Total Dynamic Head (TDH) — calculate pump head

Every pump you specify has to answer one question: how much head does the system demand at the design flow? That number is the total dynamic head (TDH) — the total equivalent height of fluid the pump must raise the flow through, measured in feet or metres. Get it right and the pump sits comfortably near its best efficiency point. Get it wrong and the pump either runs off the end of its curve delivering too much flow, or stalls short and never reaches the fixtures. TDH is the single most consequential number in pump selection, and it is nothing more than four head terms added together.

This guide breaks TDH into its four components — static head, friction head, pressure head, and velocity head — with the equations, the sign conventions engineers get wrong, three fully worked examples across residential, HVAC, and irrigation systems, the design-velocity bands that keep the duty point sane, and the Hydraulic Institute standards that govern where on the curve the pump is allowed to run. Every number traces to Crane TP-410, the ASPE Plumbing Engineering Design Handbook, or the ANSI/HI 9.6 pump standards.

The four heads that add up to TDH

A pump does exactly one thing: it adds energy to a fluid, and that energy is measured as head. The system, in turn, imposes four separate demands on that energy. The animated chart below stacks the four components for a typical booster application — watch each block build on the one below it until the total is the TDH the pump must deliver.

Not every system has all four in meaningful amounts. A closed hydronic loop has zero static and zero pressure head — it is pure friction. A tank-to-tank transfer at atmospheric pressure has no pressure head. A booster feeding a pressure vessel, as above, is dominated by pressure head. The skill of estimating TDH is knowing which terms matter for the system in front of you.

1. Static head (h_static). The net vertical elevation the pump moves the fluid through, independent of flow rate. It is the discharge liquid surface elevation minus the suction liquid surface elevation. Add the lift when the source sits below the pump; subtract it when the source floods the suction from above. In a closed loop the fluid returns to its starting elevation, so static head is zero.
2. Friction head (h_friction). Energy lost to viscous drag along the pipe wall and to turbulence in every fitting and valve. It scales with roughly the square of flow, so it is the flow-dependent heart of the "dynamic" in TDH. Computed with Darcy-Weisbach or Hazen-Williams over the actual pipe length plus the equivalent length of the fittings.
3. Pressure head (h_pressure). Any pressure the fluid must be delivered against beyond atmospheric — a pressure tank, a boiler, sprinkler operating pressure, a pressurised process vessel. Convert the required gauge pressure to feet of head: for water, psi × 2.31. Independent of flow.
4. Velocity head (h_velocity). The kinetic energy of the moving fluid as a height, V²/2g. Small at ordinary velocities and neglected whenever the fluid decelerates into a tank. It counts only for free-jet discharge to atmosphere and in the field-gauge method.

The equations you actually need

The master equation. Total dynamic head is the sum of the four component heads:

hTDH = hstatic + hfriction + hpressure + hvelocity

Every term is expressed in the same unit — feet of the fluid being pumped, or metres — so they add directly. The rigorous definition from Bernoulli's equation is that TDH equals the total head at the pump discharge flange minus the total head at the suction flange, but for design you build it up component by component from the system drawing rather than measuring flanges.

Friction head is the term that takes real work. In US practice for water, the Hazen-Williams equation is standard:

hf = 0.002083 · L · (100/C)1.852 · Q1.852 / d4.8655

where hf is friction head in feet, L is pipe length in feet (including the equivalent length of fittings), C is the Hazen-Williams roughness coefficient (≈ 150 for new PVC/PEX, 140 for new copper, 120 for new steel, dropping as pipe ages), Q is flow in US gpm, and d is inside diameter in inches. For non-water fluids or off-ambient temperatures, use Darcy-Weisbach instead, hf = f · (L/D) · V²/2g, because Hazen-Williams silently assumes water near 60 °F.

Velocity head and pressure head are one-liners. Velocity head is the kinetic term from Bernoulli:

hv = V² / 2g    and    hp = 2.31 · Ppsi / SG

with V in ft/s, g = 32.2 ft/s² (so 2g = 64.4), Ppsi the required delivery pressure, and SG the fluid specific gravity (1.0 for water). At 8 ft/s the velocity head is only 8²/64.4 = 0.99 ft, which is why it disappears next to a 100-ft static lift — but a 50 psi delivery pressure is 50 × 2.31 = 115.5 ft, which frequently dominates the whole calculation.

