The following data were obtained in a cylindrical vessel of diameter 2.54 cm (1.0 in.) that was allowed to drain through an orifice of diameter 0.109 cm (0.043 in.).

a. Fit the equation q = kh to the first five data points and estimate the error at 140.7 seconds.
b. Suppose that q = CA_o√gh (cf. Section 2.9 and Appendix 2D). Find C. How does this value compare with the value calculated from the data in Table 2.1?

Table 2.1

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(cm) 38.1 35.6 33.0 30.5 27.9 25.4 22.9 20.3 17.8 15.2 12.7 10.2 7.6 5.1 2.5 Height (in.)* 15 14 13 12 11 10 9 8 0765432 5 Time (s) 0 6.0 12.2 18.7 25.5 32.7 40.3 48.3 56.7 66.1 76.2 87.6 101.0 117.5 140.7 1 *The data were originally measured in inches and converted to centimeters.