18.3 Offsets, Travel, and the Plumbing Math the Exam Assumes

What the bulletin tells you to memorize

The PSI Candidate Information Bulletin is explicit:

It is your responsibility to know and to be able to use basic plumbing theory formulas since such knowledge may be required to work problems in the job task area of the examination entitled Job Task X: Calculations. Formulas will not be provided to you at the test center and are not allowed in during the test.

An on-screen calculator is provided (Security Procedures). So you will have arithmetic, but not the relationships. Everything below has to be in your head.

Offsets: the geometry

A simple offset moves a pipe sideways while it continues in the same general direction. Three dimensions describe it:

The fittings form a right triangle in which the offset is the side opposite the fitting angle.

                    fitting
                    /|
           travel  / | offset
                  /  |
        ---------+---+----------
              run

Since the offset is opposite the fitting angle A:

travel = offset / sin(A)
run    = travel x cos(A) = offset / tan(A)

The constants

Two anchors make the table easy to reconstruct:

• 45 degrees is the one everybody knows: 1.414 (the square root of 2) for travel, and 1.000 for run — because at 45 degrees the pipe advances exactly as far as it offsets.
• 60 degrees gives 1.155 travel and 0.577 run — a steep turn that offsets a lot for very little advance.

And the direction of the pattern: shallower fittings need much more pipe and much more room. A 6-inch offset takes 8.5 inches of travel with 45s and 34.6 inches with 11-1/4s.

Worked simple offsets

Offset of 18 inches with 45-degree fittings:

• Travel = 18 x 1.414 = 25.45 inches
• Run = 18 x 1.000 = 18 inches

Offset of 18 inches with 22-1/2 degree fittings:

• Travel = 18 x 2.613 = 47.03 inches
• Run = 18 x 2.414 = 43.45 inches

Offset of 18 inches with 60-degree fittings:

• Travel = 18 x 1.155 = 20.79 inches
• Run = 18 x 0.577 = 10.39 inches

Same offset, three answers: the 45 needs 25 inches of room along the run, the 22-1/2 needs 43, and the 60 needs only 10.

Working backward

Items often give you the travel and ask for the offset, or give the run and ask for the travel. Divide instead of multiplying:

• Travel of 30 inches on 45s: offset = 30 / 1.414 = 21.22 inches
• Run of 24 inches on 22-1/2s: offset = 24 / 2.414 = 9.94 inches, travel = 9.94 x 2.613 = 25.98 inches

Cut length is not travel. Travel is the center-to-center distance between fittings. The pipe you cut is travel minus the take-off of each fitting — the distance from the fitting's center to the end of its socket or hub. Take-offs come from the fitting manufacturer.

Rolling offsets

A rolling offset moves the pipe in two directions at once — up or down and left or right. Solve it in two steps:

1. Find the true offset with the Pythagorean theorem:

true offset = square root of (vertical offset squared + horizontal offset squared)

1. Apply the ordinary constant to the true offset.

Worked rolling offset

A pipe must rise 12 inches and move 9 inches to the side, using 45-degree fittings.

1. True offset = sqrt(12² + 9²) = sqrt(144 + 81) = sqrt(225) = 15 inches
2. Travel = 15 x 1.414 = 21.21 inches
3. Run = 15 x 1.000 = 15 inches

Recognize the 3-4-5 family (9-12-15) and the first step is instant.

Grade, fall and developed length

Worked: a 4-inch building drain runs 72 feet at the Table 704.1 minimum of 1/8 inch per foot.

• Fall = 0.125 x 72 = 9 inches

Worked in reverse: a sewer must drop 22 inches over 160 feet.

• Available slope = 22 / 160 = 0.1375 inch per foot, which exceeds 1/8 (0.125) — a 4-inch or 6-inch line at minimum slope fits.

Pressure and head

The relationships the exam assumes:

Worked: what pressure is lost rising 40 feet?

• 40 x 0.433 = 17.32 psi

Worked: how high will 60 psi lift water?

• 60 x 2.31 = 138.6 feet

Worked: what is the static pressure at the base of a 10-foot water column — the DWV water test of IPC 312.2?

• 10 / 2.31 = 4.33 psi

That last one is the arithmetic behind "a 10-foot head" appearing everywhere in Section 312.

Appendix E uses the same relationship in its sizing procedure: deduct 0.5 psi for each foot the highest outlet is above the source. The code rounds 0.433 up to 0.5 as a conservative design allowance.

Pipe volume and area

The 0.0408 constant is derived, not memorized blindly:

area (sq in) = 0.7854 x d squared
volume per foot (cu in) = 0.7854 x d squared x 12 = 9.4248 x d squared
gallons per foot = 9.4248 x d squared / 231 = 0.0408 x d squared

Worked: how many gallons are in 150 feet of 4-inch pipe?

• 0.0408 x 4² = 0.0408 x 16 = 0.653 gallons per foot
• 0.653 x 150 = 97.9 gallons

Worked: what is the circumference of a 6-inch roof drain, for sizing a secondary scupper under IPC 1108.3?

• 3.1416 x 6 = 18.85 inches of scupper width, at a minimum height of 4 inches.

Storm and supply conversions

A calculation drill