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Inside this Book – Nearly all applied science consists of performing experiments and interpreting the results. This may be done quantitatively by taking accurate measurements of the system variables which are subsequently analysed and correlated, or qualitatively by investigating the general behaviour of the system in terms of one variable influencing another. The first method is always desirable, and if a quantitative investigation is to be attempted it is better to introduce the mathematical principles at the earliest possible stage, since they may influence the course of the investigation. This is done by looking for an idealized mathematical model of the system. The second step is the collection of all relevant physical information in the form of conservation laws and rate equations. The conservation laws of chemical engineering are material balances, heat balances, and other energy balances; whilst the rate equations express the relationship between flow rate and driving force in the fields of fluid flow, heat transfer, and diffusion of matter. These are then appUed to the model, and the result should be a mathematical equation which describes the system. The type of equation (algebraic, diff*erential, finite difference, etc.) will depend upon both the system under investigation, and the detail of its model. For a particular system, if the model is simple the equation may be elemen- tary, whereas if the model is more refined the equation will be a more difficult type. The appropriate mathematical techniques are then appHed to this equation and a result is obtained. This mathematical result must then be interpreted through the original model in order to give it a physical signi- ficance.
Inside this book –Mathematical Methods in Chemical Engineering PDF Book by V.G. Jenson, G.V. Jeffreys – Most sign difficulties are a result of trying to think too deeply about them, thus causing a state of complete confusion. The temptation to anticipate the solution of the problem is very strong but it must be resisted. The formulation of equations can be reduced to a set of rules which can be systematically apphed and although it is difficult to frame such a set of rules to cover the wide variety of problems which can arise, an attempt has been made in the next section. The slavish observance of rules is not to be generally recom- mended, but it is best in the first instance to do just this because it completely eliminates any possibiHty of anticipating properties of the solution, and ensures that the signs are correct. The resulting equation can frequently be subjected to a physical sign check after it has been estabHshed.
Mathematical Methods in Chemical Engineering by V.G. Jenson, G.V. Jeffreys PDF : eBook Information
- Full Book Name – Mathematical Methods in Chemical Engineering
- Author of this Book – V.G. Jenson, G.V. Jeffreys
- Language – English
- Book Genre – Science, Mathematical, Engineering
- Download Format – PDF
- Size – 72.2 MB
- eBook Pages – 576
- Price – Free