15.1 Head, Pressure & Volume

15.1 Head, Pressure & Volume

Quick Answer: On water, psi = feet of head × 0.433 and feet of head = psi × 2.31. Mercury, if the item uses it, is psi = inches Hg × 0.491. Gallons in a full round pipe or tank are 0.0408 × D² × L (D in inches, L in feet). A rectangular tank is cubic inches ÷ 231 or cubic feet × 7.48. Convert gas input with CFH ≈ BTU/h ÷ 1,000 (natural gas) or ÷ 2,500 (undiluted propane). Part II is closed book: 5 general trade-calculation items inside 40 items, 160 minutes, 70 percent on the part, non-programmable calculator only (PSI CIB October 3, 2025).

This chapter is independent OpenExamPrep teaching for the Massachusetts journeyman plumber exam. It explains who provides the resource and which PSI Part II topics it helps you study. It is not a Board publication and it does not claim official approval.

The October 3, 2025 Candidate Information Bulletin puts General Trade Calculations at 5 items on Journeyman Plumber (Part II — Practical). The session is 40 items, 160 minutes, 70 percent, scored on its own. Bring only a non-programmable, non-printing, silent, battery-operated calculator with no alphabet keys. 248 CMR and NFPA books stay outside. These five items are not DFU table look-ups from Chapter 11 and not isometric symbol reading from Chapter 16. They are shop math you must still do when the code book is in the car.

You need 28 correct of 40 to clear 70 percent. Missing every calculation item spends 5 of the 12 misses you can afford. Do the arithmetic on scrap paper, then key it once.

Formula table — water, mercury, gallons, gas

0.433 and 2.31 undo each other: 1 ÷ 0.433 ≈ 2.31. If an item gives head and you want pressure, multiply by 0.433. If it gives pressure and you want feet of water column, multiply by 2.31. Do not multiply a psi reading by 0.433 and call it feet.

0.491 psi per inch of mercury is the same idea for a mercury instrument. A check that should look familiar: 30 × 0.491 = 14.73 psi, about one atmosphere. 14 inch water column (Massachusetts default low-pressure gas in 248 CMR 4.03) is a gas unit from Chapter 2, not a water-head number; 1 psi ≈ 27.7 inches of water column. Do not run 14 × 0.433.

The 0.0408 pipe formula is cylinder volume with units already baked in:

gal = (π × D² / 4) × (L × 12) ÷ 231 = (π / 77) × D² × L ≈ 0.0408 × D² × L

Use the inside diameter the item prints. If the stem says “2-inch pipe” and gives no actual ID, the exam math uses D = 2. On the job, Schedule 40 ID is smaller than the nominal stamp; Part II is not asking you to memorize a wall-thickness chart.

231 cubic inches per gallon and 7.48 gallons per cubic foot are the rectangular-tank pair. Mixing them — feet in one dimension, inches in the others, then dividing by 231 — is how a 90-gallon tank becomes a 12-gallon wrong answer.

Worked example 1 — Brockton head and pressure

A roof tank’s water surface stands 55 feet above a first-floor faucet (static, no flow).

Pressure at the faucet = 55 × 0.433 = 23.815 psi → 23.8 psi.

Reverse check: 23.815 × 2.31 = 55.01 feet. The two factors closed.

Same building, city main 70 psi at the curb, faucet 32 feet above that main:

Head equivalent of 32 feet = 32 × 0.433 = 13.856 psi.

Static leftover at the faucet = 70 − 13.856 = 56.144 psi → 56.1 psi.

Elevation ate pressure. A 70 psi gage at the street is not 70 psi at a third-floor hose bibb. Flowing losses in the pipe are a separate friction problem; this item is static head only.

Mercury check, if the stem shows a vacuum or a mercury gage: 16 inches of mercury × 0.491 = 7.856 psi. That is not 16 × 0.433.

