System Volume, Expansion Volume, and the Tank Size

The piping and tank volume in gallons, the expansion factor at the water temperature, the CT formula for the required tank, the pre-charge pressure, and the closed-system rule the plumbing code writes.

The sizing formula is CT = V x delta / (1 - Pa/Pw), where V is the system volume in gallons, delta is the expansion factor at the water temperature, Pa is the tank air charge at the system fill pressure, and Pw is the relief valve setting. A closed system with a check valve, a PRV, a meter check, or a boiler has nowhere to send the expanded water, so the plumbing code asks for expansion control and a pressure-relief device.

—System volume in gallons
—Expansion volume at temperature
—The CT formula and the tank size
—Tank pre-charge and the check
—The closed-system rule
—Install, test, and the relief line
How the math works
  • System volume (V): the water in the piping plus the water in the storage tank. Copper Type L holds 0.0196 gal per ft at 3/4 in, 0.0368 at 1 in, 0.0872 at 1-1/2 in, and 0.1551 at 2 in. A 50 gal heater with 60 ft of 3/4 in and 40 ft of 1 in is 97 gal of system volume, and a typical single-family home runs 70 to 120 gal.
  • The expansion factor (delta): the volumetric growth of water from the 40 F chart line to the hot temperature: 0.0224 at 100 F, 0.0286 at 110 F, 0.0357 at 120 F, 0.0466 at 140 F, 0.0524 at 150 F, 0.0695 at 180 F, 0.0827 at 200 F. Water at 140 F in a 100 gal system grows by 4.7 gal.
  • The sizing formula: CT = V x delta / (1 - Pa/Pw), where Pa is the tank air charge at the system fill pressure and Pw is the relief valve setting. A lower fill pressure and a higher relief setting give a bigger denominator and a smaller required tank; a 90 psi system with a 90 psi relief is the worst case, and a 55 psi system on a 150 psi relief is the standard case.
  • Pre-charge: the air side of a bladder and diaphragm tank is set at the system fill pressure, checked at the Schrader valve with the system drained. The charge is checked annually with a gauge, and a lost charge is the most common reason a system with a tank still drips at the relief valve.
  • The closed-system rule (IPC 501.16.1): a system with a check valve, a meter check, a PRV, a backflow preventer, a pressure-managing valve, and a boiler is closed and gets expansion control with a pressure-relief device. A water heater in a closed system gets a TPR valve at the 150 psi and 210 F setting with the discharge tube run to a floor drain, and a thermal relief valve on the hot line where the local code asks.
Planning tool on the International Plumbing Code 501.16.1, 504, and 505 and the water-heater TPR requirements as adopted locally, with the standard expansion-tank sizing chart and manufacturer formulas. The code edition in force, the local amendment, the permit, the inspection, the plumbing licensing requirement, the potable water rules, the boiler code, the backflow assembly test rule, and the pressure zone and PRV setting rule are jurisdiction calls. A well system with a bladder tank, a constant-pressure variable-speed pump, a boiler with no expansion tank, a hydronic system with a separator, a recirculating loop with a check valve, a solar thermal system, a combi boiler, a tankless with a temperature switch, a softener on a bypass, a fire sprinkler system with a check valve, an RV and a marine system, a tiny home, a cabin on a cistern, and a system on a high-rise riser are all expansion and relief questions with a device schedule, and a licensed plumber signs it. A gas and an electric water heater TPR valve is not a plumbing fitting and is a 150 psi 210 F device with a manufacturer listing, and a TPR valve with no discharge tube is a failed inspection.

Do I need an expansion tank?

Yes when the system is closed: a check valve, a pressure-reducing valve, a meter with a built-in check, a backflow preventer, a boiler, and a well pump check all close the system, and the plumbing code asks for expansion control with a pressure-relief device (IPC 501.16.1). An open system with no check valve sends the expanded water back up the cold feed, so a tank is not required by code, and a tank is still the fix for a relief valve that drips.

What size expansion tank do I need?

CT = V x delta / (1 - Pa/Pw): the system volume times the expansion factor at the hot temperature, divided by one minus the fill pressure over the relief setting. A 97 gal system at 140 F on a 55 psi fill with a 150 psi relief needs 7.1 gal of expansion volume, so the answer is the 14 gal tank: at a 55 psi fill and a 150 psi relief an 8 gal can accepts only 5.1 gal. Most single-family homes land in the 4 to 8 gal size, and a large home with a long run and a recirculating loop lands in the 10 to 14 gal size.

Where does the expansion tank go?

On the cold-water line between the check valve or PRV and the water heater, in a location that will not freeze, with a tee, an isolation valve, and a drain valve at the tank, on a 3/4 in connection with the tank supported off the floor. The tank goes above the heater on a garage and a crawl install, and a tank installed at the heater inlet with no isolation valve is a tank that cannot be changed without draining the house.

What pressure do I set the tank to?

The air side of a bladder and diaphragm tank is pre-charged to the system fill pressure, so 55 psi on a 55 psi house, checked with a gauge at the tank valve with the system drained and the isolation valve closed. The factory charge on a new tank is read off the nameplate and reset at install, and the charge is checked once a year. Set the house pressure first with the PRV: a 55 to 60 psi house is the standard setting, and a house over 80 psi is a PRV and a relief problem before it is a tank problem.

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