Static head: get the sign right

The commonest TDH error is a sign mistake on static head. The rule is unambiguous: static head is the discharge liquid-surface elevation minus the suction liquid-surface elevation. When the source is below the pump — a well, a sump, a pond in a valley — the pump lifts on the suction side and that lift adds to TDH. When the source is above the pump — a gravity tank on the roof feeding a basement booster — the fluid floods the suction, and that positive suction head subtracts from TDH. Treat a flooded suction as a lift and you over-specify the pump; treat a suction lift as flooded and you undersize it and never reach the top fixture.

Note that suction lift also has a second, independent consequence: it eats into the net positive suction head available at the impeller, and if you lift too far the pump cavitates regardless of whether it can make the TDH. Atmospheric pressure caps the theoretical suction lift for cold water near 33.9 ft, but friction, vapour pressure, and the required NPSH margin usually limit practical suction lift to roughly 15–25 ft. See the NPSH and cavitation guide for that side of the calculation.

Friction head: the flow-dependent term

Friction head is what makes TDH "dynamic." Static and pressure head do not care how fast the fluid moves, but friction grows with roughly the square of flow. The system curve below plots the head the system demands against flow: a flat static-plus-pressure offset with a friction parabola climbing on top of it. The pump can only ever operate where its own falling curve crosses this rising demand curve — that intersection is the duty point.

The practical consequence of the square law is that friction head is unforgiving of undersized pipe. Drop one nominal pipe size and the inside area falls by roughly 30–40 %, velocity rises by the same proportion, and friction head — going as velocity squared — climbs steeply. The flagship pressure-drop calculator handles the multi-segment, mixed-material, fitting-by-fitting friction bookkeeping automatically; the fittings reference supplies the Crane TP-410 K-factors and equivalent lengths for the manual version.

How to measure TDH in the field

When a pump is already installed, you can back out its actual operating TDH from two gauges rather than a drawing. Install a pressure gauge on the suction flange and one on the discharge flange, read both at the operating flow, and convert:

TDH = (Pd − Ps) · 2.31 / SG + (Vd² − Vs²) / 2g + Δz

where Pd and Ps are the discharge and suction gauge pressures in psi, Δz is the small elevation difference between the two gauge taps, and the velocity-head term corrects for the suction and discharge pipes being different sizes. This is the one place velocity head is never optional: if the discharge pipe is smaller than the suction pipe, the (Vd² − Vs²)/2g term can add a meaningful foot or two, and ignoring it means your field TDH will not match the manufacturer's test curve. Diagnostically, a measured TDH well below the curve at the observed flow means the pump is worn or the impeller is trimmed; a measured flow far to the right of design means the system curve is flatter than assumed and the pump is over-pumping.

Getting TDH right: ranked by effort

Most TDH errors are avoidable bookkeeping mistakes, not physics. In rough order of how much trouble they cause and how cheaply they are fixed:

1. Fix the static-head sign first (free). Confirm whether the suction is a lift or flooded before anything else. This is the largest single-line error and costs nothing to get right — it is a drawing question, not a calculation.
2. Include every fitting's equivalent length (cheap). A long run with a dozen elbows, a check valve, and a control valve can carry more friction in the fittings than in the straight pipe. Skipping them is the most common reason a pump lands short of its duty. Use the fitting equivalent-length reference and add them into L.
3. Use aged, not new, C-factors for design (cheap). Steel and cast iron lose roughness coefficient over decades of tuberculation; designing on the new-pipe C-factor leaves no margin for the friction head the system will actually have in year fifteen. The C-factor library gives new-and-aged pairs.
4. Add a modest safety margin, then stop (moderate). A 5–10 % head margin covers estimation error and future fouling. A larger margin is counter-productive: it pushes the duty point left of the best efficiency point, wastes energy, and often forces a throttling valve that simply burns the excess head. Oversizing is the most expensive TDH mistake over the life of the pump.

Design velocities and where the pump is allowed to run

TDH tells you the head; the design velocity tells you whether the pipe sizes producing that head are sane. Too slow and you have oversized, expensive pipe; too fast and you invite erosion, noise, water hammer, and runaway friction head. The bands below come from the ASPE Plumbing Engineering Design Handbook and the Hydraulic Institute pump-piping guideline.

