Chris Collins

Tools · building

Pumps, tanks and hot water

Size a thermal expansion tank from the heater volume, temperatures and pressures; a well pressure tank for a minimum pump run time; a well pump's total dynamic head with its curve against the system curve; a hot-water recirculation pump's flow and head from the loop's heat loss; water-heater recovery and a rough first-hour figure for gas, electric and heat-pump heaters; and a tankless heater from flow and temperature rise.

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How to use it

The equipment side of a house’s water: the tanks that soak up expansion and pump cycles, the pump that lifts water from a well, the circulator that keeps hot water at the tap, and the heater itself. US units — gallons, psi, feet, °F — with metric alongside.

A planning aid. The pump curve, tank charts and heater ratings for the equipment you buy, the maker’s instructions and the plumbing code your jurisdiction has adopted have the last word.

How to use it

Expansion tank — the water heater’s volume, the cold and hot temperatures, the supply pressure and the highest pressure you will allow (well under the 150 psi relief valve; 125 by default). Water expands (from the density of water at the two temperatures); the air in the tank, pre-charged to the supply pressure, compresses by Boyle’s law until the system reaches the maximum. The tank needed is the expansion ÷ that acceptance, rounded up to a typical size. An expansion tank is needed whenever a check valve, backflow preventer or pressure-reducing valve closes the supply (IPC 607.3, UPC 608.3).

Well tank — pump flow, the minimum run time the motor maker asks (often 1 minute), and the pressure switch’s cut-in and cut-out. The drawdown (water delivered between cut-out and cut-in) must be at least flow × run time; the drawdown factor for the switch settings gives the tank’s total volume. With a tank size you get its drawdown, the worst-case starts per hour (a demand of half the pump’s flow) and the on and off times at a steady demand. The table compares the usual switch settings.

Well pump — the flow you want, the pumping level below the well head, the height to the tank, the pressure at the tank, and the drop pipe and the run to the tank. The total dynamic head is the sum of lift, elevation, pressure head (2.31 ft a psi) and friction (Hazen–Williams), shown as a bar. Type the points of your pump’s curve from its catalogue; the chart draws it against the system curve and marks where they cross — the flow the pump will actually give. The example curve is made up.

Recirculation — the length and size of the hot supply in the loop and of the return, the insulation, the water and room temperatures and how far the water may cool round the loop. The heat lost through the pipe sets the flow, gpm = Btu/h ÷ (500 × fall); the friction at that flow (with an allowance for fittings and the valves) sets the head. Return velocity over 2 ft/s is flagged: fast hot water erodes copper.

Water heater — gas, electric or heat pump, the tank, the input and efficiency (or COP), and the temperatures. Recovery = heat into the water ÷ (8.33 × rise), also at the 90 °F rise labels quote; a rough first-hour figure (70 % of the tank plus an hour’s recovery); how long a shower lasts; and how long a full reheat takes. The rated first-hour figure on the EnergyGuide label is the one to compare heaters by. For the busiest hour your house needs, use the Water heater tab of plumbing sizing.

Tankless — the flow that runs at once, the coldest inlet of the year and the outlet temperature give the heat (500 × gpm × rise), the gas input or the electric kW and amps at 240 V. Give a unit’s rating to see the flow it manages at that rise.

How it is worked out

  • Density of water: Kell’s equation (1975), 0–150 °C.

  • Tanks: Boyle’s law with absolute pressures (gauge + 14.7). Acceptance per gallon of tank = min(1, Ppre ÷ Psupply) − Ppre ÷ Pmax. A well tank’s drawdown factor is the same with cut-in and cut-out, pre-charged 2 psi under cut-in.

  • Pump cycling: with pump flow Q and demand d, a cycle takes V ÷ (Q − d) + V ÷ d for drawdown V, shortest at d = Q ÷ 2, when it is 4V ÷ Q.

  • Friction: Hazen–Williams, 4.52 Q1.852 ÷ (C1.852 d4.87) psi per foot, with C = 140 for PE and copper, 150 for PVC and PEX, 100 for old galvanised steel, and inside diameters from the pipe standards (PE well pipe is sized by its inside diameter, the same as schedule 40).

  • Pump curve: a least-squares quadratic through your points; the operating point is found by bisection.

  • Pipe heat loss: conduction through insulation of k = 0.25 Btu·in/h·ft²·°F and a surface film of 1.65 Btu/h·ft²·°F (2.0 for bare copper), on copper tube outside diameters (ASTM B88).

  • Heaters: 8.33 lb a gallon and 1 Btu per lb per °F; 1 kW = 3,412 Btu/h.

Limits

  • Expansion and well tanks: the typical nominal sizes are a guide; makers' tanks and their acceptance charts differ a little. Constant-pressure (variable-speed) pumps need far smaller tanks — use the maker’s figure.

  • Well pump: no net positive suction head or submergence check, no motor cooling or wire-size check, no drawdown of the well itself (use the pumping level from a pump test).

  • Recirculation: a single loop; branched loops need balancing valves and a flow for each branch.

  • The first-hour figure is rough. The DOE test is what the label reports.

  • Electric tankless: the amps are the heater’s; breakers, wire and service capacity follow the maker’s instructions and the electrical code.

Related: plumbing sizing, fluid flow and pipe pressure drop, generator sizing, gas pipe sizing, pipe offsets and takeoffs.

Linking to an example

Units as in the tool: gallons, °F, psi, feet, gpm, inches for pipe sizes. The pump curve travels only in Share link's compressed ?s=.

Parameter Meaning Example

vol, cold, hot, sup, max

expansion tank: heater gallons, cold and hot °F, supply and highest psi

vol=50&sup=80

q, run, cin, cout

well tank: pump gpm, minimum run (min), cut-in and cut-out psi

q=12&cin=40&cout=60

lift, elev, psi, pq, pipe, dl, ds, rl, rs

well pump: pumping level, height to tank, psi, gpm, pipe (pe, pvc, steel, copper, pex), drop pipe length and size, run length and size

lift=150&pq=8&ds=1

sl, ss, rr, rsz, ins, t, dt

recirculation: supply length and size, return length and size, insulation (in), water °F, allowed fall °F

sl=90&ss=0.75&ins=1

type, hv, hin, eff, inlet, set

water heater: gas, electric or heatpump, gallons, input (Btu/h or kW), efficiency or COP, inlet and thermostat °F

type=electric&hv=50&hin=4.5

tq, tin, tset, fuel

tankless: gpm, inlet and outlet °F, gas or electric

tq=3&tin=50&fuel=electric

example

one of the presets below; other parameters override it

example=well-10

Presets:

  • expansion-50 — 50 gal heater, 60 psi supply, 50 → 140 °F

  • expansion-80 — 80 gal heater on 80 psi city water

  • well-10 — 10 gpm pump on a 40/60 switch, 1 minute minimum run

  • well-head — submersible: 120 ft pumping level, 1¼″ PE, 60 psi at the tank

  • recirc-house — 120 ft hot loop in ¾″ with a ½″ return, ½″ insulation

  • heater-gas50 — 50 gal gas heater, 40,000 Btu/h

  • heater-hp — 65 gal heat pump water heater

  • tankless-winter — two showers in winter: 4 gpm from 40 °F to 120 °F

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