Air entrainment in a draining tank (Figure 3A.7) a molasses storage tank 60 ft in diameter is to be built with a draw-off line 1 ft in diameter, 4 ft from the sidewall of the tank and extending vertically upward I ft from the tank bottom. It is known from experience that, as molasses is withdrawn from the tank, a vortex will form, and, as the liquid level drops, this vortex will ultimately reach the draw-off pipe, allowing air to be sucked into the molasses. This is to be avoided. It is proposed to predict the minimum liquid level at which this entrainment can be avoided, at a draw-off rate of 800 gal/min, by a model study using a smaller tank. For convenience, water at 68^oF is to be used for the fluid in the model study. 

Determine the proper tank dimensions and operating conditions for the model if the density of the molasses is 1.286 g/cm³ and its viscosity is 56.7 cp. It may be assumed that, in either the full-size tank or the model, the vortex shape is dependent only on the amount of the liquid in the tank and the draw-off rate; that is, the vortex establishes it-self very rapidly.