Pumps & Physics Essay

What’s new? When I was thinking about which aspect of physics to investigate for my investigation, I knew it was a good idea to choose something that really interested me. At the time I was becoming more and more fascinated by subatomic particles. I liked the fact that much of it was new and not understood properly, unlike the classical physics that everyone associates the subject with. Unfortunately, high energy physics does not translate into good practical coursework. However, while reading Six Easy Pieces, a book adapted from Richard Feynman’s famous textbook The Feynman Lectures on Physics, I noticed that a very common everyday phenomenon is still not properly understood by physicists. Encouraged by the prospect of discovering something new, I read on. Chaotic ideas Feynman wrote (on page 66) â€Å"There is a physical problem that is common to many fields, that is very old, and that has not been solved†¦It is the analysis of circulating or turbulent fluids†¦No-one can analyse it from first principles† â€Å"Wow – something science can’t explain† I thought. I looked on the internet for further details and I found a poster from World Maths Year 2000 (http://www.newton.cam.ac.uk/wmy2kposters/march/), showing just the type of unpredictable fluid motion that Feynman was writing about. It’s a new and exciting branch of maths called chaos theory and it is just beginning to be understood mathematically. The main idea is that simple systems can show very complicated behaviour that seems to have no repeating pattern. The sums that describe these systems are difficult to get your head round and appear to be way beyond my abilities as an A-Level maths student. Despite this, I felt something chaotic was an excellent phenomenon to look into for this task – it’s a chance to do some experimental work where there isn’t a perfect formula or a flawless explanation in any textbook. I couldn’t rely on distorting my results to fit a simple law, so my experimentation had to be rigorous. Limitations It was important to find a subject that was practical to investigate at school. While I was watching water swirl down the drain as I filled the kettle at home, I wondered how widely-used machines like ship’s propellers cope with the unpredictable world of chaos. Propellers have an unusual and distinctive shape designed to reduce turbulence. I wanted to investigate why this particular shape works so well – and if it can tell us anything about turbulent flow. Conveniently, water and propellers are easy-to-use in school labs (or so I thought!). Best of all, I thought, if I could model the situation but ignore the effect of turbulent water, I could look at the mechanics of the propeller, and then compare the theory with what happens in real life. It seemed like a good mix of fresh ideas and traditional physics problems. I talked about my plans to some of my teachers and one of them mentioned that his son had done a PhD degree in the formation of bubbles by marine propellers – an effect called cavitation. This encouraged me to continue with this project, knowing that it relates to current areas of research and is an important and worthwhile topic. Research It turns out that one of the most interesting applications of pumps is in fire engines. As fire services are public organisations they make available plenty of high-quality, free information online. Engineering sites were also useful. * The Physics Behind Firefighting American high-school physics project http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/Matt_Taylor/Matt1.dwt * How Fire Engines Work General information http://science.howstuffworks.com/fire-engine.htm * Bedfordshire & Luton Fire and Rescue Service My local fire brigade, who I actually went to visit to find out more http://www.bedsfire.gov.uk/index.htm * American Turbine: Pump Calculations Web-based program for working out quantities in pumping http://americanturbine.net/formulacalc/pump.htm * Impeller Design The engineering that goes into pumps http://homepage.mac.com/mrbach/mixdesign.htm * Firefighting.com Useful data on pumps but uses frames so I can’t give a full URL http://www.firefighting.com * How Things Work A simple explanation of propellers and aerofoils Lesley Firth, Kingfisher, 1983 p13 * The Physics of Firefighting Some simple principles explained Physics Teacher, vol 28, p 599 * Firefighting Contains a bit of physics but interesting background information Jack Gottschalk, Dorling Kindersley, 2002, ISBN: 0789489090, p128 * Go with the flow Article about modelling granular and fluid motion New Scientist, 2 August 2003, p38-39 Preliminary Experiments I wanted to find the most efficient propeller design. From research I found out that propellers have different shapes for different tasks, so