An open concrete flume is to be constructed to carry water from a plant unit to a cooling lake by gravity flow. The flume has a square cross section and is $1500 \mathrm{ft}$ long. The elevation at the upstream end is $10 \mathrm{ft}$ higher than the lower discharge end. If the flume is to be designed to carry $10,000 \mathrm{gpm}$ of water when full, what should its size (i.e., width) be? Assume rough cast concrete.