Trace every number back to a condition
- 01Stored volume × expansion factor
50 US gal × 0.0150 = 0.75 US gal of expanded water.
- 02Apply the pressure factor
At 60→80 psig: DPF = (80 + 14.7) / (80 − 60) = 4.735.
- 03Keep both volume requirements
Theoretical total = 0.75 × 4.735 ≈ 3.55 US gal. Expanded-water acceptance is a separate check.
Expansion factors and the 40°F starting condition
The following factors come from Amtrol MC10007 page 2, Table 1 (opens source in a new tab). Their base is 40°F. The percentage column below is calculated directly from the coefficient, so its displayed precision can differ from the rounded percentage printed in the manufacturer table. No interpolation or substitute factor is silently used.
| Design water temperature | Factor from 40°F | Calculated increase |
|---|---|---|
| 100°F | 0.0062 | 0.62% |
| 120°F | 0.0100 | 1.00% |
| 130°F | 0.0124 | 1.24% |
| 140°F | 0.0150 | 1.50% |
| 150°F | 0.0179 | 1.79% |
| 160°F | 0.0209 | 2.09% |
| 170°F | 0.0242 | 2.42% |
| 180°F | 0.0276 | 2.76% |
The ideal air-cushion calculation
Expanded water = stored US gal × factor
AF = (Pmax − Pi) / (Pmax + 14.7)
DPF = 1 / AF
Ideal minimum total = expanded water × DPF
Pressures entered as psig are converted using a fixed 14.7 psia atmospheric reference. The ideal model assumes isothermal compression and a matching pre-charge condition. Altitude, actual gas/diaphragm behavior and product acceptance ratings are not modeled. A displayed decimal is not a tolerance guarantee.
Amtrol’s 240 gal / 150°F / 60→125 psig example uses a rounded table DPF of 2.1 and reports about 9.0 gal. Applying the continuous formula to those inputs gives approximately 9.23 gal before selection. These are different rounding paths; our worksheet uses the equation, not a claim that an exact result must equal the rounded table. Both acceptance and total volume must be checked under the actual manufacturer selection method.
A deliberately bounded explanatory worksheet
The static-pressure range is 20–80 psig; the design-ceiling range is 50–125 psig and must exceed static. The entered ceiling must not exceed the entered component limit or 85% of the entered relief rating. The latter adopts a margin from Watts ETP · source record as our conservative scope restriction. Combining this guard with Amtrol’s factor does not make the worksheet an approved implementation of either brand’s full method. Temperatures are design inputs, not instructions to adjust a thermostat.
Cold-start recovery and efficiency
The energy model uses 8.33 lb/US gal, 1 BTU/(lb·°F), 3,412 BTU/h per kW and the user’s stated heat-to-water efficiency. It assumes a constant active input and uniform whole-tank cold start, with no draw or additional losses. Inputs outside the gas/resistance model are withheld. It does not generate certified FHR or accept UEF as thermal efficiency. The published FHR definition (opens source in a new tab) and manufacturer UEF guidance (opens source in a new tab) describe those separate quantities.
Illustrations, evidence and corrections
The source-linked HTML diagrams and calculated bars explain exact paths, assumptions and quantities. Generated editorial illustrations help distinguish equipment and conceptual states; they are not actual equipment photographs, measured events, manufacturer documents or installation drawings. Each illustration has a caption stating its purpose and limitations. Refer to the labeled diagrams and primary documents for technical conditions.
Sources are attached to the relevant page and reviewed on 2026-11-15. Current manuals for the actual model and applicable professional/local requirements take precedence. This site does not diagnose faults, supply universal pressure-adjustment instructions, assert nationwide code compliance or promise traffic or rankings. If a source changes or conflicts with the installed-model instructions, retain the discrepancy and stop using the affected result until it is reviewed.
Sources and limits
Reviewed 2026-11-15. The linked method and your model manual take precedence over an explanatory example.
- Amtrol MC10007 · sizing and placement (opens source in a new tab)
03/19. Pages 2–3: 40°F-base factors, DPF, pre-charge example and placement. Manufacturer-specific guidance; local and model requirements still apply.
- Amtrol · plumbing and hot-water support (opens source in a new tab)
Live FAQ. Pre-charge matching, cold-inlet location and supported orientation. Use the installation manual for the actual model.
- Watts · potable expansion sizing conditions · source record
Live tool instructions. Distinct initial/final pressure and temperature conditions. Its 85%-of-relief ceiling and 90°F starting-water note must not be silently mixed with another method.
- A.O. Smith University · expansion calculator (opens source in a new tab)
Live tool. Separate supply pressure, pre-charge, relief rating and temperatures; separate acceptance and total-volume outputs. Interface read; no independent certification of its algorithm.
- Watts LFRC105 · bypass and high pressure (opens source in a new tab)
IS-LFRC105 1633 (2016). Page 1: this regulator’s bypass behavior and possible high-pressure causes. Not a rule for every PRV.
- A.O. Smith · relief-valve Bulletin 52 (opens source in a new tab)
Bulletin 52; publication date not stated. Temperature/pressure relief roles and rating limits. An observation form cannot establish a specific fault.
- A.O. Smith · what UEF measures (opens source in a new tab)
Live explainer. UEF is a standardized usage-based efficiency rating; it is not a direct heat-to-water efficiency input for this cold-start equation.
- U.S. DOE · residential water heater guidance (opens source in a new tab)
Guidance updated May 2024. Heat-pump modes use the compressor and resistance elements differently. Supports excluding a single fixed resistance model from heat-pump recovery predictions.
- 10 CFR 430 · Appendix E, first-hour rating (opens source in a new tab)
2025 published edition, Appendix E §1.5. FHR begins with a fully heated non-flow-activated heater. This reference establishes the distinction, not current legal compliance or a certified rating for any product.
