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 $\frac{2}{3}$ of the initial volume depends on

the initial liquid depth, $l,$ the cylinder diameter, $D,$ the liquid viscosity, $,$ and the

liquid specific weight, $.$ The data shown in the following table were obtained in the

laboratory. For these tests $l=54mm,D=67mm,$ and $=9\mathrm{.}60\frac{N}{m^3}.$

$($a$)(5$ Points$)$ Perform a dimensional analysis, and based on the data given, determine

if the variables used for this problem appear to be correct. Explain how you

arrived at your answer.

$($b$)(5$ Points$)$ If possible, determine an equation relating the pouring time and vis$-$

cosity for the cylinder and the liquids used in these tests. If it is not possible,

indicate what additional information is needed.