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 2/3 of the initial volume depends on the initial liquid depth (), the cylinder diameter (D), the liquid viscosity (4), and the liquid specific weight (). The data shown in the following table were obtained in the laboratory. For these tests, it is known that: 1= 45 mm, D = 67 mm, and y= 9.60 kN/m³. (a) Perform a dimensional analysis and based on the data given, determine if variables used for this problem appear to be correct; (b) If it is 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 informot dod

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.