Plan Reading, Math, and System Layout
Plan reading is where the other domains get applied. A plumbing set usually includes floor plans showing fixtures and routes, an enlarged plan for tight areas, a single-line riser diagram showing stacks, branches, and vents, detail sheets, and schedules listing fixtures and equipment.
Read the title block, the scale (1/4 in = 1 ft is common for floor plans), the north arrow, and the legend before you measure anything. Symbols are fair game: gate or ball valve, check valve, floor drain (FD), roof drain (RD), water closet (WC), vent through roof (VTR), and cleanout (CO), along with material abbreviations. Never assume a pipe size that is not labeled. Notes such as 'by others' or 'not in contract' are classic traps.
Layout math is mostly right triangles and offsets. A 45 degree offset forms an isosceles right triangle: travel (the diagonal) equals offset times 1.414, and the run equals the offset. A 22-1/2 degree offset uses roughly 2.6 times the offset for travel. Add fitting take-outs to measured center-to-center lengths to get developed length before ordering pipe.
Worked example: a stack must offset 12 in horizontally using 45s. Travel = 12 x 1.414 = 16.97, about 17 in, and the horizontal run is also 12 in, so mark the pipe 17 in between fitting centers. Scale conversion is tested the same way: a 3 in line on a 1/4 in = 1 ft plan represents 12 ft in the field.