my first goal was to get a propeller up and working, and then look at what I could change to make it run more efficiently. These are the variables I aimed to evaluate for their effect on power transfer efficiency in preliminary tests: * The speed of rotation * The size of the propeller * Since speed of rotation is less time consuming to collect data for, I’ll look at it first. I intend to plot a graph of speed of rotation vs. output flow rate. Considering the shape of a ship’s propeller, I expected to be looking at these variables later on: * The number of blades on the impeller * The shape of the blades * The orientation of the blades (what angle they are in relation to the axis of rotation) The physics principles that are important here are mechanical ones. The efficiency of the propeller depends on how much of its power goes into pushing water outwards and how much is wasted on heating the water up or causing it to form whirlpools. New Scientist’s article Go with the flow mentioned the Bernoulli Effect, which is observed on aircraft wings and on propeller blades. Lower pressure Higher pressure A blade with a curved plane and a flat plane forces some air or water on a longer route over the curve, and the rest takes the shorter flat route. The longer journey over the curved plane causes a drop in pressure, which translated to lift in planes, and thrust in propellers. According to all the textbooks, the optimum number of blades, the blade angle, the speed of rotation and the size of propeller all contribute to the efficiency. It seems like I’ve got my work cut out for me. I’m going to concentrate on rotation speed and its effect on water flow rate outwards. Let’s see what the preliminary tests show. Water flows in Axle Propeller Watertight casing Water flows out Planning Risk Assessment1,2 Apparatus or procedure Hazard Precautions All apparatus Accident or fire Supervise the experiment at all times and clear away at the end of the session. Store all equipment safely and securely. Boiling water for shaping polypropene propellers Risk of scalding Take care with boiling water, paying attention at all times. Stand well back from the saucepan and do not move it while the water is hot. Use a heat-insulating towel to manipulate the hot polypropene. Electric circuit in general Risk of fire from short circuiting etc. Use insulated wires, keep connections clean and dry, and always supervise the apparatus while current is flowing. Do not leave the set-up unattended without unplugging the mains supply. Use wires of appropriate diameter to prevent overheating resulting in fire. Rapidly rotating propeller Possibility of injury from contact with rotating blades of propeller Leave motor switched off until ready to record data. Take care to keep your distance from the propeller, especially fingers. Heavy equipment (power pack, retort stands) Falling equipment could injure Ensure stands etc. are sturdily placed and avoid placing equipment near the very edge of the work bench. Power pack Output: 13V 5A DC Input: 230V mains AC Risk of electrocution from mains input (risk of injury from output voltage is minimal) Keep power pack away from the wet part of the apparatus (to prevent conduction through water). In my experiment, I will keep all the electrics on a shelf above the level of the water-containing apparatus. Ensure all water-containing equipment is as waterproof as possible, and have towels to hand to soak up spills. Do not leave the set-up unattended without unplugging the mains supply. Preliminary findings In the research and rationale section, I identified variables I wanted to investigate. I conducted preliminary experiments to found out which variables were the most practical to focus on. The basic aim is to narrow my search down to one or possibly two variables and then find the most power-efficient value for each variable. Size of propeller was very difficult to control since I found that the propeller will only stir the water unless it tightly fits the container. Small propellers did not displace any water. Only propellers with a diameter 1 or 2mm less than the diameter of the container were effective in pumping water. As such, I decided not to consider investigating this variable. Angle of propeller blade inclination is possible to vary, but I found the range of angles possible with the materials I had chosen were too limited. I developed a method of cutting out rectangles of polypropene sheeting, boiling them in water and bending them to the right shape, but the blades often snapped and it was tricky to get the blades to remain at the chosen angle as they cooled and hardened. I decided to keep blade inclination constant. 