The time, \(t\), it takes to pour a certain volume of liquid from a cylindrical container depends on several factors, including the viscosity of the liquid. Assume that for very viscous liquids the time it takes to pour out two-thirds of the initial volume depends on the initial liquid depth, \(\ell\), the cylinder diameter, \(D\), the liquid viscosity, \(\mu\), and the liquid specific weight, \(\gamma\). The data shown in the following table were obtained in the laboratory.

For these tests \(\ell=45 \mathrm{~mm}, D=67 \mathrm{~mm}\), and \(\gamma=9.60 \mathrm{kN} / \mathrm{m}^{3}\).

(a) Perform a dimensional analysis, and based on the data given, determine if variables used for this problem appear to be correct. Explain how you arrived at your answer.

(b) If possible, determine an equation relating the pouring time and viscosity for the cylinder and liquids used in these tests. If it is not possible, indicate what additional information is needed.

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(Ns/m) 11 17 39 61 107 I(S) 15 23 53 83 145