Low-Cost Venturi Meter: Understanding Bernoulli s Equation Through A Demonstration Renan P. Limjuco 1, Fr. Francisco G. Glover, and Isagani M. Mendez 1 Abstract This study intended to concretize Bernoulli s principle through a low-cost Venturi meter designed and constructed by the researchers. Specifically, this paper aimed to improvise a device that can measure flow speeds of water both in the wide and narrow portions of a horizontal piping system for which the pressure difference is provided by a differential height revealed in the attached manometer. A mechanism which regulates volume flow rate of liquid was attached to Venturi meter to generate several trials required to establish accuracy of setup in demonstrating Bernoulli s principle. This investigation about improvisation of apparatus required experimental development method especially in assembling various components which included PVC pipe, aluminum pipe, manometer, DC pump, variable flow controller, and a plastic container as water reservoir. The final model of the apparatus evolved from a series of functionality test sessions with experts and consultants. To determine the accuracy of the instrument, nine trials--that is three each for the three adjusted flow rates, were performed. Findings revealed that the improvised Venturi meter can concretize Bernoulli s principle. Its accuracy in flow speed determination was high since average percentage of error for minor turbulent flow was 1.5 per cent while that for laminar was 3.86 per cent. Keywords: Bernoulli s principle, fluid, pressure, speed, Venturi meter 1 University of the Immaculate Conception Ateneo de Davao University UIC Research Journal.011.17():85-94 85
Limjuco, et al. Engineering and Engineering Education Introduction The best way to understand a physical law is through experimentation. There is much validation in the process as the empirical relationship between variables is being established or tested. However, the accuracy of this scientific task primarily depends on the precision of devices or apparatuses that aid in measurements. According to Young, Freedman, and Ford (009), physics is an experimental science and as such, the observed phenomena of nature that are revealed by patterns and empirical connections are verified only through experimentations. In fact, as what Galileo Galilei, the Father of Experimental Science, has established long time ago, only through experimental investigations can a theory becomes a physical law. Thus, it is a given fact that every physical law encountered in physics has been formulated through rigorous observations and repeated experimentations using accurate apparatuses. Furthermore, experiments are indeed used to test existing theories or new hypotheses in order to support them or disprove them (Harris 007). In physics instruction, a theory can best be understood through demonstration or laboratory activity. This is the reason why a 5 or 4 unit course in physics consisting of 3 lecture hours and 6 or 3 laboratory hours, is imperative in any science or engineering curriculum. As cited by Limjuco et.al., (011), experiments and laboratory activities are designed to concretize the concepts being discussed in the lecture sessions to reinforce and enrich students learning. They also stressed that each experiment should require a great deal of process skills, practical laboratory skills, computational skills, and more importantly critical skills from the students. This vision can only be achieved if the physics laboratory stockroom is equipped with functional and accurate apparatuses. As cited by Bhukuvhani et. al. (010), while real experimentation with conventional laboratory apparatus and equipment is desired, schools in the Philippines still face challenges of limited resources particularly financial resources for acquiring apparatus and materials for imparting effective and efficient science education. Improvised laboratory experimentation serves as a convenient substitute for activity requiring devices that are not found in the 86