45à ¯Ã‚ ¿Ã‚ ½ might seem to be an appropriate angle of inclination to choose for all the propellers I will compare, but most propellers I found photographs of from my research showed shallower angles of blade inclination. I have decided that all my propellers will be inclined at 30à ¯Ã‚ ¿Ã‚ ½ because it is easier to make the propellers this shape and I assume that this is a more efficient angle than 45à ¯Ã‚ ¿Ã‚ ½ since many propellers are about this angle. Speed of rotation turned out to be very simple to control with the use of the variable voltage power pack. I investigated the effect of power input on rotation speed (or angular velocity of the propeller as I call it from here on in). Using a stroboscope, I determined the linear relationship between the voltage supplying the motor (V) and the angular velocity (?) of the propeller shaft in air. I adjusted the frequency of the strobe light until the propeller appeared not to rotate. At this frequency, the time between flashes of the strobe and the time for one blade of the propeller to reach the former position of the blade before it is equal. If you find the angle in radians (?) between two adjacent blades and multiply it by the frequency (f) of the stroboscope (the time between flashes), you are left with the angular velocity (?) of the propeller, i.e. the rate of rotation. ? = ?f In the table below, V and f were determined experimentally and ? was calculated by multiplying f by ?. Since the frequency is only known to two significant figures, the angular velocity can only be determined to 2 s.f. Angle between blades, ? degrees 72 Angle between blades, ? radians 0.4? V V 0 2.25 4.25 6.25 8.75 10.00 13.00 à ¯Ã‚ ¿Ã‚ ½0.25 f s-1 0 13 26 36 50 57 74 0.5 ? rad s-1 0 16 32 45 63 72 93 0.5 Once the propeller is immersed in water the relationship between ? and V changes. The relationship is non-linear and, unlike the graph above, is different for every propeller. In light of the preliminary experiments I will modify this method to vary the power supplied to the drill that drives the propeller. It will not matter that the speed of rotation varies depending on how much the water resists the motion of the propeller. The only data that are needed to calculate the efficiency of the system are power input and useful power output. Efficiency At this point it is important to mention that I am concentrating on the efficiency of the propeller at displacing water. Percentage efficiency = useful power output / power input à ¯Ã‚ ¿Ã‚ ½ 100%, or rewritten in symbols, ? = Puseful out / Pin. Also, power input is proportional to input voltage since current is constant at 5 A in my equipment. P = VI and I = 5   Power (Watts) = 5 x voltage (Volts). Review of purpose of investigation The focus of this investigation is to determine the optimum number of blades for a propeller to have to maximise energy-efficiency. Experiments will compare propellers with 2, 4 and 6 blades. The energy efficiency of the three propellers when displacing water will be determined and compared. Their efficiency may not be independent of the rate of rotation. This too will be investigated and analysed. The analysed results will show which of the three propellers is most energy efficient in at each rate of rotation investigated. Extract from Eric Weisstein’s World of Physics http://scienceworld.wolfram.com/physics/Screw.html A screw is a simple machine that is actually a version of the inclined plane. The pitch of the screw corresponds to the inclination of the plane: a higher pitch (i.e., more threads per length) means less inclination, and thus easier turning, but also more turning that needs to be done to travel a given length. As with the other simple machines, the required force is reduced, but the amount of work done is the same. Apparatus 13V max. variable voltage power pack Retort stands and clamps 15 cm ruler Silicone polymer window sealant Garden hosepipe Expanded polystyrene for supports Multimeter (0.25V, 0.25A tolerance) Polypropene sheet for making propellers PET lemonade bottles (2 Litre capacity) Plastic funnel for filling Stopwatch Collection bottle with 2 litre mark ( 0.002 L) Cordless electric screwdriver/drill Steel axle Volumetric burette PET pudding basins to contain propeller Water Colour-coded wires and crocodile clips Saucepan, hotplate and tongs for heating and reshaping polypropene into propellers Scissors and craft knife for cutting out propeller shapes from polypropene sheet Apparatus set-up These diagrams show how I designed the equipment. The circuit diagram connected to the drill represents the power pack, and its voltage selector is displayed as a variable resistor. The plastic volute is the container that houses the propeller. To begin with, water fills the water tank and the plastic volute. Activating the power pack supplies an electric current to the drill, which rotates