Worked example 2 — gallons in pipe, then weight

How many gallons in 120 feet of 4-inch ID pipe, and what does that water weigh?

gal = 0.0408 × 4² × 120 = 0.0408 × 16 × 120 = 0.6528 × 120 = 78.336 gallons.

Check with feet and 7.48:

Radius = 2 inches = 2/12 = 1/6 ft.

Volume = π × (1/6)² × 120 = 3.1416 × 0.027778 × 120 = 10.472 cu ft.

Gallons = 10.472 × 7.48 ≈ 78.33 gallons. The shortcut survived.

Weight ≈ 78.336 × 8.33 ≈ 652.5 pounds (about 653 lb on a three-digit display). That is why a long charged sprinkler main or a solar loop is not “just pipe.”

A shorter piece you can do in your head: 10 feet of 2-inch ID → 0.0408 × 4 × 10 = 1.632 gallons. 50 feet of 2-inch → 8.16 gallons. If you forget to square D you get half of that (0.0408 × 2 × 50 = 4.08), which is a classic distractor.

Worked example 3 — round tank, rectangular tank, BTU-to-CFH recap

Round tank. A vertical storage tank is 48 inches inside diameter and holds 5 feet of water.

gal = 0.0408 × 48² × 5 = 0.0408 × 2,304 × 5 = 94.0032 × 5 = 470.02 gallons.

Check: radius 2 ft, π × 2² × 5 × 7.48 = 12.566 × 5 × 7.48 = 62.83 × 7.48 ≈ 470.0 gallons.

Pressure on the bottom from that 5-foot water depth: 5 × 0.433 = 2.165 psi. Diameter does not change static pressure; depth does. A 48-inch tank and a 12-inch riser of the same water height read the same psi at the bottom.

Rectangular tank. A steel box 48 in. × 24 in. × 18 in. inside:

48 × 24 × 18 = 20,736 cubic inches.

20,736 ÷ 231 = 89.766 gallons → 89.8 gallons.

Same box in feet: 4 × 2 × 1.5 = 12 cu ft × 7.48 = 89.76 gallons. If you treat 48, 24, and 18 as feet and then divide by 231, you invent thousands of gallons. If you stop at 12 cu ft and never multiply by 7.48, you report 12 gallons.

BTU versus CFH recap (Chapter 2.2 does the longest-length table walk; Part II still asks the conversion). Capacity tables are cubic feet per hour, not BTU/h.

A 96,000 BTU/h natural-gas furnace, conventional 1,000 BTU per cubic foot:

96,000 ÷ 1,000 = 96 CFH.

Same nameplate on undiluted propane at about 2,500 BTU per cubic foot:

96,000 ÷ 2,500 = 38.4 CFH.

38.4 CFH is not a license to open a natural-gas 0.60-specific-gravity table. Propane is denser; it uses the LP table family. CFH is demand, not diameter. 248 CMR 5.06 left NFPA 54-2012 Chapter 6 unamended; Massachusetts still defaults ordinary building piping to 0.5 PSIG / 14 inch water column. This section only gets the number you take to that method.

If the item prints a heating value, divide by that value. Do not force 1,000 when the stem already says 1,050.

What the five items are not

They are not 248 CMR 10.15 Table 2 DFU columns (Chapter 11). They are not offset travel (Section 15.2) or grade between inverts (Section 15.3), except that those sections reuse the same calculator. A head-pressure stem that also mentions a 4-inch drain is still a 0.433 problem unless it asks for fall.

Official resources

• PSI Massachusetts plumbing Candidate Information Bulletin — Part II 40 items / 160 minutes / 70 percent; General Trade Calculations 5; calculator limits (CIB dated October 3, 2025)
• 248 CMR 4.03 / 5.06 (Mass.gov fuel gas) — 0.5 PSIG / 14 inch WC default; Chapter 6 pipe sizing unamended
• Chapter 2.2 of this guide — longest-length method after you have CFH