Physics of Buildings

Pressure tank drawdown and run-time calculator

Tank, precharge, switch and pump in; drawdown, run time and starts per hour out.

Defaults: a 20-gallon tank, 38 psi precharge, 40/60 switch and a 10 gpm pump, which fails the one-minute rule. Change any box; the working is shown below the results.

How it is calculated

The tank’s air obeys Boyle’s law with absolute pressures (gauge plus 14.7 psi at sea level) [1][2]. The water in the tank at a gauge pressure P is the tank volume minus the air volume, and the drawdown is the difference between cut-out and cut-in:

drawdown = V · (P0 + Pa) · [ 1/(Pin + Pa) − 1/(Pout + Pa) ](1)

That holds when the precharge P0 is at or below the cut-in. If it is above, the tank is empty at P0 and the drawdown is V·[1 − (P0 + Pa)/(Pout + Pa)]; at or above the cut-out it is zero. Pump timing is volume bookkeeping. The pump refills the drawdown at its flow less the household use, and the house drains it at the use rate:

run = drawdown / (Q − d)
rest = drawdown / d
starts per hour = 60 / (run + rest)(2)

The shortest run, drawdown ÷ Q, happens with no water in use. The minimum-run check compares it with one minute for motors up to ¾ hp and two minutes above, the basis of Amtrol’s sizing table [3] and in line with Franklin Electric’s one-minute minimum [4]. The most starts per hour any steady use can cause is 15 × Q ÷ drawdown, reached when the house uses half the pump’s flow.

Worked example

A 20-gallon tank at 38 psi precharge on a 40/60 switch: absolute pressures are 52.7, 54.7 and 74.7 psia, so the drawdown is 20 × 52.7 × (1/54.7 − 1/74.7) = 5.16 gallons. Amtrol lists 5.4 gallons for its 20-gallon tank at 40/60, which is the same formula with the precharge at 40 [3]. With a 10 gpm pump the shortest run is 5.16 ÷ 10 = 0.52 minutes, about 31 seconds: short of the one-minute rule. A one-minute run needs 10 gallons of drawdown, which at these settings takes a tank of about 39 gallons; Amtrol’s quick-sizing table picks its 34-gallon model for this pump, whose listed drawdown at 40/60 is 9.1 gallons, so treat the one-minute figure as a target rather than a sharp line [3].

Assumptions and valid range

  • Bladder or diaphragm tank; air at constant temperature (Boyle’s law); bladder stretch and tank-wall stretch ignored. Fast cycles compress the air partly adiabatically, which gives somewhat less drawdown than shown; makers’ tables use Boyle’s law too [5].
  • Pump flow constant across the switch band. Use the flow your pump gives between cut-in and cut-out, not its open-discharge rating.
  • Pressures are gauge pressures at the tank. Precharge is the air pressure with the tank empty of water. Atmospheric pressure defaults to 14.7 psi; at altitude it is lower, which raises the drawdown slightly.
  • Accepted inputs: tank 1–500 gal, precharge 0–100 psi, cut-in 5–100 psi, cut-out above cut-in up to 120 psi, pump 0.5–100 gpm, use 0–100 gpm. Results are rounded for display; the copied result and shared links keep your exact inputs.
  • This is an estimate for understanding and comparison, not a sizing guarantee or a code determination. Tank and pump makers’ instructions, local codes and a licensed installer decide what goes in.

Before changing anything. The pressure switch carries line voltage: power off at the breaker first, and call a licensed well or pump professional if you are unsure. Precharge checks happen with the tank drained and the pump off, and Amtrol reserves them for licensed professionals [6].

Sources

  1. Flowers, P., Theopold, K., Langley, R. & Robinson, W. R. (2019). Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law. OpenStax, Rice University. textbook Boyle's law: at constant temperature and amount, the volume of a gas is inversely proportional to its pressure (PV = constant); ideal-gas assumptions.
  2. Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI), NIST SP 811, Appendix B.8 Factors for units listed alphabetically. National Institute of Standards and Technology. standard Standard atmosphere = 1.01325 × 10⁵ Pa; 1 psi = 6.894757 × 10³ Pa; so 1 atm = 14.696 psi.
  3. Amtrol (Worthington Industries) (2019). Well-X-Trol: Next Generation Well Tanks Featuring Antimicrobial Protection (specifications and ESP quick sizing table), form MC 7025 (04/19). Amtrol, West Warwick, RI. manufacturer data sheet Drawdown at 30/50, 40/60 and 50/70 psig for WX-101 to WX-350 (e.g. WX-202, 20 gal: 6.2 / 5.4 / 4.7 gal); factory precharge 38 psig; sizing table built on 1-minute run time for pumps up to 3/4 hp and 2 minutes above; note that drawdown depends on temperature and pressure.
  4. Franklin Electric (2026). AIM Manual: 60 Hz Submersible Systems, Application · Installation · Maintenance, 2026 edition. Franklin Electric Co., Fort Wayne, IN (copy hosted by the Nebraska Department of Water, Energy, and Environment). manufacturer manual p. 4 Frequency of Starts: excessive cycling damages control components, splines, bearings and windings; run motors at least one minute; maximum starts per 24 h (300 for encapsulated motors up to 0.75 hp); p. 7 check valves hold pressure when the pump stops; VFD section: small tank, 10–20% of pump output per minute, max 200 starts/24 h.
  5. Pentair Residential Filtration (2014). WellMate In-Line Pressure Tanks data sheet, WM01 Rev D. Pentair, Milwaukee, WI. manufacturer data sheet Drawdown volume multiplier chart 'based on Boyle's Law' (e.g. 20/40: .35; 40/60: .25); tank size = pump gpm × minimum run time ÷ multiplier; recommends at least 1 minute run time.
  6. Amtrol (2019). Well-X-Trol Installation and Operation Instructions, 9015-868 MC10185 (06/19). Amtrol, West Warwick, RI. manufacturer manual How a well tank works (air above the diaphragm compressed as water enters); set precharge 2 psig below cut-in (38 psig for 40/60); adjust only with the tank drained and the system off, at ambient temperature; explosion hazard warnings; only licensed professionals should check or re-charge; licensed professional inspection yearly.