A Fluids Experiment for Remote Learners to Test the Unsteady Bernoulli Equation Using a Burette
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A Fluids Experiment for Remote Learners to Test the Unsteady Bernoulli Equation Using a Burette Matthew J. Traum Luis Enrique Mendoza Zambrano University of Florida University of Florida Gainesville, FL, USA Gainesville, FL, USA ABSTRACT The COVID-19 pandemic illuminated the critical need for 1. INTRODUCTION flexible mechanical engineering laboratories simultaneously Bernoulli’s equation is often taught as the interchangeability deployable in multiple modalities: face-to-face, hybrid, and between kinetic, potential, and pressure energy in moving fluid remote. A key element in the lesson portfolio of a forward- under energy conservation assumptions. However, the additional looking engineering instructor is economical, hands-on, unsteady term representing convective energy to either accessible, “turn-key” lab activities; kits that can be deployed accelerate or decelerate fluid streamlines is almost always both in brick-and-mortar teaching labs and mailed home to neglected owing to assumption of steady state flow. Nonetheless, remote learners. The Energy Engineering Laboratory Module the unsteady Bernoulli’s equation models numerous fluids (EELM™) pedagogy, described elsewhere, provides an phenomena induced by impulsive action including water underpinning theoretical framework and examples to achieve hammer, manometer oscillations, Coriolis flow metering, and the these features. In addition, instructional lab kits must first moments of tank draining. Thus, its coverage in demonstrate foundational engineering phenomena while undergraduate fluids courses is beneficial. maintaining measurement accuracy and fidelity at reasonable At the core of the experiment reported in this paper is a 50 cost. In the energy-thermal-fluid sciences, achieving these mL acrylic burette with manual stopcock to regulate flow. This conditions presents challenges as kits require energy and matter robust instrument is commonly used in high school and lower- transport and conversion in real time at scales large enough to division college chemistry laboratories for titration experiments. reveal measurable phenomena but not so large as to become For this fluids experiment, learners fill the burette with water, hazardous to users. This paper presents theoretical underpinning determine the static water column height, and then fully open the and experimental verification of a fluid mechanics lab stopcock to facilitate draining. The burette’s accurate scale and experiment appropriate for undergraduate engineering students ability to drain to a precise, reproduceable volume enables that 1) meets all the above-described criteria, 2) costs less than transient experiments with repeatable initial conditions. $30 in materials, and 3) can be easily mailed to remote learners. Manually clocking the burette draining process enough Keywords: Energy Engineering Laboratory Module times (N ≥ 12) to conduct statistical uncertainty analysis (EELM™), Unsteady Bernoulli’s Equation, Remote Lab establishes experimental drain time and uncertainty in this value. Instruction. Comparing experimental results to theoretical drain time derived from Bernoulli’s equation reveals need to consider both steady NOMENCLATURE and unsteady expressions to predict drain time correctly. This lab Hereunder, the required nomenclature used to derive the experiment demonstrates the utility of simple and flexible theoretical findings for the control volume analysis is presented. activities to illuminate important energy-thermal-fluid science phenomena for students in multiple simultaneous learning A cross-sectional area modalities, especially remote and hybrid where students use A1 cross-sectional area of burette water column mailed kits to facilitate labs with hands-on learning. A2 cross-sectional area at stopcock valve c speed of sound in fluid 2. BACKGROUND d1 diameter of burette water column An incredible tradition exists in college chemistry and d2 diameter at stopcock valve physics courses for using simple glassware and available lab g acceleration due to gravity components to demonstrate engineering phenomena. For K bulk modulus of elasticity of fluid example, Muiño and Hodgson used an Erlenmeyer flask to create L water column height Hero’s Engine [1]; Jackson and Laws used syringes to make Lo initial water column height thermometers, hydraulic pumps, and heat engines [2]; and P pressure Steffensena combined a precision bore Pyrex tube with an tdrain drain time associated to inertial motion inexpensive pressure transducer to perform Rüchardt’s gas test drain time associated to impulsive motion specific heat ratio measurement [3]. tinfo time of information propagation in the water column The burette-based experiment