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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 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.
Metadaten
Author:Claudia SchäfleORCiD, Christian KautzORCiD
URL:https://doi.org/10.1103/PhysRevPhysEducRes.17.010147
Parent Title (English):Physical Review Physics Education Research
Publisher:American Physical Society
Document Type:Article (peer reviewed)
Language:English
Publication Year:2021
Tag:Strömungsmechanik
Concepts& Principles; Instructional materials development; Instructional strategies; Physics Education research
Volume:17
Issue:1
Page Number:16
First Page:010147
Peer reviewed:Ja
Project Title:Physik und Mathematik in Rosenheim kontinuierlich Just-in-Time verstehen
Acronym:PRo-Aktjv 1 und 2
Funding Agency:Bayrisches Staatsministerium für Wissenschaft und Kunst
Grant Number:MINTER Aktiv und BayernMINT
faculties / departments:Fakultät für Angewandte Natur- und Geisteswissenschaften
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik