A horizontal drum, a cross-section of which is shown

Chapter 2, Problem 2.16

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A horizontal drum, a cross-section of which is shown below, is being filled with benzene (density 0:879 g/cm3) at a constant rate m_ (kg/min). The drum has a length L and radius r, and the level of benzene in the drum is h. The expression for the volume of benzene in the drum is V L r2 cos1 r h r r h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 r h 2 q (a) Show that the equation gives reasonable results for h 0, h r, and h 2r. (b) Estimate the mass of benzene (kg) in the tank if L 10 ft, r 2 ft, and h 4 in. (c) Suppose there is a sight glass on the side of the tank that allows observation of the height of liquid in the tank. Use a spreadsheet to prepare a graph that can be posted next to the sight glass so that an operator can estimate the mass that is in the tank without going through calculations like that in Part (b). 2 r