described here follows in ttotal total drain time spirit the works of these teacher/scholars. It is an elegant but v flow velocity tractable experiment that uses simple and readily available z elevation of fluid with respect to reference datum laboratory components, and it enables students to explore z1 initial water elevation with respect to reference datum relevant engineering phenomena themselves. However, to be z2 final water elevation with respect to reference datum effective and adopted by college and high school instructors, ρ water density such experiments must be hands-on, accessible, student- 1 centered, economical, and “turn-key”. The project hardware Egypt are organizing a lab-based virtual exchange program must be affordable for an institution with limited resources, and where students from both institutions complete lab experiments the experiments must be buildable and operable by students remotely and collaboratively for fluids lab courses co-taught without situated knowledge or access to specialized tools. The simultaneously at both institutions. This exchange facilitates Energy Engineering Laboratory Module (EELM™) pedagogy, both technical and culture discourse for large engineering student which is described elsewhere [4-5], provides underpinning populations not possible in brick-and-mortar teaching theoretical pedagogical framework. Examples that achieve these environments [18]. A complete fluid mechanics lab kit has been features at the college level include 1) a series of building energy posited [19] and experiments successfully demonstrated audit exercises that harvests existing buildings as living including a circular hydraulic jump [20], a benchtop fan curve laboratories suitable for quantitative evaluation using an performance measurement apparatus [21], and an internal pipe inexpensive audit tool kit [6] and a small, inexpensive inverted flow velocity interrogator [22-23]. Individual experiments for a downdraft wood gasifier for processing pine chips into syngas future thermodynamics kit are also in development, including a using metal vacuum-flask-style thermos bottle [7]. Examples at desktop-scale Tesla turbine [24] tied to a Prony Brake the high school level include 1) Design / Build / Fly / Analyze / dynamometer capable of demonstrating aerospace Redesign / Build / Fly rocket curricula [8-9] and use of standard turbomachinery operation [25]. benchtop physics laboratory equipment to introduce hands-on When used in an in-person instructional environment, kits machining fabrication techniques in science classes [10]. enable a single space to be used for multiple different classes in In the energy-thermal-fluid sciences fields, achieving parallel to make more efficient use of limited space. This EELM™ conditions presents challenges as the experiments approach was used at Jacksonville University to teach require energy and matter transport and conversion in real time electronics engineering lab, mechanics of materials lab, and at scales large enough to reveal measurable phenomena but not product develop courses in the same physical laboratory space in so large as to become hazardous to users. Thus, additional benefit one semester [26-27]. If an incident drives instruction all-online is obtained by structing these experiments in kit form where they again, students using the kits in a brick-and-mortar setting can are both contained in size but also capable of being used in simply take the kits home and continue the lab class remotely multiple learning modalities (in-person, remote, and hybrid) by without disruption. students without need for instructor or technician intervention. While no fully online ABET-accredited mechanical 3. EXPERIMENTAL SEP-UP engineering bachelor’s degree programs yet exists [11], The experiment is conducted using a 50 mL capacity EISCO examples from the mechanical engineering education literature CH0233B Acrylic Burette with 0.1 mL graduations and a PTFE show that online laboratory instruction matches or exceeds stopcock ($19.75 on Amazon.com at time of writing) mounted traditional face-to-face education with benefits including 1) vertically to a sturdy table using a mini jeweler clamp ($5.99 on increased accessibility, 2) increased retention and completion, 3) Amazon.com at time of writing) as shown in Figure 1. increased flexibility, and 4) increased interaction and engagement [12]. In fact, the literature shows that many students favor remote lab experiences over on-site laboratories [13-14]. For example, Corter and colleagues explored student achievement of learning objectives using cantilever beam experiments where content was delivered in three different environments: 1) brick-and-mortar labs, 2) lab kits at home, and 3) remote labs via computer simulation. These researchers found that at home, hands-on experiments were at least