Consider a hypothetical problem where a scientist has identified six dimensional variables a, B, 7, 8,...

  

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Consider a hypothetical problem where a scientist has identified six dimensional variables a, B, 7, 8, €, and p. 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), 8 (length), e (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 as your repeating parameters. (b) Now the scientist hypothesizes that a actually depends on either ß or y, 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 and non-dimensional a versus non-dimensional y and determine if there is any relation.) a (m) 3 (kg/m³) y (m²/s) 8 (m) e (kg.m²/s³) (s) 0.9 4.0 1.2 0.31 2.01 0.19 2.3 4.7 1.7 2.52 0.4 3.4 0.9 0.29 5.0 2.9 0.6 0.062 4.9 3.2 0.7 0.43 5.1 3.1 2.6 4.0 1.85 3.54 436.1 2.13 Consider a hypothetical problem where a scientist has identified six dimensional variables a, B, 7, 8, €, and p. 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), 8 (length), e (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 as your repeating parameters. (b) Now the scientist hypothesizes that a actually depends on either ß or y, 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 and non-dimensional a versus non-dimensional y and determine if there is any relation.) a (m) 3 (kg/m³) y (m²/s) 8 (m) e (kg.m²/s³) (s) 0.9 4.0 1.2 0.31 2.01 0.19 2.3 4.7 1.7 2.52 0.4 3.4 0.9 0.29 5.0 2.9 0.6 0.062 4.9 3.2 0.7 0.43 5.1 3.1 2.6 4.0 1.85 3.54 436.1 2.13

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a Using dimensional analysis procedure Buckingham II theorem we can determine the functional depende... View the full answer