14.3 Plumbing Math III: Gas Math, Meter Readings, BTU & Pressure Conversions

14.3 Plumbing Math III: Gas Math, Meter Readings, BTU & Pressure Conversions

Quick Answer: cfh = (3,600 × dial size) ÷ seconds per revolution. The official PSI sample question — a one-cubic-foot hand that revolves once in 84 seconds — gives 3,600 ÷ 84 = 42.86, which rounds to 43 cubic feet per hour.

Gas Appliances and Piping is 40 of the 100 scored questions, so the gas-flavored arithmetic inside the Plumbing Mathematics domain is worth far more than its 7-question share suggests. All of it rests on three ideas: a gas meter is a volume counter you can time with a stopwatch, gas volume converts to heat through a heating value, and fuel-gas pressure is measured in a unit that must be converted before it means anything in psi.

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Clocking a Diaphragm Gas Meter

A residential diaphragm meter carries one or two small test dials (also called proving dials), each labeled with the volume that one full revolution represents — typically 1/2, 1, 2, 5 or 10 cubic feet. To clock an appliance, shut off every other gas appliance including standing pilots, fire the appliance under test at high fire until it reaches steady state, then time one complete revolution of the test hand.

cfh = (3,600 × dial size in cubic feet) ÷ time in seconds

The 3,600 is nothing more than the number of seconds in an hour, so the formula reads "cubic feet per second, scaled up to an hour."

Worked Example 1 — The Official PSI Sample Question

"The one-cubic-foot hand revolves once in 84 seconds. Gas is passing through the meter at how many cubic feet per hour?"

• (3,600 × 1) ÷ 84 = 3,600 ÷ 84 = 42.857
• Rounded: 43 cubic feet per hour

Worked Example 2 — The Same Timing on a 2-Cubic-Foot Dial

You timed the 2 ft³ hand because the 1 ft³ hand was spinning too fast to read, and it took the same 84 seconds:

• (3,600 × 2) ÷ 84 = 7,200 ÷ 84 = 85.7 cfh

Twice the volume per revolution in the same time means exactly twice the flow. Dropping the dial-size multiplier is the most common arithmetic error on this problem type.

Worked Example 3 — A 1/2-Cubic-Foot Dial

A furnace turns the 1/2 ft³ hand once in 22 seconds:

• (3,600 × 0.5) ÷ 22 = 1,800 ÷ 22 = 81.8 cfh

Turning Cubic Feet into BTUs

A British thermal unit (BTU) is the heat required to raise one pound of water 1°F. Gas volume becomes heat through the fuel's heating value:

The IFGC 2018 pipe-sizing tables in Section 402.4 are built on these values, which is why converting an appliance's nameplate input rating into cfh is always the first step of a sizing problem.

Worked Example 4 — Total Connected Load

Run the identical appliances on propane and the required volume falls to 240,000 ÷ 2,500 = 96 cfh, because each cubic foot of propane carries roughly 2.5 times the heat of natural gas. Note that the BTU/h load has not changed — only the volume of gas needed to deliver it.

Worked Example 5 — Verifying an Appliance's Actual Input

The 100,000 BTU/h furnace above is clocked, and its 1 ft³ dial turns once in 36 seconds. The utility reports a heating value of 1,030 BTU per cubic foot.

• cfh = 3,600 ÷ 36 = 100 cfh
• BTU/h = 100 × 1,030 = 103,000 BTU/h

That is 3 percent over nameplate, which is normal variation in gas quality. A clocked reading 15 or 20 percent high means the appliance is genuinely overfired and the manifold pressure or the burner orifice is wrong.

Percent Efficiency

Efficiency = output ÷ input, expressed as a percent. An 80 percent furnace with a clocked input of 103,000 BTU/h delivers 103,000 × 0.80 = 82,400 BTU/h of useful heat. Turned around, an appliance that must deliver 60,000 BTU/h of output at 78 percent efficiency requires 60,000 ÷ 0.78 = 76,923 BTU/h of input — and it is input, never output, that gas piping is sized for.

Pressure Conversions

Fuel gas reaches appliances at pressures well below 1 psi, so the trade measures it in inches of water column (in. w.c.) — the height of a water column the gas will support in a manometer.

Two directions, one constant: psi × 27.7 = in. w.c., and in. w.c. ÷ 27.7 = psi. One ounce per square inch works out to 27.7 ÷ 16 = 1.73 in. w.c., which is how older gas literature states very low pressures.

Worked Example 6. Convert a 2 psi service to inches of water column: 2 × 27.7 = 55.4 in. w.c. Convert a manometer reading of 6.5 in. w.c. to psi: 6.5 ÷ 27.7 = 0.235 psi.

The bottom row of that table explains a field rule. IFGC 2018 Section 406.4.1 requires a test pressure of at least 1 1/2 times the maximum working pressure but never less than 3 psig. Three psig is 83 inches of water column — far past the range of any manometer — so the test is read on a spring or digital gauge, not on a water column.

The Water-Heating Formula

One BTU raises one pound of water 1°F, and the specific heat of water is 1.0, so:

BTU = weight in pounds × temperature rise (°F) × 1.0

Because water is stored and sold by the gallon, substitute 8.33 pounds per gallon:

BTU = gallons × 8.33 × temperature rise

Worked Example 7 — Heating a Full Tank

How much heat is required to raise a full 50-gallon water heater from a 50°F inlet to a 130°F setting?

• Temperature rise = 130 − 50 = 80°F
• 50 gal × 8.33 lb/gal = 416.5 pounds
• 416.5 × 80 × 1.0 = 33,320 BTU

Worked Example 8 — Recovery Rate

A 40,000 BTU/h gas water heater with 75 percent recovery efficiency must produce a 90-degree rise.

GPH = (input BTU/h × efficiency) ÷ (8.33 × temperature rise)

• (40,000 × 0.75) ÷ (8.33 × 90)
• = 30,000 ÷ 749.7
• = 40.0 gallons per hour

Omit the efficiency factor and you get 40,000 ÷ 749.7 = 53.4 GPH — a number that will be waiting in the answer choices every time.

Exam Trap: On clocking problems the distractor is nearly always the answer you get by ignoring the dial size: a 2-cubic-foot dial timed at 84 seconds is 85.7 cfh, but "43" — the 1-cubic-foot answer — will be offered right beside it. On pressure problems the trap is swapping the two water constants. 27.7 is inches of water column per psi; 2.31 is feet of head per psi. They describe the very same column of water (2.31 ft × 12 = 27.7 in), so any answer that is off by a factor of 12 means you reached for the wrong one.