Low-Cost Venturi Meter: Understanding Bernoulli s Equation Through A Demonstration Limjuco, et al. laboratory stockroom. Thus, every teacher must be equipped with creative skills to design a laboratory task to deliver science concepts despite of such limitation. One of the things he or she can do is to improvise laboratory apparatus especially that which can concretize a physical law. Inyenga & Tompson (00) in Bhukuvhani et. al. (010) believe that improvisation is a pedagogical intervention strategy that teachers may use to address similar situations by being resourceful in the making and use of locally available materials where conventional equipment and or apparatus may be inadequate or not available at all. Low-cost materials produced through improvisation are not an attempt to provide a watered down science education, but low cost in the mentioned sense is highly creative and highly productive, provides opportunities for creativity and development of manipulative abilities and concepts are learnt and internalized by concrete and unspectacular work than proceeding with chalk and teacher talk in teaching science (Pimpro, 005). This is supported by Dewey (1938) s pragmatist philosophical justification for the need and inclusion of experience in education who argue that knowledge is based on experience and reality is found through interaction of individuals with the environment. The teachers role is therefore to cultivate critical thinking (Ornstein & Hunkins, 004). Findings from the study of Bhukuvhani et. al. (010) emphasized that the use of improvised apparatus in science teaching could be a panacea to a problem on inadequate number of laboratory devices since a lot of schools did not have well-equipped laboratories. Most schools in developing countries have problems of securing proper science equipment and apparatus since these are very expensive. Also, results of the same study indicated that improvisation equally develops science conceptual understanding during teaching and really requires technical skills on the part of the teacher and that teacher-training courses should include a subject on improvisation of technical skills. This result was supported by Pimpro (005) who says, teachers need to be trained in manual and methodical skills to be able to properly use locally available materials in practical work lessons. Realizing the need to supply appropriate apparatus that can concretize specific physical laws such as Bernoulli s principle, and being aware of the cost of sophisticated commercially available devices, the researchers UIC Research Journal.011.17():85-94 87
Limjuco, et al. Engineering and Engineering Education have recognized the need to conduct a study on improvisation of a flow speed measuring instrument called Venturi meter (Cutnell & Johnson, 010). The main objective of the study was to concretize Bernoulli s principle using an improvised Venturi meter. This study aimed also to test the functionality of the device by describing the parts of the apparatus and explaining the functions of each to establish the feasibility of making real the Bernoulli concept for effective demonstration of the physical law. Further, this effort was also pursued to determine the accuracy of the device in flow speed measurement using actual experimental data for percent error calculation to gauge the success of concretization. Method Experimental Development. The appropriate method for this research on improvisation of Venturi meter is that approach embedded in experimental development. As defined in OECD Frascati Manual (00), experimental development is systematic work, drawing on existing knowledge gained from research and/or practical experience, that is directed to producing new materials, products or devices; to installing new processes, systems and services; or to improving substantially those already produced or installed. Since this study aimed to develop an apparatus to concretize a physical law, specifically, the Bernoulli s principle, the research design would be a concoction of scientific processes such as analyzing, designing, constructing, and testing. Basically, the descriptive approach was used to update the development of the improvised apparatus (analysis, design, construction) while experimental design is used in testing the accuracy of the apparatus making use of experimental data. All these stages are part of experimental development. Instrumentation Design and Construction. As shown in Figure 1, the horizontal piping system constructed by welding 8 mm ID Al pipe into 15. mm ID PVC is elbow-connected to a portion of PVC acting as water pipeline and support. A manometer consisting of two stable and verticallypositioned glass tubes was mounted on the horizontal pipes; each of them entrenched to wide and narrow portions of the PVC pipe. The water pipeline 88
