Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation

We report on an investigation of student thinking about steady-state pipe flow of an incompressible fluid. About 250 undergraduate engineering students were given a test consisting of two hydrodynamics questions, combining multiple-choice format with subsequent open-ended explanations. There is subs...

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Autores principales:	Claudia Schäfle, Christian Kautz
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/556f7c52c4b9424a9993404a3c180b0c
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spelling	oai:doaj.org-article:556f7c52c4b9424a9993404a3c180b0c2021-12-02T17:49:14ZStudent reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation10.1103/PhysRevPhysEducRes.17.0101472469-9896https://doaj.org/article/556f7c52c4b9424a9993404a3c180b0c2021-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevPhysEducRes.17.010147http://doi.org/10.1103/PhysRevPhysEducRes.17.010147https://doaj.org/toc/2469-9896We report on an investigation of student thinking about steady-state pipe flow of an incompressible fluid. About 250 undergraduate engineering students were given a test consisting of two hydrodynamics questions, combining multiple-choice format with subsequent open-ended explanations. There is substantial evidence that students have difficulty applying and prioritizing the two basic principles of mass conservation (expressed in the continuity equation) and energy conservation (i.e., Bernoulli’s equation). When faced with questions that involve gravity, dissipative effects (“friction”), or a visible pressure drop, a considerable number of students did not invoke the continuity equation in situations where applying it is a necessary step for arriving at the correct answer. Instead, even after lecture instruction on this topic, many of the first-year students based their answers on ill-supported assumptions about local pressures. Some of them used formal arguments from a simplified Bernoulli equation (“lower pressure means higher velocity”), while others based their answer on intuitive arguments (“higher pressure leads to higher velocity”). We also found reasoning based on analogies to single-particle motion (“flow velocity decreases when flowing upwards or friction is present”). Contrary to other researchers, we did not see any evidence for the hypothesis that students think of water as a compressible fluid. Instead, students’ answers often indicate a lack of understanding of the conservation of mass or its implications for incompressible fluids or of the role that this principle plays in the context of fluid flow. In addition, our data indicate that some students have more general difficulties in describing and reasoning about technical situations, such as applying equations containing multiple variables, distinguishing spatial differences in a quantity from its changes with respect to time, or realizing the meaning of idealizations. We also present some evidence that different levels of activation of students during instruction influence the prevalence of these difficulties and discuss some implications for instruction.Claudia SchäfleChristian KautzAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Physics Education Research, Vol 17, Iss 1, p 010147 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Special aspects of education LC8-6691 Physics QC1-999
spellingShingle	Special aspects of education LC8-6691 Physics QC1-999 Claudia Schäfle Christian Kautz Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
description	We report on an investigation of student thinking about steady-state pipe flow of an incompressible fluid. About 250 undergraduate engineering students were given a test consisting of two hydrodynamics questions, combining multiple-choice format with subsequent open-ended explanations. There is substantial evidence that students have difficulty applying and prioritizing the two basic principles of mass conservation (expressed in the continuity equation) and energy conservation (i.e., Bernoulli’s equation). When faced with questions that involve gravity, dissipative effects (“friction”), or a visible pressure drop, a considerable number of students did not invoke the continuity equation in situations where applying it is a necessary step for arriving at the correct answer. Instead, even after lecture instruction on this topic, many of the first-year students based their answers on ill-supported assumptions about local pressures. Some of them used formal arguments from a simplified Bernoulli equation (“lower pressure means higher velocity”), while others based their answer on intuitive arguments (“higher pressure leads to higher velocity”). We also found reasoning based on analogies to single-particle motion (“flow velocity decreases when flowing upwards or friction is present”). Contrary to other researchers, we did not see any evidence for the hypothesis that students think of water as a compressible fluid. Instead, students’ answers often indicate a lack of understanding of the conservation of mass or its implications for incompressible fluids or of the role that this principle plays in the context of fluid flow. In addition, our data indicate that some students have more general difficulties in describing and reasoning about technical situations, such as applying equations containing multiple variables, distinguishing spatial differences in a quantity from its changes with respect to time, or realizing the meaning of idealizations. We also present some evidence that different levels of activation of students during instruction influence the prevalence of these difficulties and discuss some implications for instruction.
format	article
author	Claudia Schäfle Christian Kautz
author_facet	Claudia Schäfle Christian Kautz
author_sort	Claudia Schäfle
title	Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
title_short	Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
title_full	Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
title_fullStr	Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
title_full_unstemmed	Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation
title_sort	student reasoning in hydrodynamics: bernoulli’s principle versus the continuity equation
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/556f7c52c4b9424a9993404a3c180b0c
work_keys_str_mv	AT claudiaschafle studentreasoninginhydrodynamicsbernoullisprincipleversusthecontinuityequation AT christiankautz studentreasoninginhydrodynamicsbernoullisprincipleversusthecontinuityequation
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Student reasoning in hydrodynamics: Bernoulli’s principle versus the continuity equation

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