Deformations of an elastic pipe submitted to gravity and internal fluid flow |
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| Institution: | 1. Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA;2. Department of Mathematics & Computer Science, Valdosta State University, 2072 Nevins Hall, Valdosta, GA 31698-0040, USA;1. LMD – École normale supérieure de Paris – CNRS, 75005 Paris, France;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada;1. LMD/IPSL, CNRS, École normale supérieure, PSL Research University, École polytechnique, Université Paris-Saclay, Sorbonne Universités, UPMC Université Paris-6, 24, rue Lhomond, 75005 Paris, France;2. Department of Mathematical and Statistical Sciences, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G1 Canada |
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| Abstract: | This paper describes the deformation of an elastic pipe submitted to gravity and to an internal fluid flow. The pipe is clamped horizontally at one end and free at the other end. As the fluid velocity increases, the shape changes from an elastic beam deflected by its own weight towards an horizontal position. The shape of the pipe is characterized experimentally and is compared with a theoretical model based on the Euler–Bernoulli approximation and the conservation of the fluid momentum. We study how the determination of the pipe deformation provides an estimation of the conveyed fluid flow. Finally, the vertical force produced by the conveyed fluid to lift off a mass is deduced. |
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| Keywords: | Elastic pipe Fluid flow Mass lifting Flow rate measurement |
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