EVERYDAY EXAMPLES OF ENGINEERING ONEPTS F5: Momentum opright 014 This work is licensed under the reative ommons Attribution-Nonommercial-NoDerivs 3.0 Unported License. To view a cop of this license, visit http://creativecommons.org/licenses/b-nc-nd/3.0/ or send a letter to reative ommons, 444 astro Street, Suite 900, Mountain View, alifornia, 94041, USA. Everda Eamples from www.realizeengineering.wordpress.com 1 of 5
This is an etract from 'Real Life Eamples in Fluid Mechanics: Lesson plans and solutions' edited b Eann A. Patterson, first published in 011 (ISBN:978-0-98414-3-5) which can be obtained on-line at www.engineeringeamples.org and contains suggested eemplars within lesson plans for Sophomore Fluids ourses. The were prepared as part of the NSF-supported project (#0431756) entitled: Enhancing Diversit in the Undergraduate Mechanical Engineering Population through urriculum hange". INTRODUTION (from 'Real Life Eamples in Fluid Mechanics: Lesson plans and solutions') These notes are designed to enhance the teaching of a sophomore level course in fluid mechanics, increase the accessibilit of the principles, and raise the appeal of the subject to students from diverse backgrounds. The notes have been prepared as skeletal lesson plans using the principle of the 5Es: Engage, Eplore, Eplain, Elaborate and Evaluate. The 5E outline is not original and was developed b the Biological Sciences urriculum Stud 1 in the 1980s from work b Atkin & Karplus in 196. Toda this approach is considered to form part of the constructivist learning theor 3. These notes are intended to be used b instructors and are written in a stle that addresses the instructor, however this is not intended to eclude students who should find the notes and eamples interesting, stimulating and hopefull illuminating, particularl when their instructor is not utilizing them. In the interest of brevit and clarit of presentation, standard derivations, common tables/charts, and definitions are not included since these are readil available in tetbooks which these notes are not intended to replace but rather to supplement and enhance. Similarl, it is anticipated that these lesson plans can be used to generate lectures/lessons that supplement those covering the fundamentals of each topic. It is assumed that students have acquired a knowledge and understanding the following topics: first and second law of thermodnamics, Newton s laws, free-bod diagrams, and stresses in pressure vessels. This is the fourth in a series of such notes. The others are entitled Real Life Eamples in Mechanics of Solids, Real Life Eamples in Dnamics and Real Life Eamples in Thermodnamics. The are available on-line at www.engineeringeamples.org. Eann A. Patterson A.A. Griffith hair of Structural Materials and Mechanics School of Engineering, Universit of Liverpool, Liverpool, UK & Roal Societ Wolfson Research Merit Award Recipient 1 Engleman, Laura (ed.), The BSS Stor: A Histor of the Biological Sciences urriculum Stud. olorado Springs: BSS, 001. Atkin, J. M. and Karplus, R. (196). Discover or invention? Science Teacher 9(5): 45. 3 e.g. Trowbridge, L.W., and Bbee, R.W., Becoming a secondar school science teacher. Merrill Pub. o. Inc., 1990. Everda Eamples from www.realizeengineering.wordpress.com of 5
ONTROL VOLUME ANALYSIS 5. Topic: Momentum Engage: Take a hairdrer, stand and clamp, some balloons, and paperclips into class. Set up the hairdrer with the stand and clamp so that it is blowing verticall up on its cold setting. Blow up a balloon and place it in the air-stream and it will probabl be pushed up to the ceiling. Eplore: apture the balloon and attach a paperclip to the neck of the balloon and again place it in the airstream. As ou add more paperclips the balloon will float lower and lower in the airstream. To save time ou could use a series of balloons inflated to the same diameter with various numbers of paperclips attached. There is a nice video of school kids performing this eperiment 4. Eplain: Eplain that when the balloon hovers at a stable height, based on Newton s second law applied to the balloon, the force on the balloon from the jet of air is equal to the weight of the balloon. We can draw a clindrical control volume around but not including the balloon and equate the change in momentum to the eternal forces on the control volume, i.e. F m ( v 1 ) In this case the eternal force is the weight of the balloon. Sometimes it is easier to consider three components of this vector epression, i.e. F m v 1 F m v 1 F z m v 1 z z scalar 4 www.planet-scicast.com/view_clip.cfm?cit_id=709 Everda Eamples from www.realizeengineering.wordpress.com 3 of 5
Elaborate: onsider the clindrical control volume around the balloon. Assume that the velocit of the airstream leaving the hairdrer is a uniform 50m/s and that all of air leaves the control volume at the same speed but at an angle, = 30 from the horizontal. In practice this angle will var from about zero close to the bottom of the balloon and approach 90 close to the horizontal diameter of the balloon. The mass flow rate at entr, m air Av 1. 0.06 50 0. 17kg/s 4 Assuming the hairdrer has a circular nozzle with an outlet diameter of 6cm. The momentum of the fluid crossing AB will be m v AB 0.1750 8.48N And in the -direction for clindrical surface, given that continuit demands the total mass flow across the surface equals that across AB, m v AD sin 0.1750sin30 4.4N So, appling the momentum equation, 1 sin30 4. 4 W mv N AB This hair drer could keep a balloon and tail of paperclips weighing 4.4N (=0.4kg) in the air. The airstream is slowed down b entrapment of the surrounding air and so the nozzle velocit will not be achieved at all heights above the hairdrer, which is wh the balloon sinks down as it is loaded with paperclips. Evaluate: Invite students to attempt the following eamples: Eample 5.1: alculate the force eerted b the water from the tap in our kitchen sink on a coffee cup held in the flow when the tap is open to its maimum. Solution: Estimate the water flow b how long it takes to fill a measuring jug. In the editor s kitchen it took 5 seconds to fill a 1 liter measuring jug, so the mass rate is 1000 0.001 OV m H 0. T 5 kg/s The diameter of the orifice in the tap is 17mm and so velocit of the flow is A B flow the Everda Eamples from www.realizeengineering.wordpress.com 4 of 5
wind 5E Lesson Plan No.F5 m 0. v A 0.017 1000 4 0.88m/s Hence, the momentum of the water leaving the tap at AB is m v AB 0. 0.88 0.176N The water is turned through 180 in the cup and so emerges with a momentum of equal and opposite sign so that the total change in momentum is m 0. 35 N. This is about one third of the weight of the editor s best porcelain coffee cups. v AB Eample 5. alculate the force required to hold an umbrella against a 30mph wind. Assume the wind is blowing horizontall so ou are holding our umbrella head into wind, i.e., the handle is parallel to the wind direction and the umbrella deflects the wind to leave at an angle of 45. The umbrella is smmetrical about the handle with a projected area perpendicular to the wind, which is a circle of diameter 1.m. Solution: onsider a control volume such that wind enters at AB with a velocit of 13.4 m/s ( 30mph) and leaves at 45 to this along B. can appl the momentum equation in the direction of the wind such that F m v 1 and Av v cos45v 1.9 13.41 cos451 76. 8 A B umbrella 1. F air 1 1 1 N 4 Force, F If ou were walking into the wind, then it would be necessar to construct velocit diagrams for the wind velocit at entr and eit to, what would become, a moving control volume. We Everda Eamples from www.realizeengineering.wordpress.com 5 of 5