Dripping Down the Drain Brisbane School of Distance Education Dripping Down the Drain REPORT STUDENT NAME: Comment by VENUGOPAL, Aruna: Do not forget to fill this! CLASS: TEACHER NAME: Student...

Can someone fix the notes from my teacher on the side please?


Dripping Down the Drain Brisbane School of Distance Education Dripping Down the Drain REPORT STUDENT NAME: Comment by VENUGOPAL, Aruna: Do not forget to fill this! CLASS: TEACHER NAME: Student declaration By submitting this item, I declare that the work submitted: · is my own work and has not been written by any other person, · contains no plagiarised material, and has not been obtained from any other source except where due acknowledgement has been made. Table of Contents 1.Introduction3 2.Considerations3 2.1.Variables3 2.2.Observations3 2.3.Assumptions3 2.4.Outline of mathematical concepts and procedures3 2.5.Use of technology3 3.Mathematical Process3 3.1.Rates of dripping taps3 3.2.Equations of dripping taps3 3.3.Graphs of dripping taps4 3.4.Interpretation4 4.Evaluation4 4.1.Evaluate the solution4 4.2.Strengths and Limitations4 4.2.1Strengths4 4.2.2Limitations4 5.Conclusion4 References5 Appendix 1: INSERT TITLE HERE6 Appendix 2: INSERT TITLE HERE7 1. Introduction We have 3 different sources of advertisement to create awareness about wastage of water. All the source state a different value for water lost is a year by a dripping tap. There may be truth in some of them. The total volume of water lost depends on the rate at which water flows out of the tap. The average accepted volume of a drop of water is 0.05 ml. 2. Considerations The dripping of water from the tap can be modelled by assuming constant rate of loss over a period Variables · t= time in sec · v= volume in ml · r = rate of flow ml/sec · d= drops/sec ObservationsComment by VENUGOPAL, Aruna: Anything you observe about the task ? You could write a few lines on that · If a tap is opened to the minimum dripping possible it drips at approximately 1 drop /sec. This is for a tap in good condition. So, if the tap dripping is faulty tap there may be a few drops per second. · Rate of dripping is not a constant, because it depends on the amount of leak in tap. · Height of the tap effects the rate of dripping. Assumptions · a drop of water is 0.05 ml. · rate of flow is constant Outline of mathematical concepts and procedures Mathematical procedure Mathematical formula Volume flow is equal to the rate at which drop flow for a time Volume lost V= 0.05*d*t (r=0.05*d)Comment by VENUGOPAL, Aruna: What about metric conversions? The lesson is on slope and equation of a straight line. That is the concept we are using in this lesson – we are looking at slope being the rate of water loss. Table ##: Mathematical formula used Use of technology · Differential equation to represent the flow and integrating it over the time.Comment by VENUGOPAL, Aruna: Jonathan let us rename the subheading as technology and materials. Write all the technology used – hardware and software such as your laptop, desmos graphing software, MS Word, a timer , tap - whatever you have used for this task. Mathematical Process Rates of dripping taps Dripping tap claim Given rate Converted Rate 76 litres lost per day Comment by VENUGOPAL, Aruna: You have the 3 claims for dripping taps from 3 agencies that was given to you. You need to prove or disprove the claims. To do this you need to do an experiment. Let your tap drip slowly and count the number of drops for a minute. Note the value. Then let the tap drip faster and count the drops for a minute. Note that too.Use this link and convert the drops to millilitres. http://convert-to.com/conversion/volume/convert-drop-to-ml.htmlThat becomes your given rate.Then convert to litres per hourMake all of the rates to L/hr 76 lit/ day 18 drops/ sec 21 litres lost per day 21 lit/ day 5 drops/ sec 9000 litres lost per year 24.6 lit/ day 6 drops/ sec Table ## Rates for the loss of water from a dripping tap Equations of dripping taps Dripping tap claim Rate Mathematical model (equation) 76 litres lost per day 18 drops/ sec V= 0.05*18*t = 0.88*t 21 litres lost per day 5 drops/ sec V= 0.05*5*t = 0.24*t 9000 litres lost per year 6 drops/ sec V= 0.05*6*t = 0.29*t Table ## Mathematical models for the loss of water from a dripping tap Graphs of dripping taps Comment by VENUGOPAL, Aruna: Looks like a scatter graph – make sure dots are joined we need to see a line of best fit Interpretation The rates 21 lit/day and 9000 lit/ year are almost similar in loss of water. 76 lit/day is much deviated claim from the other two. Evaluation Evaluate the solution Water dripping at a rate of 5-6 drops / second for a faulty tap seems reasonable and matches the observations in daily life also. Strengths and Limitations 1. 2. 3. 4. 4.1 4.2 4.2.1 Strengths · Simple Model · Quick estimation, less time taken to solve the problem 4.2.2 Limitations · Physics of the dynamics is totally neglected. Conclusion The claims 21 litres/ day and 9000 / year are almost similar claims and match our day-to-day observations. The claim of 76 litres/ day seems a bit exaggeration and is much deviated (by a factor of approx. 3 .5) from the other two claims. So, to conclude a dripping tap lose 21 to 24 litres of water a day. References • How much water are you wasting?: https://dorringtonplumbing.com.au/water-wasted-from-leaking-tap/ • Experiment – Water leaking from a dripping tap: https://www.youtube.com/watch?v=sCwJwTBLdIE • Convert water weight to millilitres: https://calculator-converter.com/milliliters-to-grams.htm • Convert drips to ml: http://convert-to.com/conversion/volume/convert-drop-to-ml.html • Desmos: https://www.desmos.com/calculator Appendix 1: INSERT TITLE HERE Appendix 2: INSERT TITLE HERE Volume of water lost at different rates of dripping 76 Lit/ Day012345678910111213141516171819202122232403.16666666666666656.3333333333333339.512.66666666666666615.8333333333333321922.16666666666666825.33333333333333628.50000000000000431.66666666666667134.8333333333333363841.16666666666666444.33333333333332947.49999999999999350.66666666666665753.83333333333332156.99999999999998660.1666666666666563.33333333333331466.49999999999998669.66666666666665772.8333333333333297621 Lit/ Day012345678910111213141516171819202122232400.875000000000000111.75000000000000022.62500000000000043.50000000000000044.37500000000000095.25000000000000096.12500000000000097.00000000000000097.87500000000000098.75000000000000189.625000000000001810.50000000000000211.37500000000000212.25000000000000213.12500000000000214.00000000000000214.87500000000000215.75000000000000216.62500000000000417.50000000000000418.37500000000000419.25000000000000420.12500000000000421.0000000000000049000 Lit/ year012345678910111213141516171819202122232401.02739726027397272.05479452054794543.08219178082191814.10958904109589085.13698630136986366.16438356164383637.1917808219178098.21917808219178179.246575342465753510.27397260273972511.30136986301369712.32876712328766913.35616438356164114.38356164383561315.41095890410958416.43835616438355617.46575342465752818.493150684931519.52054794520547220.54794520547944421.57534246575341522.60273972602738723.63013698630135924.657534246575331Time In Hours Volume of Water in Litres Student NamePage 9 of 9