shadopanda Posted June 6, 2018 Report Share Posted June 6, 2018 For my IA this year, I was given the topic of exploring surface area and drag. The assessment requires me to produce a graph with a meaningful gradient. I am using the drag equation to formulate my graph (where Fd = 1/2 p u^2 Cd A) and when I plot drag force against area I get the gradient as (2 Cd/ pu^2). My question is if this gradient is useful? Surely the graph implies the the drag coefficient is a constant, but surface area is changing. Any improvements and/or changes to my possible graph would be much appreciated. Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 6, 2018 Report Share Posted June 6, 2018 I am not supposed to exactly provide the answers to an independent IA but hope I can be of some assistance. Even without theoretical data that you can compare your results to, a linear dependency could be justified as either correct and incorrect, depending on your evaluation of the experimental set up and theory. Consider the following Number of data points. Are you using enough data points to get data from multiple magnitudes? Accuracy and precision in measurements of of Fd and A. How big are the uncertainties? Can conclusions from your experiment be conclusive? Validity of the model. Wikipedia says that Cd depend on the Reynold's number (Re), then proceeded to say that Re depend on the sqrt of the surface area. While this is dimensionally sound, sqrt (A) is usually substituted by the hydraulic diameter, and the two may or may not be the same. Suppose they are same or close enough, are you exploring a wide range of Re? How strong is the dependency on the Re? (I should add that Reynold's number cannot be compared across different geometries. For example Re of 1000 of sphere flowing in water is different from Re of 1000 of water flowing in a pipe.) I think you are doing the experiment correctly but you should evaluate the above and additional factors to determine just how convincing are the results. 1 Reply Link to post Share on other sites More sharing options...
shadopanda Posted June 6, 2018 Author Report Share Posted June 6, 2018 I understand what you are saying, but I mainly need help on the graph only. The experiement and values measured are fine, but I do not understand what the gradient of my graph would give me, as drag coefficient would increase as surface area increases, but the graph gradient would imply that the coefficient is a constant (as the gradient is constant). My teacher said that the gradient needed to mean something but surely have the drag coefficient as the gradient would not work? Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 6, 2018 Report Share Posted June 6, 2018 You don't need to have Cd as slope but you should use slope to determine value of Cd. Then use what I said in previous reply justify whether what you have found is valid or not. Reply Link to post Share on other sites More sharing options...
shadopanda Posted June 6, 2018 Author Report Share Posted June 6, 2018 What do you mean by using the slope to determine the value of Cd? I don't see the difference that has to the slope being Cd. Do you mean that the gradient of my surface area to drag force graph would show how the drag increases per unit area, and then (similar to a working voltage) I would pick out a certain point on the slope to figure out a specific Cd? Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 7, 2018 Report Share Posted June 7, 2018 The slope should be some expression of Cd. Then you know the slope from linear regression/line fitting, you can solve for Cd. I thought that's what you have done. You cannot just say it's supposed to be 1/2 Cd but you got 2 Cd. The point of fitting to a line is not to compare between 1/2 and 2 but to find out value of some constant. Reply Link to post Share on other sites More sharing options...
shadopanda Posted June 7, 2018 Author Report Share Posted June 7, 2018 What I have done is made the slope equal to 1/2 p u² Cd, and yes I can solve that for Cd, but my question is that surely that isn't the correct value for Cd, as it changes with surface area and is not the same for every size of car? Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 7, 2018 Report Share Posted June 7, 2018 If I am not giving the answer you are looking for, maybe you should ask someone else? 1. Usually the slope is not manipulated to a specific value. 2. Since you are finding a constant Cd for all the experimental conditions, it is up to you to justify whether you believe that to be valid or not. This breaks down to whether you believe more in the theory or in your data. Reply Link to post Share on other sites More sharing options...
shadopanda Posted June 7, 2018 Author Report Share Posted June 7, 2018 If the slope is not manipulated to a specific value, then what would be the significance of it in terms of my investigation? If I did have the slope equal to a constant Cd, would it be wrong to say in my conclusion and evaluation that it is likely the value is incorrect, due to the surface area changing? If we were to just ignore Cd althogether, would there be a way for my to answer the question of how surface area affects drag using a graph? Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 7, 2018 Report Share Posted June 7, 2018 Ok. Ignore #1 in previous point. Basically you are asking about what to graph, I am saying your plot is fine, but you should justify or refute what the plot shows. You should provide detailed and rigorous justification as to why you believe the constant (surface area-independent) value of Cd is valid or not valid. "The value is incorrect, due to the surface area changing" is an extremely insufficient answer. It is quite possible that sufficient evidence can be provided for both why data is right and why data is wrong. Examiners will not penalize you for a well-justified response even if they evaluate the data differently. Finally, a side note: 10 hours ago, shadopanda said: Do you mean that the gradient of my surface area to drag force graph would show how the drag increases per unit area, and then (similar to a working voltage) I would pick out a certain point on the slope to figure out a specific Cd? I found this from November 2010 SL Paper 2, which may be what you were referring to. Here instead of slope you would pick individual points and find resistance. However this smoothed curve has no zero-offset error but your line of best fit would very likely have a non-zero y-intercept. Curves with zero-offset error cannot be forced through the origin. Reply Link to post Share on other sites More sharing options...
shadopanda Posted June 7, 2018 Author Report Share Posted June 7, 2018 Thank you for your feedback, I'll act on your last point in my write up. Reply Link to post Share on other sites More sharing options...
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