Sizing the pump for the right head is only half the job — the duty point also has to land in a healthy part of the pump's own curve. ANSI/HI 9.6.3-2024 defines two regions relative to the best efficiency point (BEP): the preferred operating region (POR), roughly 70–120 % of BEP flow, where reliability and efficiency are highest, and the wider allowable operating region (AOR), outside which vibration, recirculation, and bearing loads climb. A pump selected so its TDH duty point sits inside the POR will outlast one that is technically "big enough" but forced to run at 40 % of BEP behind a throttling valve.

Codes and standards engineers should know

Pump selection and the head/flow envelope are governed by a stack of Hydraulic Institute standards plus the plumbing design handbook. The working set for TDH and pump sizing in the U.S. is:

• ANSI/HI 9.6.3-2024 — Guideline for Operating Regions. Defines the preferred (≈ 70–120 % BEP) and allowable operating regions; the TDH duty point should sit inside the POR.
• ANSI/HI 9.6.1-2024 — Guideline for NPSH Margin. The suction-side companion to TDH; the 2024 edition moved from the NPSH3 basis toward NPSHR and consolidated the margin recommendations by market segment.
• ANSI/HI 9.6.6-2022 — Rotodynamic Pumps for Pump Piping. Suction and discharge piping arrangement and the recommended maximum suction velocity that keeps NPSH intact.
• ANSI/HI 1.3 — Rotodynamic (Centrifugal) Pumps for Design and Application. The base design-and-application standard for the centrifugal pumps most TDH calculations feed.
• ISO 9906:2012 — Rotodynamic pumps, hydraulic performance acceptance tests. Defines the grades to which a manufacturer's head/flow curve — the curve you match TDH against — is verified.
• ASPE Plumbing Engineering Design Handbook, Vol. 4. Source for the building-service design-velocity bands and fixture-based demand used to set the design flow.
• Crane Technical Paper 410 (TP-410). The K-factor and friction-loss reference behind the friction-head half of TDH.

When hand calculation stops being enough

A single pump on a single pipe run is a hand calculation — build the four heads, add them, read the curve. Real systems outgrow that quickly, and the point where you reach for software is where the system curve stops being a single parabola:

• Branched networks. Once flow splits among parallel paths, each branch has its own friction head and the flows redistribute until every path reaches the same node pressures. Hydraulic network solvers — EPANET (free, from the US EPA), Bentley WaterGEMS/WaterCAD, and Pipe-Flo — iterate that balance for you.
• Variable-speed and multi-pump systems. When a VFD moves the pump curve or lead-lag pumps stage on and off, the duty point sweeps a region rather than sitting at one intersection. The affinity laws describe how the curve shifts with speed; a system model overlays the family of curves.
• Transient events. TDH is a steady-state number. Pump trips and fast valve closures produce pressure spikes far above the steady head — see the water-hammer guide — and need a Method-of-Characteristics transient solver, not a TDH calculation.

Worked examples

Example 1 — Residential booster to a pressure tank

System: booster pump drawing from a cistern, delivering 15 gpm through 120 ft of 1″ copper (C = 140) with ~30 ft of fitting equivalent length, up 30 ft of static lift, into a pressure tank held at 50 psi.

Velocity in 1″ type-L copper (ID ≈ 1.025″) at 15 gpm is about 5.8 ft/s — at the top of the comfortable band, a hint to consider 1¼″ pipe. Static head is 30 ft. Pressure head is 50 × 2.31 = 115.5 ft. Friction head over 150 ft of equivalent length by Hazen-Williams is roughly 17 ft. Velocity head, V²/2g = 5.8²/64.4 ≈ 0.5 ft, is neglected because the fluid decelerates into the tank. So TDH ≈ 30 + 17 + 115.5 = 162.5 ft, and the pressure requirement dominates — the surprising but typical result for any system delivering into a pressure vessel. Size the pump for ~163 ft at 15 gpm plus a 5–10 % margin.

Example 2 — Commercial chilled-water circulator (closed loop)

System: a closed chilled-water loop, 200 gpm through roughly 400 ft of 4″ schedule-40 steel total equivalent length (pipe + coils + valves + fittings), returning to the same elevation it left.

