The building drain leaves the foundation with its invert at elevation 100.60 feet. The invert of the public sewer at the point of connection is at elevation 96.85 feet, and the building sewer will run 340 feet of developed length between those two points. Take the minimum slope for the 6-inch pipe being used as 1/8 inch per foot, given. What grade is available, and does it work?
- AAbout 0.011 inch per foot, far below the minimum, so the sewer has to be pumped
This divides feet of fall by feet of run and then reports the answer as inches per foot. The result, 0.011, is the grade in feet per foot; multiplying by 12 converts it to the 0.13 inch per foot the question asks for.
- BAbout 3.75 inches per foot, well above the minimum, so gravity drainage works easily
This treats the 3.75 foot elevation difference as though it were the slope itself. A grade of nearly four inches per foot would be a stair, not a sewer.
- CAbout 0.13 inch per foot, which falls short of the minimum, so the sewer has to be pumped
The arithmetic here is right but the comparison is wrong. One eighth of an inch is 0.125, and 0.13 is larger than 0.125, so the available grade clears the minimum rather than falling short of it.
- About 0.13 inch per foot, which meets the minimum, so gravity drainage works
Why D is correct
Fall is 100.60 minus 96.85, or 3.75 feet, which converts to 45 inches. Divided by 340 feet that is about 0.13 inch per foot, just above the 0.125 inch per foot the minimum works out to, so the line drains by gravity. The margin is two and a half inches over the whole run, which means the grade has to be held carefully during installation.
What this question is testing
This checks whether you can convert an elevation difference into a grade in inches per foot without a unit slip, and whether you can compare a decimal grade against a fractional minimum correctly.
On the job
This is the calculation that decides whether a building gets a gravity sewer or an ejector package, and it is worth doing before the foundation elevation is set rather than after. When the margin is this thin, the things that eat it are real: a deeper tie-in than the utility drawing showed, an unexpected rock ledge, or a crew that lays the first hundred feet a little rich and runs out of fall at the end.
Memory technique
Feet of fall times twelve, divided by feet of run, equals inches per foot.
Exam tip
Convert the fall to inches before dividing, and turn the fractional minimum into a decimal before comparing.
Where to look it up
Minimum slope by pipe size is in IPC 704.1; building sewer requirements are in IPC Chapter 7. UPC sets its own minimum slopes and applies them to different size breaks than the IPC does, so check the figure against the code your state has adopted.