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![]() ![]() As a simple example, we can use the Colebrook equation relating the Moody friction factor ( f M), Reynolds number ( Re), pipe inside diameter ( D i), and pipe roughness (ε) for turbulent flow: I suggest taking advantage of Excel’s Iterative Solver to converge circular calculations. For cases of nonconvergence, numerical methods are available, notably that of Wegstein, that may force convergence. It is possible in some cases to reformulate this problem mathematically to eliminate the circular calculation, but that leaves the scheme in an unnatural format that is more difficult to manage and understand.Ĭircular calculations that use a simple substitution method do not always converge, but in chemical engineering problem-solving they commonly do converge. ![]() The strategy for solving such calculations is to specify a starting value and then “recycle” the value calculated later until the loop converges. ![]() In such a situation, a value is needed to continue the calculation, but that value is calculated later in the scheme. In a more general sense, many process calculations, when laid out in logical sequence, involve circular calculations. A process with a recycle stream involves a circular calculation that cannot proceed automatically because of its iterative nature. One of the main reasons chemical engineers became attracted to spreadsheets was for their ability to carry out flowsheet calculations. Do you have some tips of your own about spreadsheets? If you're a member, I'd love you to share them on AIChE Engage. ![]()
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