A 3-inch waste line can drop only 9 inches between its upstream end and the stack because of a beam overhead. Take the required slope for that pipe size as 1/4 inch per foot, given. What is the longest developed length that the available fall will support?
- A18 feet
Eighteen feet comes from using 1/2 inch per foot. That slope belongs to smaller drainage sizes in the slope table, not to 3-inch pipe.
- 36 feet
- C72 feet
Seventy-two feet comes from using 1/8 inch per foot. That slope is permitted for larger pipe sizes and using it on a 3-inch line both overstates the reach and understates the required grade.
- D108 feet
One hundred eight feet is the result of treating the slope as 1/12 inch per foot, which is what you get by dividing 1 inch by 12 rather than reading the slope from the table.
Why B is correct
Available fall divided by slope gives maximum developed length: 9 inches divided by 0.25 inch per foot equals 36 feet. Framing the problem as a division rather than a multiplication is what makes the constraint useful, because the fixed quantity here is the vertical space, not the run.
What this question is testing
The item tests inversion of the slope relationship to solve for length, and whether the candidate uses the slope stated in the problem rather than defaulting to a remembered value for a different pipe size.
On the job
Every remodel in a finished building runs into this. You have a ceiling height to protect below and a floor to stay under above, and the fall you have is all the fall you will get. Measure the actual available drop from the underside of the beam to the finished ceiling before you promise a fixture location, and remember to count the fitting drop at the trap arm and any offsets, because those eat into the same 9 inches.
Memory technique
Inches of drop divided by inches per foot equals feet of run.
Exam tip
Fall divided by slope gives length. Length times slope gives fall. Know which one the question is asking for.
Where to look it up
Chapter 7, the drainage piping slope table by pipe size. Minimum slopes by size differ between IPC and UPC, so use the value given in the problem and verify table values against your adopted code.