A chemical intermediate with a specific gravity of 1.00 will be diverted to an empty flat-bottom tank with a diameter of 6 feet that is 12 feet high at a flow of 4 gallons per minute. Approximately how long will it take to fill the tank?
A. 6 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. 14 hours
The tank volume can be calculated using the given dimensions as (3.14 x 3 x 3 x 12) or 339 cubic feet. The volume can then be converted to gallons as (339 x 7.48 gallons/cubic foot) or 2,537 gallons, from which the fill time can be calculated as (2,537/4) or 634 minutes or 10.6 hours.
The flow will vary somewhat, so the tank will take approximately 10 hours to fill (Answer C). However, it may be pragmatic to start checking the tank level after (say) six or eight hours to reduce the probability of creating an overflow condition due to a higher-than-normal flow rate.
Additional complicating factors
The working volume of the tank will likely be somewhat less than the calculated value because the tank should not be filled to the overflow pipe, thus providing a margin of safety to avoid overflowing the tank.