373-374 Master curves, 21 746-747 uses for, 21 747 Master flowmeters, 11 653 Master Oscillator Power Amplifier (MOPA) configuration, 14 697 Masticatory substance, 12 32 Mastic, for protecting art, 11 410, 411 MAT a cells, 26 453 Matched die molding, 20 117 Material balance problems, 10 748 Material balances, in minerals processing, 16 606... 

Stockman, L. Yield and Quality — a Balance Problem. Svensk Papper-tid. 68, 572—577 (1955). 

Answer Immediately arrange for an evaluation of the CSF. If the CSF reveals leukemic cells, you can consider administering methotrexate 12 mg in-trathecally every day for 4 days. With such a regimen, subsequent evaluations of the CSF often indicate no leukemic cells present. The headaches and balance problems typically disappear. Six months later, most patients show no evidence of leukemia. 

Accdg to Cook (Ref 32b, p 172), the initiation of deton is fundamentally a heat-balance problem which may be expressed by the following simplified equation ... 

Because the single-scattering albedo depends sensitively on the imaginary part of the refractive index there has been keen interest in determining optical constants of atmospheric particles. These are used to calculate the important parameters in the heat balance problem for present and predicted aerosol... 

Cerebrum and cerebellum Motor nerve tracts Sensory nerve tract Balance problems, speech problems, coordination, tremors Muscle weakness, spasticity paralysis, vision problems, bladder, bowel problems Altered sensation, numbness, prickling, burning sensation... 

Kinetic data, whether they are obtained classically from isothermal decompn studies or by DSC, can be used to calculate the critical temp at which any size of an expl can self-heat to expln. The heat-balance problem has been examined by Frank-Kamenetskii (Ref 1) and by Zinn and Mader (Ref 4). The resulting relationship between kinetic and geometric factors is as follows. ... 

V. CAUSES OF AND APPROACHES TO SOLVING MASS BALANCE PROBLEMS... 

V. Causes of and Approaches to Solving Mass Balance Problems. 186... 

Sample balancing problem. Let us consider the multi-cavity injection molding process shown in Fig. 6.54. To achieve equal part quality, the filling time for all cavities must be balanced. For the case in question, we need to balance the cavities by solving for the runner radius R2. For a balanced runner system, the flow rates into all cavities must match. For a given flow rate Q, length L, and radius R, solve for the pressures at the runner system junctures. Assume an isothermal flow of a non-Newtonian shear thinning polymer. Compute the radius R2 for a part molded of polystyrene with a consistency index (m) of 2.8 x 104 Pa-s" and a power law index (n) of 0.28. Use values of L = 10 cm, R = 3 mm, and Q = 20 cm3/s. 

Thumping or racing heart Walking or balance problems ... 

Figure 1 Distillation process mass balance problem...

These two examples have illustrated some of the key steps in solving mass balance problems. In particular, the number of mass balance equations that are available for ensuring you have zero degrees of freedom and the use of the system box to limit yourself to the streams that are of interest. These steps are also key points for the analysis of energy balances in processes, the topic of Section 1.3 in this chapter. 

Kneile, R. G., "Solution of Material Balance Problems for Process Design", Ph.D. Thesis in Chemical Engineering (December 1975). 

The mass-balance problem can be solved graphically. The median connecting the vertex C with the AB edge corresponds to the transformation of an equimolar AB mixture into C. Extending this line with an equal segment gives the position of the pole n of coordinates (0,1) and (1,0). From this point, stoichiometric lines can be drawn for any initial composition of the reaction mixtures. When the reaction preserves the number of moles (v, = 0) the stoichiometric lines are parallel. 

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