We decided that a spiral was too inefficient regarding the surface area of algae exposed. According to our calculations (seen below), the pipe would need to be around 25 meters long to attain prime surface area (80,000 cm2). An Archimedian spiral would still need a massive radius to achieve the proper surface area. The pipe in question was to have a diameter of 10 cm, with an unknown thickness. The sheer length of pipe needed was enough to deter us from pursuing this kind of shape.
Instead of a spiral, we decided to create sheets to attain the optimal surface area of 80,000 cm2. Many thin sheets of algae will be placed consecutively next to each other. We inserted a picture below for convenience.
Calculations:
Pipe with radius r = 5 cm;
Surface area of cylinder = 2πrh+2πr2
Height = 2560.32 cm, or about 25 m
Archimedian spiral would need to be about 25 m long, which is too big.