Because the loop is closed, the fluid returns to its starting elevation and static head is zero; there is no delivery pressure to overcome either, so pressure head is zero. TDH is entirely friction head. Velocity in 4″ steel at 200 gpm is about 5 ft/s. Hazen-Williams (C = 120) over 400 ft of equivalent length gives roughly 12 ft of friction head. So TDH ≈ 12 ft at 200 gpm — a low-head, high-flow duty that is exactly why building circulators are squat, wide-impeller machines rather than tall multistage pumps. The whole selection hinges on getting the loop's total equivalent length right, since nothing else contributes.

Example 3 — Irrigation main from a pond to a sprinkler zone

System: 40 gpm through 500 ft of 2″ PVC (C = 150) from a pond up 25 ft of static lift to a sprinkler zone that must see 45 psi operating pressure at the manifold.

Velocity in 2″ PVC (ID ≈ 2.047″) at 40 gpm is about 3.9 ft/s — comfortably mid-band. Static head is 25 ft. Pressure head is 45 × 2.31 = 104 ft (the sprinklers' operating pressure, which already accounts for the nozzle exit velocity, so no separate velocity-head term is added). Friction head over 500 ft by Hazen-Williams is about 14 ft. So TDH ≈ 25 + 14 + 104 = 143 ft at 40 gpm. As with the booster, the required delivery pressure dominates; the long PVC run contributes less than the elevation because the velocity is modest. Raising the flow would grow the friction term steeply — a reminder to check the duty point stays inside the pump's POR before committing.

FAQ

What is total dynamic head (TDH)?

Total dynamic head is the total equivalent height of fluid a pump must raise the flow through, expressed in feet or metres of head. It is the sum of the static lift the pump overcomes, the friction losses through pipe and fittings, any pressure the fluid must be delivered against, and — for free-jet discharge — the velocity head. TDH is the y-axis value you read off a pump curve at your design flow, so getting it right is the difference between a pump that hits its duty point and one that runs off the end of its curve.

What is the formula for total dynamic head?

TDH = static head + friction head + pressure head + velocity head, or h_TDH = h_s + h_f + h_p + h_v. Static head is the net elevation change (add suction lift, subtract a flooded suction). Friction head comes from Darcy-Weisbach or Hazen-Williams over the pipe plus the equivalent length of every fitting. Pressure head is any delivery pressure converted to feet (psi × 2.31 for water). Velocity head, V²/2g, is usually neglected unless the fluid exits as a free jet.

How do you calculate TDH for a pump?

Work out each component separately then add them. First find the net static head from the elevation drawing. Second, compute friction head at the design flow with Hazen-Williams or Darcy-Weisbach, including the equivalent length of every elbow, tee, and valve. Third, add any pressure the fluid is delivered against (sprinkler operating pressure, boiler pressure, a pressurised tank). Add velocity head only for a free jet. The four numbers add to TDH, which you match against a pump curve at the same flow.

What is the difference between static head and dynamic head?

Static head is the part that does not change with flow rate — the vertical elevation the pump must lift the fluid, plus any fixed delivery pressure. Dynamic head is the flow-dependent part, dominated by friction, which grows roughly with the square of flow. On a system curve, static head is the y-intercept at zero flow and dynamic head is the rising parabola above it. Total dynamic head is the sum of both at the design flow, despite the name implying only the dynamic part.

Is TDH the same as total head or pump head?

Yes — total dynamic head, total head, pump head, and system head at the duty flow all refer to the same quantity: the head the pump delivers, which by definition equals the head the system demands at the operating point. Manufacturers plot it as "head" on the pump curve. The word "dynamic" distinguishes it from static head alone; it does not mean the static component is excluded.

Does TDH include suction lift?

Yes. If the pump draws fluid up from a source below its centreline (a well, a sump, a pond below grade), that suction lift is part of the static head and adds to TDH. If instead the source is above the pump so fluid floods the suction (a rooftop tank feeding a basement pump), that positive suction head subtracts from TDH. The sign convention matters: lift adds, flooded suction subtracts. Suction lift also erodes NPSH available, so it is limited independently of TDH.

How do I convert PSI to feet of head?

For water at ambient temperature, multiply psi by 2.31 to get feet of head, and multiply feet of head by 0.433 to get psi. The exact factor is 2.307 at 60 °F and shifts slightly with fluid density, so for any fluid use head (ft) = 2.31 × psi ÷ specific gravity. A pump delivering to a 50 psi pressure tank therefore has to supply 50 × 2.31 = 115.5 ft of pressure head on top of static lift and friction.

