Mccabe thiele method

A saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line).[2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed. Example q-line slopes are presented in Figure 2. The number of steps between the operating lines and the equilibrium line represents the number of theoretical plates (or equilibrium stages) required for the distillation. For the binary distillation depicted in Figure 1, the required number of theoretical plates is 6.Constructing a McCabe–Thiele diagram is not always straightforward. In continuous distillation with a varying reflux ratio, the mole fraction of the lighter component in the top part of the distillation column will decrease as the reflux ratio decreases. Each new reflux ratio will alter the gradient of the rectifying section curve.When the assumption of constant molar overflow is not valid, the operating lines will not be straight. Using mass and enthalpy balances in addition to vapor-liquid equilibrium data and enthalpy-concentration data, operating lines can be constructed using the Ponchon–Savarit method.[5]If the mixture can form an azeotrope, its vapor-liquid equilibrium line will cross the x = y line, preventing further separation no matter the number of theoretical plates.

A McCabe–Thiele diagram for the distillation of a binary (two-component) feed is constructed using the vapor-liquid equilibrium (VLE) data—which is how vapor is concentrated when in contact with its liquid form—for the component with the lower boiling point.Figure 1: Typical McCabe–Thiele diagram for distillation of a binary feedOn a planar graph, both axes represent the mole fractions of the lighter (lower boiling) component; the horizontal (x) and vertical (y) axes represents the liquid and vapor phase compositions, respectively. The x = y line (see Figure 1) represents the scenarios where the compositions of liquid and vapor are the same. The vapor-liquid equilibrium line (the curved line from (0,0) to (1,1) in Figure 1) represents the vapor phase composition for a given liquid phase composition at equilibrium. Vertical lines drawn from the horizontal axis up to the x = y line indicate the composition of the inlet feed stream, the composition of the top (distillate) product stream, and the composition of the bottoms product (shown in red in Figure 1).The rectifying section operating line for the section above the inlet feed stream of the distillation column (shown in green in Figure 1) starts at the intersection of the distillate composition line and the x = y line and continues at a downward slope of L / (D + L), where L is the molar flow rate of reflux and D is the molar flow rate of the distillate product, until it intersects the q-line. The stripping section operating line for the section below the feed inlet (shown in magenta in Figure 1) starts at the intersection of the red bottoms composition line and the x = y line and continues up to the point where the blue q-line intersects the green rectifying section operating line.Figure 2: Examples of q-line slopesThe q-line (depicted in blue in Figure 1) intersects the point of intersection of the feed composition line and the x = y line and has a slope of q / (q - 1), where the parameter q denotes mole fraction of liquid in the feed. For example, if the feed is

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About Quartile Calculator The Quartile Calculator is used to calculate the first quartile, second quartile and third quartile of a set of numbers (Step by Step).QuartileIn descriptive statistics, a quartile, a type of quantile, is one of three points that divide a data set into four equal groups, each representing a fourth of the distributed sampled population. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The first quartile, also called the lower quartile, is equal to the data at the 25th percentile of the data. The second (middle) quartile is another name for the median of a data set. The third quartile, also called the upper quartile, is equal to the data at the 75th percentile of the data.Calculating QuartilesThere are several different methods for calculating quartiles.[1] This calculator uses a method described by Moore and McCabe to find quartile values. The same method is also used by the TI-83 to calculate quartile values. With this method, the first quartile is the median of the numbers below the median, and the third quartile is the median of the numbers above the median. How to use Quartile Calculator? References You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

1. IntroductionIn this tutorial, we’ll explain how to calculate the cyclomatic complexity of a software module.According to the rational asset analyzer software documentation, cyclomatic complexity is a measurement of the stability and confidence of a software module. The higher the cyclomatic complexity of a software module, the more defects it has. Therefore, it is recommended that a complex software module is split into smaller modules.2. Problem DescriptionLet be a software module. The cyclomatic complexity of is the number of linearly independent paths through .For example, let’s say we have the following module (in pseudocode):algorithm CheckTheInteger(x): // INPUT // x = an integer // OUTPUT // No output if x There are two linearly independent paths.The higher the cyclomatic complexity of a software module, the more complex it is. A use case for this is in software development. Software developers are always designing modules, and it’s important for them to know whether the module is complex.Cyclomatic complexity was developed by Thomas J. McCabe in 1976.A control flow graph (CFG) is an abstract representation of a software module. Each node (in the CFG) represents a single block of code, with statements without any jumps. Each directed edge (in the CFG) represents a jump between nodes. A linearly independent path of a software module is a path from the entry to the exit node of the module’s CFG:The number of linearly independent paths in the CFG above is three.There are two known methods for calculating the cyclomatic complexity of a software module.3.1. Method 1Given an input module , we compute its corresponding CFG . Then we count the number of nodes , the number of edges , and the number of connected components in . The cyclomatic complexity value is equal to – + 2.3.2. Method 2McCabe showed that the cyclomatic complexity of a software module is equal to one plus the number of decision statements in the software module. According to McCabe, decision statements can be:Loop statements (i.e., D0, DO-WHILE)The CASE alternatives in a SWITCH statement (the default/ the else case is excluded)Each logical operator in an IF statementIn a CFG, a decision node corresponds to a decision statement.Given an input module , we compute its corresponding CFG . Then we count the number of decision nodes in and add one to the value.The number of nodes in the CFG of a software module with no decision statements is one. Hence, the cyclomatic complexity is zero.4. ExampleLet’s work out an example from a lecture on cyclomatic complexity:algorithm CheckTheInteger(x): // INPUT // x = an integer // OUTPUT // No output while x 5: print x else: print x "is less than 6" x First, we compute its corresponding CFG:4.1. Method 1We count the number of edges, the number of nodes, and the number of connected components in the CFG.Finally, we compute the cyclomatic complexity, which is 7 – 6 + 2(1) = 3. This means that there are three linearly independent paths in the module. These are highlighted in blue in the