What total dynamic head actually measures
A pump does not know about pressure, elevation or pipe size separately. It sees one number: the energy per pound of water it has to add between the suction flange and the discharge, and the industry expresses that energy as a height of water in feet. That height is total dynamic head.
Feet are used rather than psi for a practical reason. A pump impeller of a given diameter turning at a given speed produces very close to the same head in feet no matter what liquid it is moving, because the head it develops comes from the tip speed of the impeller. Pressure in psi, on the other hand, depends on the density of the liquid. Manufacturers therefore publish curves in feet, and if you arrive at the curve with a number in psi you have to convert before you can read it. Divide feet by 2.31 to get psi for water; multiply psi by 2.31 to go the other way.
The word dynamic matters. Static head alone is what the system demands standing still, with the valves shut. The moment water moves, friction appears, and friction grows roughly as the square of flow. A system that needs 70 ft at a trickle can easily need 150 ft at design flow. That is why a pump chosen from static lift alone runs out of head, delivers less than you wanted, and gets blamed for a fault that was never in the pump.
Three quantities make up the total. The static term is pure geometry, measured with a tape. The friction term depends on flow, pipe bore, pipe roughness and length. The pressure term is whatever residual pressure the equipment at the end needs to work - a rotor sprinkler wants 45 psi at the nozzle, a garden tap wants nothing at all. Add the three and you have the head at one flow rate. Do it again at several flows and you have the system curve, which is what the calculator plots for you.
The three terms, and where each number comes from
Static head is the vertical distance from the source water surface to the point of discharge. Split it into suction lift and discharge rise because those two halves behave differently: the suction side is limited by atmospheric pressure and by cavitation, the discharge side is not. Enter the suction lift as a positive number when the water is below the pump and as a negative number when the pump sits below the water and the suction is flooded. A flooded suction genuinely subtracts from the work the pump has to do.
Note that horizontal distance contributes nothing to static head. A 400 ft run across flat ground adds friction and no lift at all. Note also that the source level is the level the water will sit at when you are pumping - a well drawn down 40 ft below its static level is a 40 ft deeper lift than the tape measure suggests.
Friction head here uses the Hazen-Williams equation, the convention that AWWA and most irrigation and fire-protection work follows for water at ordinary temperatures. In the form used above, Q is gallons per minute, d is the actual inside diameter in inches, C is the roughness coefficient, and the answer is feet of head lost per 100 ft of pipe. Two features of that equation drive every practical decision you will make. Flow appears to the power 1.852, so doubling flow multiplies friction by about 3.6. Diameter appears to the power 4.87 in the denominator, so going up one pipe size cuts friction by roughly two thirds. Pipe size is by far the cheapest head you will ever buy.
The C value is the honest weak point. It is a single number standing in for the entire roughness history of the pipe. New PVC is around 150 and stays there because it does not corrode; unlined iron starts near 130 and can fall below 90 after decades of tuberculation. If you are sizing a system that has to still work in twenty years, run it twice and see how much of the head is age allowance. For a more careful treatment of the roughness question, or for anything other than water at ordinary temperature, use the Darcy-Weisbach method instead, which handles viscosity properly.
Fittings are handled here as a percentage added to the straight length. That is the field method: 25% is a common allowance for a normally-fitted run, 50% or more for a compact plant room stuffed with elbows and valves. It is an approximation of the rigorous approach, which is to convert every fitting to an equivalent length of straight pipe or to sum K factors and add K·v²/2g. If you have already done that, set the allowance to zero and put the developed length in directly.
Pressure head is the last term. Whatever pressure the outlet device needs is real work the pump has to do, and 2.31 ft of water per psi converts it. Thirty psi at a hose bibb is 69.3 ft of head - very often larger than the lift, and the term people forget. The psi to feet of head converter covers that conversion on its own.
Worked example: a 50 gpm booster feeding a tank 60 ft up
Take the default case. Water sits 10 ft below the pump. The discharge point is 60 ft above the pump. There is 25 ft of 2 in bore suction pipe and 200 ft of 2 in bore discharge pipe, both PVC at C = 150, and you want 30 psi left at the top. Design flow is 50 gpm. Add 25% to each straight run for fittings.