the propeller. Variables to control Variable How I will control it Viscosity of water Constant at constant temperature and pressure Power and speed of rotation of propeller Use a power pack instead of a battery to supply the cordless drill. Use the same power pack, axle and drill throughout the experiment. Rotation speed does not vary linearly with power but carefully designing the experiment can avoid problems. Room temperature and pressure Constant at 20à ¯Ã‚ ¿Ã‚ ½C due to central heating. Atmospheric pressure changes are insignificant to this experiment. Plan for laboratory sessions Session and duration Targets Before lab work begins Build the waterproof sections of the apparatus and seal them with silicone polymer. Buy a cordless drill. First two hours Set up all apparatus, construct the propellers and test the experiment to ensure it works as planned Second two hours Measure the time taken to raise 2 Litres of water through 50cm vertically by each of the three propellers, with 65W power input Third two hours Repeat the previous session’s experiment, but with the power set at 35W. Fourth two hours By considering the results collected before this session, decide which range of power input to investigate in detail Fifth two hours Continue gathering results for chosen range of power inputs Remaining time Investigate turning points and anomalies as necessary In between lab sessions Complete results tables, draws graphs as appropriate and start to analyse findings. Use analysis to modify strategy and to make decisions on how to progress. While I was designing which equipment to use and how to use it, I thought carefully about accuracy and sensitivity. The major difficulty with this experiment is the unpredictable nature of the propellers – unlike many other things physics, it is not easy to find a good estimate of what will happen in textbooks or online. One way of ensuring good results is to measure the variables to a reasonable number of significant figures. The multimeter I chose to use is quick to respond to changes in current or potential difference and has fine graduations on its scale, providing high sensitivity. It also has very tight tolerances as it is designed for use in high performance electronics, which contributes to the accuracy of the results I will gather. The multimeter is significantly more accurate and sensitive some of the digital alternatives at school. It responds to changes much quicker too. I have had to design and build quite a large amount of equipment just to make this project possible. To measure the volume of water pumped out by the system, I will calibrate the water collection bottle with graduations. To make sure they are very sensitive and accurate, I will use the high quality, high accuracy laboratory glassware available at school for use in chemistry and biology. The percentage error on the volume graduations on these pieces of equipment is very small (around 0.0003%). References for planning section 1. Cambridge University Department of Physics Physics risk assessment form http://www.phy.cam.ac.uk/cavendish/hands/forms/RAform.pdf 2. CLEAPSS Secondary Schools website http://www.cleapss.org.uk/secfr.htm Implementing Modifications to plan Problem Solution How to water-seal the entire system Careful application of silicone sealant and gaffer tape at all junctions. Apparatus tested underwater by pressurising with air using a bike pump. Leaks located by bubbles escaping where seals were incomplete. How to get water to flow from the water reservoir into the propeller cavity, without providing any extra pressure that would reduce the workload of the propeller Height of water reservoir bottle adjusted until water just reaches the top of the propeller cavity, without spilling out the output hole How to accurately measure the volumes of water used in each experiment Volumetric glassware borrowed from chemistry department Calculation of power efficiency of pumping system ?E = mg?h P = Et-1 Useful power output = power spent on raising water against the force of the Earth’s gravitational field Useful power output = (mass of water raised (mwater) à ¯Ã‚ ¿Ã‚ ½ strength of gravity at sea level (g) à ¯Ã‚ ¿Ã‚ ½ height through which the water is raised (?h)) / time taken (t) Pout = mwaterg?ht-1 The mass of water is proportional to its volume at constant temperature and atmospheric pressure. In these experiments, the temperature and pressure have been constant at 293K (20à ¯Ã‚ ¿Ã‚ ½C) and 105 Pa respectively. Under these conditions, water has a density of 998.2 kgm-3 (according to the Nuffield Advanced Science Data Book, Nuffield-Chelsea Curriculum Trust, Longman, 1984). Therefore, the time taken to raise the water and the number of blades on each propeller are the only variables in my experiment.