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Mass balance lever rule

Since the derivation of the lever rule depends only on a mass balance, the rule is valid for calculating the relative amounts of the two phases present in any two-phase region of a two-component system. If the diagram is drawn in terms of mass fraction instead of mole fraction, the level rule is valid and yields the relative masses of the two phases rather than the relative mole numbers. [Pg.300]

The shorter arm on a balanced lever has the greater mass. The lever rule tells us that the shorter arm on a tie line has the greater number of moles. [Pg.172]

The lever rule states in order to balance the lever (i.e. create an equilibrium) then ml = m l where m is the mass of the object and / is the length from the pivot. [Pg.41]

To a first approximation, the composition of the distillate and bottoms of a single-feed continuous distillation column lies on the same residue curve. Therefore, for systems having separatrices and multiple regions, distillation composition profiles are also constrained to lie in specific regions. The precise boundaries of these distillation regions are a function of reflux ratio, but they are closely approximated by the RCM separatrices. If a separatrix exists in a system, a corresponding distillation boundary also exists. Also, mass balance constraints require that the distillate composition, the bottoms composition, and the net feed composition plotted on an RCM for any feasible distillation be collinear and spaced in relation to distillate and bottoms flows according to the well-known lever rule. [Pg.446]

More precisely, we can determine the relative molar amounts / liq, / vap of the two phases (and therefore the remaining composition variable xBx of the total system) by means of a simple lever rule that expresses the overall mass balance of the system. Intuitively, we can see from Fig. 7.9 that xBl must be intermediate between %Bap and xBq, as expressed... [Pg.241]

Equation (7.52) is equivalent to the simple rule for balancing a schoolyard seesaw if the fulcrum divides the board into lengths L1 L2, then the masses mi, m2 at the two ends should satisfy m Li = m2L2 (i.e., the heavier weight should be at the shorter end) to balance the seesaw. The proof of (7.52) is presented in Sidebar 7.9. The lever rule makes it easy to determine the relative amounts of each phase present from the tie-line ratio, and thus to determine the final unknown composition variable Xg1 from (7.51). [Pg.242]

The lever rule can be derived from the mass balance as well as from the balance of the amount of substance. On a straight line we can show a mixture X lying in between two pure components A and B and their respective mole fractions and the amount of substances ... [Pg.108]

The lever-arm rule is a graphical alternative to solving a mass balance. [Pg.60]

A special case of the lever-arm rule, which renders it applicable to extraction analysis, is an equilibrium-limited stage for a three-phase system (Figure 3.22). Everything stated for the lever-arm rule still applies here since the mass balances around the control volume (equilibrium stage) are still the same. The compositions of the three streams will still lie on a straight line, and stream ratios can still be calculated as before. [Pg.61]

The final mixture composition is on a straight line connecting the two feed compositions. This is another example of the lever rule, and is merely a result of the mass balances being linear equations. Note also that the composition of the final mixture is found at tworthirds of the distance from the first feed to the second feed in accordance with their relative amounts. This graphical linear relation between the two feeds and the final mixture is the opposite case to that of a single feed that splits into two equilibrium streams, which is the case in liquid-liquid extraction. ... [Pg.612]

The design is performed by equating the mass-balance relationship (lever rule. Equation 2.3.2-14) ... [Pg.100]

Flash calculations and the application of the lever rule (overall mass balance relating the feed, distillate and bottoms product streams) to predict feasible sharp splits for a given feed condition. [Pg.146]

Solutions of (6.14) and (6.15), the rectifying and stripping cascade flash trajectories, can be represented in mole fraction space (three dimensional for the IPOAc system). However, we represent the solutions in transformed composition space, which is two dimensional for IPOAc system (for a derivation and properties of these transformed variables [46]). This transformed composition space is a projection of a three dimension mole fraction space onto a two dimensional transformed composition subspace for the IPOAc system. Even though the correspondence between real compositions and transformed compositions is not one-to-one in the kinetic regime, we will make use of these transforms because of ease of visualization of the trajectories, and because overall mass balance for reactive systems (kinetically or equilibrium limited) can be represented with a lever rule in transformed compositions. We use this property to assess feasible splits for continuous RD. [Pg.157]

Note that calculating the flash trajectories at (f> = 0.5 does not provide the entire feasible product regions for continuous RD, but instead generates a subset of the feasible products. Selecting an iterate on the stripping cascade trajectory as a potential bottoms and an iterate on the rectifying cascade trajectory as a potential distillate does not guarantee that these products can also be obtained simultaneously from a RD column. This is simply because these product compositions may not simultaneously satisfy the overall mass balance for a reactive column. However, when the flash trajectories are used in conjunction with the lever rule for a continuous reactive column, the feasible splits for continuous RD can be quickly predicted. [Pg.160]

This result states that if two forces with magnitude Xl and Xv act on points L and V, respectively, their torques with respect to point E are equal. This property gives the name lever rule to eq. f2.iol. The lever analogy has be used as a mnemonic trick to memorize the equation. No memorization is required, however eq. r2.io ) can be derived easily when needed by applying a straightforward mass balance. [Pg.46]

Hence, the amount of solvent Eq determines the position of the mixing point in the concentration space. The point Mj represents the overall concentration of the two phases. It has to lie within the two-phase region (miscibility gap). Points R and define the concentrations of the raffinate and the extract, respectively. Their amounts are determined via mass balances or, graphically, via lever rule. [Pg.354]

The calculation method proceeds as follows. 1) Plot the locations of S and F on the triangular equilibrium diagram 2) Draw a straight line between S and F, and use the lever-arm rule or Eqs. tl3-31i to find the location of the mixed stream M. Now we know that stream M settles into two phases in equilibrium with each other. Therefore, 3) construct a tie line through point M to find the compositions of the extract and raffinate streams. 4) Find the ratio E/R using mass balances. We will follow this method to solve the following exanple. [Pg.537]

C. Plan. Plot streams F and S. Find mixing point M from the lever-arm rule or from Eqs. tl3-31). Then a tie line through M gives locations of streams E and R. Flow rates can be found from mass balances. [Pg.538]

Equations (4.20) and (4.21) are called the lever rule. The lever rule is easily verified by analyzing the system with a mass balance (see Exercise 3.23). Think of the tie line as a fulcrum. What mass is needed on the right side to balance the fulcrum shown in Figure 4.59 ... [Pg.172]

E) Calculate the flow rate of stream 8 and the flow rate of stream 7. You may use the lever rule and/or mass balances. Note that the flow rate of stream 4 may be changed by the addition of the second flash drum. [Pg.204]

Shown below is a phase diagram for mixtures of G and H. Graphical methods can be applied to diagrams of this type to calculate a mass balance. For example, one may apply the lever rule to a tie line spanning the two-phase region to calculate the relative sizes of the liquid and vapor phases. [Pg.231]

The mass balances that lead to Equations (E8.4D) and (E8.4E) are general and not limited to the vapor and liquid phases thus, the lever rule can be applied to find the relative amounts of any two phases in equilibrium. The fraction of material present in one phase can be computed by taking the length of the tie line from the overall composition to the composition of the other phase and then dividing by the total length of the line. [Pg.475]


See other pages where Mass balance lever rule is mentioned: [Pg.446]    [Pg.246]    [Pg.32]    [Pg.57]    [Pg.60]    [Pg.147]    [Pg.298]    [Pg.312]    [Pg.541]    [Pg.520]    [Pg.712]    [Pg.249]    [Pg.307]    [Pg.55]   
See also in sourсe #XX -- [ Pg.63 , Pg.66 ]




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