- Static head. 10 ft of lift + 60 ft of rise = 70.0 ft.
- Friction gradient. 0.2083 × (100/150)1.852 × 501.852 ÷ 24.8655. Working through: (100/150)1.852 = 0.4720, 501.852 = 1401.1, 24.8655 = 29.148. So 0.2083 × 0.4720 × 1401.1 ÷ 29.148 = 4.726 ft per 100 ft.
- Developed lengths. Suction 25 × 1.25 = 31.25 ft. Discharge 200 × 1.25 = 250 ft.
- Friction head. Suction: 4.726 × 31.25 ÷ 100 = 1.48 ft. Discharge: 4.726 × 250 ÷ 100 = 11.81 ft. Total 13.29 ft.
- Pressure head. 30 psi × 2.31 = 69.3 ft.
- Total dynamic head. 70.0 + 13.29 + 69.3 = 152.6 ft, which is 152.6 ÷ 2.31 = 66.1 psi.
- Velocity check. 0.4085 × 50 ÷ 2² = 5.11 ft/s in both pipes. Acceptable on the discharge, right at the practical limit on the suction.
- Water horsepower. 50 × 152.6 ÷ 3960 = 1.93 hp delivered to the water. At a pump efficiency of 60% that is 3.2 shaft horsepower, so a 3 hp motor is marginal and 5 hp is the safe pick.
Read that as: the biggest single item is not the lift, it is the 69.3 ft you are spending on outlet pressure. If the equipment at the top would accept 20 psi instead of 30, the pump gets 23 ft easier and you may drop a motor frame size.
Taking the number to a pump curve
A pump curve plots head against flow. Your system produces the mirror image: a curve that starts at the static-plus-pressure head at zero flow and rises as flow increases. The pump will operate at exactly one point - where the two curves cross. Nowhere else is possible, because that is the only flow at which what the pump can give equals what the system demands.
This is why the table above matters more than the single answer. If you specify 50 gpm at 152.6 ft and the pump you buy makes 170 ft at 50 gpm, it will not politely deliver 50 gpm; it will run out along its curve to a higher flow until the extra friction absorbs the surplus head. That is usually harmless on a centrifugal pump, but it can push the motor past its service factor on a pump with a rising power curve, and it can drive the pump out to the right-hand end of its curve where efficiency collapses and NPSH required climbs steeply.
Check three things on the curve before you commit. First, that your duty point lies within the middle third of the curve, near best efficiency - a pump run far off best efficiency vibrates, wears bearings and seals faster, and costs more to run. Second, that the shut-off head at the left-hand end exceeds your static-plus-pressure head, or the pump will never start delivering. Third, that NPSH available at your suction exceeds NPSH required at the duty flow with a margin, typically at least 2 to 3 ft. Total dynamic head tells you nothing about cavitation, and cavitation is what actually destroys pumps.
Motor sizing comes from water horsepower divided by efficiency. Take the water horsepower this calculator gives, divide by the pump efficiency read off the curve at your duty point, and you have brake horsepower at the shaft - the calculation the brake horsepower calculator sets out. Then check that the motor nameplate covers brake horsepower at every point the pump could be driven to, not just at your design flow.
Pipe size as an energy decision, not just a velocity check
The friction term here is not a fixed property of the job the way static head is. It is a choice, made once at rough-in, that the pump then pays for on every gallon it moves for as long as the system runs. A larger pipe costs more once; a smaller one costs more in water horsepower, hour after hour, for the pump's life.
That asymmetry is why the Hydraulic Institute and Europump guide to pump life cycle costs treats pipe sizing as an energy decision, not only a hydraulic one. On a system that runs many hours a year, the electricity spent overcoming friction head typically outweighs the pump's purchase price over its service life, so the friction term above carries more leverage over total cost than a number only needing to clear a velocity limit.