Low-Cost Venturi Meter: Understanding Bernoulli s Equation Through A Demonstration Limjuco, et al. Venturi Meter Figure 1 and support is fit into a 1-V variable frequency pump immersed in a body of water contained in a plastic reservoir. A variable flow controller outside the reservoir regulates the water intake of the pump. Thus, if the Venturi meter is in operation, the pump will force water to be elevated at the horizontal piping system, to pass through from the wide portion (venturi inlet) to the narrow portion (venture neck or throat) and to finally exit as a streamline flow spout to be collected back by the reservoir. Functionality Test Procedure. For each trial, adjust the flow controller in such a setting which produces a laminar flow. Measure the difference in height h, in cm, of water levels in the manometer to evaluate pressure difference in pipes. Determine the flow rate R, in cm 3 /s by collecting a measured volume of fluid in certain duration of time. With D 1 and D as the diameters of the venture inlet and venture neck, respectively, in cm, calculate the experimental velocity v 1, in cm/s, by using the formula UIC Research Journal.011.17():85-94 89
Limjuco, et al. Engineering and Engineering Education v 1 = {gh/[(d 1 /D ) 4 1]} 1/. For comparison, compute theoretical v 1, in cm/s, from the formula v 1 = R/A 1, where A 1 = πd 1 /4, cm. Assess the accuracy of the flow speed determination by computing the percentage error based on the two values of v 1. Results and Discussions Bernoulli s Principle and the Improvised Venturi Meter. Bernoulli s equation, p 1 p = ½ (v v 1 ) + g(y y 1 ), states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow. The first term on the right member of the equation is the pressure difference associated with the change of speed of the fluid. The second term is the additional pressure difference caused by the weight of the fluid and the difference in elevation of the two ends (Young, Freedman, & Ford, 009). This equation is valid only for incompressible, steady flow of fluid with no internal friction. Expressing Bernoulli s equation in a more convenient form gives the formula p 1 + gy 1 + ½ v 1 = p + gy + ½ v, where the subscripts 1 and refer to any two points along the flow tube. Thus, we can also write the equation in the form p + gy+ ½ v = constant. If the two points of the fluid are at the same vertical coordinate (y 1 = y ) and if these fluid points are on different cross section areas of the pipe, then a Venturi meter can be used to measure flow speed in a pipe. What follows is the derivation for flow speed v 1 (speed of the fluid in venturi inlet) in terms of the diameters D 1 and D, of the pipe and the difference in height h of the liquid levels in the two vertical tubes. We start from Bernoulli s Equation, p 1 + gy 1 + ½ v 1 = p + gy + ½ v. Since the two points are at the same vertical coordinate (y 1 = y ), the equation is simplified to p 1 + ½ v 1 = p + ½ v. Rearranging the terms gives the expression p 1 - p = ½ v ½ v 1. Considering v = (A 1 /A )v 1 from the continuity equation, and replacing v, it is easy to establish p 1 - p = ½ [(A 1 /A )v 1 ] ½ v 1. To continue, 90
Low-Cost Venturi Meter: Understanding Bernoulli s Equation Through A Demonstration Limjuco, et al. p 1 - p = ½ v 1 {[(A 1 /A )] 1} gh= ½ v 1 {[(A 1 /A )] 1} gh= ½ v 1 {[(A 1 /A )] 1}. Therefore, v 1 = {gh/[(a 1 /A ) 1]} 1/ Finally, v 1 = {gh/[(d 1 /D ) 4 1]} 1/. To measure flow speed v 1 of water at the wider portion (venturi inlet) of the pipe using the improvised Venturi meter, we just have to accurately measure the difference in height h of the water levels as observed directly from the manometer attached to the pipes during the laminar flow. Laminar flow is set using the flow controller of the power supply that regulates the DC pump. With the inside diameters D 1 and D readily known, experimental v 1 is computed directly from the formula v 1 = {gh/[(d 1 /D ) 4 1]} 1/. Theoretical v 1 on the other hand is determined from volume flow rate formula, R = A 1 v 1, where A 1 = πd 1 /4. Experimental Data and Accuracy of Flow Speed Determination Table 1 shows the experimental and theoretical values of water flow speeds at a wider portion of the horizontal piping system of the improvised Venturi meter. Trials 1 