What is velocity head and can I ignore it?

Velocity head is the kinetic energy of the moving fluid expressed as a height, V²/2g. At typical pipe velocities below about 8 ft/s it is under 1 ft, so it is small next to static and friction head. You can neglect it whenever the fluid decelerates into a tank or reservoir, because the velocity — and therefore the velocity head — goes to zero at the destination. It genuinely counts in two cases: discharge as a free jet to atmosphere, and the field-gauge method, where the correction is (V_d² − V_s²)/2g between the discharge and suction flanges.

What is TDH for a closed-loop HVAC system?

In a closed loop — a chilled-water or hydronic heating circuit — the fluid returns to the same elevation it started from, so the static head cancels to zero. TDH is then entirely friction head: the pipe friction plus the equivalent length of coils, valves, and fittings around the loop, at the design flow. This is why circulator pumps for closed loops are low-head, high-flow machines; a large building loop might only need 30–60 ft of head despite moving hundreds of gpm.

How does flow rate affect TDH?

The static and pressure components of TDH are independent of flow, but friction head grows with roughly the square of flow (the Hazen-Williams exponent is 1.85, Darcy-Weisbach is close to 2 in turbulent flow). Doubling the flow roughly quadruples the friction head. That is why the system curve is a parabola sitting on top of the static offset, and why oversizing a pump — then throttling it back — pushes the duty point up a steep part of the curve and wastes energy.

What happens if I oversize the pump head?

A pump specified for more head than the system actually needs runs out to the right on its curve, delivering more flow than intended at a lower head. That over-pumping can push the operating point past the allowable operating region (ANSI/HI 9.6.3), raise velocities into the water-hammer and erosion range, overload the motor, and drop NPSH available. The usual field symptom is a pump running far from its best efficiency point, throttled with a partly closed valve that simply burns the excess head as heat.

How is TDH related to NPSH?

TDH is a demand on the discharge side — the head the pump must add. NPSH is a constraint on the suction side — whether enough absolute pressure exists at the impeller eye to avoid cavitation. They are independent calculations: a pump can meet its TDH duty and still cavitate if suction lift, friction, or fluid temperature leave too little NPSH available. Size the pump for TDH first, then verify NPSH available exceeds NPSH required with the margin recommended by ANSI/HI 9.6.1-2024.

Sources and further reading

• Hydraulic Institute, ANSI/HI 9.6.3-2024 — Rotodynamic Pumps, Guideline for Operating Regions. Preferred and allowable operating regions relative to BEP.
• Hydraulic Institute, ANSI/HI 9.6.1-2024 — Rotodynamic Pumps, Guideline for NPSH Margin. Suction-side margin recommendations.
• Hydraulic Institute, ANSI/HI 9.6.6-2022 — Rotodynamic Pumps for Pump Piping. Suction/discharge piping and recommended suction velocity.
• Hydraulic Institute, ANSI/HI 1.3 — Rotodynamic (Centrifugal) Pumps for Design and Application.
• ISO 9906:2012, Rotodynamic pumps — Hydraulic performance acceptance tests, Grades 1, 2 and 3. Basis for the manufacturer head/flow curve.
• ASPE, Plumbing Engineering Design Handbook, Vol. 4. Design-velocity bands and demand estimation.
• Crane Company, Technical Paper 410: Flow of Fluids through Valves, Fittings, and Pipe. K-factors and friction-loss reference.

Open the tools

• Pump sizing calculator — builds TDH from static lift, multi-segment friction, and delivery pressure, then adds NPSH-available and energy-cost-of-friction
• Flagship pressure-drop calculator — the multi-segment, mixed-material friction-head engine behind the friction term
• Velocity calculator — check the design velocity against the bands above before fixing pipe sizes
• Hazen-Williams calculator — the single-equation friction-head quick calc for water
• Fitting equivalents reference — Crane TP-410 K-factors and equivalent lengths for the friction term
• Pump curves explained — read the manufacturer curve you match TDH against
• NPSH & cavitation — the suction-side constraint that TDH selection must not violate
• Pump affinity laws — how a VFD shifts the head/flow curve
• Methodology — full formulas, density/viscosity tables, and citations