Question

2. Consider a hypothetical problem where a scientist has identified six dimensional variables a,B, 7, 8, €, and o. The scientist wishes to find a functional relationship between the quantity a and other dimensional variables involved in the problem. The scientists knows that: the quantity a has units of length, ß has units of mass per volume, ✅ (length squared per time),♂ (length), € (mass times length squared per time cubed), and ☀ (time). (a) Using dimensional analysis procedure (Buckingham II theorem), determine the functional dependence of a in terms of non-dimensional parameters (or II groups). Use d, e, and øas your repeating parameters. (b) Now the scientist hypothesizes that a actually depends on either 3 or 7, but not both.To test his hypothesis, she does some experiments and collects five data points as shown in the table (each row represents a data point). Based on this data, determine whether a depends on 6 or 7. Explain your answer briefly. (Note: to find this out, you will have to plot the non-dimensional a versus non-dimensional ß and non-dimensional a versus non-dimensional y and determine if there is any relation.)

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