to 3 reveal the data for a minor turbulent flow as set by the variable flow controller. As observed, there is a discrepancy in the values of speeds resulting to relatively higher percentage errors registered at 11.15 %, 10.99 % and 15.41%. This error is expected since Bernoulli s principle is valid only for incompressible, steady flow of a fluid with no internal friction (Kirkpatrick, 010). If the flow is not streamline, the effects of friction are too big to be neglected. Hence, this condition will result to inaccuracy of measurement. Trials 5 to 6 show data of flow speeds with improved precision. In this part of experimentation, the variable flow controller was adjusted to UIC Research Journal.011.17():85-94 91
Limjuco, et al. Engineering and Engineering Education Trials h, cm Experimental v, cm/s Table 1 Flow Speed of Water at the Venturi Inlet (D 1 = 15. mm, D = 8 mm) Volume Time V, cm 3 t, s Flow Rate, R, cm 3 /s Theoretical v, cm/s Percent Error 1 7.00 33.77 40 6.09 68.97 38.01 11.15 7.00 33.77 400 5.81 68.85 37.94 10.99 3 7.00 33.77 460 6.35 7.44 39.9 15.41 4 6.50 3.54 460 7.58 60.69 33.45.7 5 6.50 3.54 480 7.56 63.49 34.99 7.00 6 6.50 3.54 470 7.59 61.9 34.1 4.63 7 5.75 30.60 450 8.75 51.43 8.34 7.97 8 5.75 30.60 470 8.66 54.7 9.91.31 9 5.75 30.60 500 9.1 54.8 30.1 1.9 minimize turbulence in the flow. For this set of trials, a significantly lower percentage errors at.7%, 7.00%, and 4.63% were registered. When the flow controller was set to really achieve a laminar flow, a more accurate measurement was revealed. For trials 7 to 9, the percentage errors were reduced to a minimum level at 7.97%,.31% and 1.9%. Thus, from this straightforward and simple experiment, it can be shown that the improvised Venturi meter was successful in concretizing the Bernoulli s principle in liquid. Further examination of the data establishes the linear relationship between the difference in height and flow speed or flow rates. Also, trending of the data for difference in height of the levels of liquid in manometer and speeds of the fluid strongly implies that pressure increases as flow rate is increased. Conclusion The improvised Venturi meter consists of a horizontal piping system composed of 8 mm ID aluminum and 15. mm ID PVC pipes with glass manometer entrenched to the wide and narrow portions. It has a 1-V variable frequency DC pump that is connected to a flow control mechanism to regulate the flow rates inside the pipes. To sustain the supply of fluid, a plastic container acts as the water reservoir. 9
Low-Cost Venturi Meter: Understanding Bernoulli s Equation Through A Demonstration Limjuco, et al. Findings revealed that the improvised Venturi meter can concretize Bernoulli s principle. Its accuracy in flow speed determination was high since average percentage of error for minor turbulent flow was 1.5 per cent while that for laminar was 3.86 per cent. References Bhukuvhani, C.,Kusure L.,Munodawafa, V., Sana,A. and Gwizangwe, I. (010). Pre-service Teachers use of improvised and virtual laboratory experimentation in Science teaching. International Journal of Education and Development using Information and Communication Technology (IJEDICT), 010, Vol. 6, Issue 4, pp.7-38. Cutnell, J., and Johnson, K. (010). Introduction to Physics. 8 th Ed. John Wiley & Sons,Inc., Harris, Randy (007). Modern Physics nd Ed., Addison Wesley Inyega, J. and Tompson, N. (00) Change in Attitudes towards Teaching Strategies in Secondary School Teachers in Kenya Following In-service Professional Development. Paper presented at annual conference of SAETS, 00, Kennesaw, GA. Kirkpatrick, L., and Francis, G. (010). Physics 7th Ed.,Brooks/Cole, Cengage Learning. Limjuco, R., Deypalubos, R., and Gravino, Ma. T. (011), Physics 1B, General Physics, A Compilation of Laboratory Experiments, UIC Printing House. OECD (00) Frascati Manual, 6 th Ed.,, para. 64, page 30. UIC Research Journal.011.17():85-94 93
Limjuco, et al. Engineering and Engineering Education Ornstein, A.C. and Hunkins, F.P. (004) Curriculum: Foundations. Principles and Issues 4th Ed. USA: Pearson Education Inc. Pimpro, P.K (005) Improvisation in Science: Teaching of Physics at Low- Cost with Locally Available Materials. Retrieved from www.sec.org.za/ physics/pkpimpro.html [Accessed 1 January 005] Young, H. Freedman, R. and Ford, L. (009) University Physics with Modern Physics 1th Ed., Pearson Education, Inc. 94