The parallel pipeline equation based on the dissipation model The BT equation of the parallel pipeline is recursive, which brings inconvenience to practical use. Based on the circuit transmission line theory, the following paper uses mathematical induction to derive the dissipation model equation for parallel pipelines (limited to (The case where the length and inner diameter of the parallel pipeline are the same), to make up for the deficiencies that the original dissipation model equation can only be used for the series pipeline.
Prove with mathematical induction: the first step: for the case of only two parallel input tubes.
Comparison of equations, dissipation models and experimental values ​​In order to verify the consistency of the BT equation and the fluid pipeline dissipation model, these two mathematical models are used to analyze different pipeline systems, and the calculated pipeline frequency response function and experiment The values ​​are compared. The main index of the pipeline system: there are two input pipes (length 15mm) and the volume of the 96mm3 pneumatic main pipe is connected to a PVC pipe with an inner diameter of 1.4mm and a length of 800mm; the main index of the pipeline system: there are four input pipes ( (The length is 15mm) and the volume of the 256mm3 pneumatic main pipe is connected to the PVC pipe with an inner diameter of 1.4mm and a length of 1200mm. The results show that the calculation results of the BT equation and the dissipation model are exactly the same (the curves in the figure completely overlap). The consistency of the calculation results of the two equations also verifies the correctness of the derivation model parallel pipe formula derivation.
in conclusion
Based on the theory of circuit transmission line, this paper uses mathematical induction to deduce the equations for parallel pipelines, and further improves the dissipation model. The obtained parallel pipe dissipation model is of great significance for further study of multi-channel pressure measurement system in the future. Two different piping systems were analyzed with the BT equation and the fluid pipe dissipation model. The results show that the BT equation and the dissipation model have the same calculation results and are in good agreement with the experimental values. This also proves the theoretical derivation Correctness.
The non-recursive form of the dissipation model will bring greater convenience to the calculation, and may become the basis for in-depth analysis (such as optimization) of the pipeline system. The dissipation model of the parallel pipeline proposed in this paper has been used in engineering practice to analyze the frequency response function of the multi-channel pressure measurement system.
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