Question Asking to Graph a Dimensionless ratio as a Parameter on a Graph Constructed From Experimentally Determined Data1

We conducted an experiment to determine the relationship between the heat transfer coefficient for forced convection over a cylindrical rod due to varying air flow velocities. The relationship that was found was plotted with the heat transfer coefficient on the Y axis and the air flow velocity on the X axis. The question then asks to graph the dimensionless ratio(which we calculated for all ten test which we ran) as the parameter. So I have the list of dimensionless values that correspond to each of the ten tests that we ran but I don't know how to apply this dimensionless number to the graph as a parameter.

  1. What does this mean?
  2. What is a Parameter on a graph?
  3. How would I go about plotting something that is dimensionless, when both the x and y axis clearly have units?
  • 1
    $\begingroup$ Can you define the parameters "d" & "S", and the relationship between the heat transfer coefficient and approach velocity? $\endgroup$
    – r13
    Apr 22 at 19:15
  • $\begingroup$ Do you know how to use a spreadsheet? Put the numbers for X an Y in a column , compute the ratio X/Y in the 3rd column then copy that formula down 10 cells. Then select the array and choose plot XY then after choose X/Y plot for the option on Secondary Y axis on the right. X could be your velocity or voltage on fan and T the temperature. $\endgroup$ Apr 22 at 19:29
  • $\begingroup$ @TonyStewartSunnyskyguyEE75 I would not say I am proficient in using spread sheets but I am capable. But I am experienced using mat lab if that helps $\endgroup$ Apr 22 at 20:05
  • $\begingroup$ @r13 the d and s variables were the diameter of the cylindrical rod that we were testing and the S is the separation distance between the heated cylindrical rod and an obstruction rod that was placed in front of the heated rod. The diameter for both rods were 0.5 inches and the separation distance between the two center points of the rods were given as S for each test. Therefore the dimensionless ratio of d/s was 0.5/S(with S changing each of the 10 tests). This created a dimensionless ratio for each of the ten tests that we performed. How does this become a parameter on the graph? $\endgroup$ Apr 22 at 20:10
  • $\begingroup$ I see. Your graph shall be just like the chart NMech provided below. For each d/S, through the varying velocity (x_i), you can calculate the heat transfer coefficient (y_i), and plot the interception point, that represents the unitless parameter d/S. If the velocity ranges from 0 - 100, with 10 be the increment, you will need to make 10 repetitive calculations to draw the d/S curve for each test, and 100 such calculations for 10 tests. Excel is perfect to handle a huge amount of repeating calculations like this. Hope I didn't make mistake that mislead you. $\endgroup$
    – r13
    Apr 22 at 21:56

A similar graph from a another discipline is the following

enter image description here

Basically you will need to plot for each test (which I assume had a different d/S), the values of your experiment.

So for each d/S you calculated different values of the convective heat coefficient at different air speeds. So you need to plot 10 different graphs.

enter image description here

  • $\begingroup$ I understand the concept of how to make graphs using the data in a spread sheet. What I don’t understand is how does my d/s value correlate to the data we measured during the experiment(heat transfer coefficient and velocity)? Do I take the velocity (independent variable values) and divide it by the dimensionless ratio parameter value ? Do I divide the heat transfer coefficient(dependent variable values) by the d/s? I just don’t get how can I get a curve for each test we ran based on the parameters. $\endgroup$ Apr 26 at 14:14
  • $\begingroup$ if you could update your question with a graph of your data, I could have a look and tell you my opinion. $\endgroup$
    – NMech
    Apr 26 at 15:32
  • $\begingroup$ Also, IMHO, you would also be better off creating another question, because the title on this one would be a bit misleading, and you are asking too many questions in a single post. Your previous comment could very well serve as the basis of the other question, along side with the graph and a rough sketch of the experiment. $\endgroup$
    – NMech
    Apr 26 at 15:41

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