That makes it a different question from the one the velocity table above answers. The smallest bore that stays under the practical velocity limit is a minimum, protecting against erosion and noise, but it rarely minimizes lifetime cost, because friction head keeps falling as bore increases well after velocity stops being a concern. One size past the velocity minimum often buys a worthwhile cut in friction head - and water horsepower - for a modest rise in pipe cost, especially on a long discharge run.
Flow limits and friction by pipe bore
| Inside diameter | Flow at 5 ft/s (gpm) | Flow at 8 ft/s (gpm) | Friction at 5 ft/s (ft per 100 ft) |
|---|---|---|---|
| 0.75 in | 6.9 | 11.0 | 14.2 |
| 1.00 in | 12.2 | 19.6 | 10.2 |
| 1.25 in | 19.1 | 30.6 | 7.8 |
| 1.50 in | 27.5 | 44.1 | 6.3 |
| 2.00 in | 49.0 | 78.3 | 4.5 |
| 2.50 in | 76.5 | 122.4 | 3.5 |
| 3.00 in | 110.2 | 176.3 | 2.8 |
| 4.00 in | 195.8 | 313.3 | 2.0 |
Read this as a sizing shortcut: find your flow in the 5 ft/s column and that is the smallest bore you should normally use on a suction line. The 8 ft/s column is the usual erosion and noise ceiling for discharge piping.
Mistakes that make a TDH number wrong
- Using nominal pipe size as the diameter. Two inch schedule 40 steel has a 2.067 in bore, two inch schedule 80 has 1.939 in, two inch SDR 21 PVC has about 2.149 in. Because diameter carries the power 4.87, the difference between schedule 40 and schedule 80 is about 14% more friction for the same nominal size.
- Measuring the static level instead of the pumping level. In a well, the water drops while you pump. The lift that matters is measured from the drawn-down level at design flow, which you get from the well driller's test.
- Leaving out the outlet pressure. The most common single error, and often the largest term. Anything with a nozzle, a filter, a float valve or a pressure switch needs residual pressure, and every psi of it is 2.31 ft of head.
- Forgetting the check valve and foot valve. A swing check in a 2 in line is worth roughly 12 to 15 ft of equivalent pipe; a foot valve with strainer can be worth 50 ft or more. A blanket fitting percentage covers ordinary elbows well and covers these badly, so add them explicitly.
- Treating TDH as the whole design. It says nothing about NPSH, nothing about water hammer when the check valve slams, and nothing about what happens on start-up against an empty riser. Size the pump from TDH, then check those separately.
- Adding a safety factor twice. A generous C value, a generous fitting percentage and then a 20% margin on top compound into a pump that is badly oversized, runs off the left of its curve, and short-cycles. Pick one place to be conservative.
Which friction method applies to your job
Hazen-Williams is an empirical fit for water flowing in the turbulent range at ordinary temperatures, roughly 40 to 75 F, in pipes of about 2 in and larger. It is the basis of AWWA water distribution practice and of NFPA 13 fire sprinkler hydraulic calculations. Inside that envelope it is accurate and fast, and it is what the reviewing authority will expect to see. Outside it - viscous liquids, hot water, compressed air, very small tubing, laminar flow - it is simply the wrong equation and can be far off. Use the Darcy-Weisbach approach with a friction factor from the Colebrook equation in those cases.
Key terms
- Static head
- The vertical height difference the water must be raised, independent of flow. Measured from the pumping water level to the discharge point.
- Friction head
- Energy lost to shear against the pipe wall and turbulence in fittings, expressed as feet of water. Grows with flow to roughly the power 1.85.
- Duty point
- The single flow-and-head pair at which a given pump and a given system will actually operate: the crossing of the pump curve and the system curve.
- Shut-off head
- The head a pump produces at zero flow, at the far left of its curve. If shut-off head is below your static plus pressure head, no water moves at all.
- NPSH available
- Absolute pressure at the pump suction above the vapour pressure of the liquid, in feet. It must exceed the pump's NPSH required or the liquid boils in the eye of the impeller and the pump cavitates.