title: "Total Dynamic Head Calculation: Formula and Pump System Example"
description: "Learn the formula, units, assumptions, and a worked example, then see how to avoid common pump calculation errors in real industrial systems."
Consider two water transfer systems. The first pumps through 500 meters of horizontal pipe with 5 meters of elevation gain. The second lifts water 30 meters through 50 meters of vertical pipe. A contractor calculating pump requirements from elevation alone will select a 5-meter pump for the first system and a 30-meter pump for the second. Both choices fail. The horizontal system needs 15 to 20 meters of head to overcome pipe friction. The vertical system, with its short run and large pipe, may require only 32 meters. Elevation change is one component of total dynamic head, but friction loss, pressure boundaries, and velocity head together determine the head the pump must deliver.
Total dynamic head (TDH) is the sum of static elevation difference, friction losses through pipes and fittings, pressure head differences between suction and discharge boundaries, and velocity head changes. TDH represents the energy per unit weight of liquid that the pump must add to move the specified flow rate through the installation. Engineers calculate TDH in meters or feet of liquid column, regardless of liquid density, so a single value describes the hydraulic requirement. That value guides pump selection, verifies operating range, and defines the system curve used to find the duty point.
要点
- TDH equals static head plus friction head plus pressure head plus velocity head; omitting any component produces an undersized pump or flooded motor.
- Static head is the vertical distance from suction liquid surface to discharge liquid surface, measured at minimum and maximum operating levels to capture the full range.
- Friction loss in piping, fittings, valves, and equipment depends on flow rate squared; doubling flow quadruples friction head.
- Pressure head converts gauge pressure differences to equivalent head using liquid specific gravity; atmospheric tanks and vented systems have zero pressure head.
- Calculate TDH at design flow first, then repeat at minimum and maximum expected flow to verify the pump curve covers the operating envelope.
- Plot multiple flow and TDH points to construct the system curve, then overlay the pump curve to confirm the duty point falls in the stable operating region near best efficiency point.
Define the System Boundaries before Calculating TDH
Identify where the pump takes suction and where it delivers liquid. The suction boundary is the point at which the system supplies liquid to the pump inlet—an open tank surface, a pressurized vessel connection, or a defined source elevation in a piping network. The discharge boundary is the point at which liquid leaves the pump’s responsibility—a storage tank surface, a pressure vessel connection, a spray nozzle, or a downstream process inlet. Every component and elevation change between these boundaries contributes to TDH.
Draw a single-line diagram showing suction source, pump location, discharge destination, and all piping, fittings, valves, heat exchangers, filters, or other equipment in the flow path. Mark the liquid level or pressure at suction and discharge boundaries. Label the vertical distance from pump centerline to each boundary. Note pipe sizes, lengths, materials, and the number and type of fittings. This diagram becomes the reference for every term in the TDH equation and prevents double-counting or omitted losses.
Record the design flow rate, liquid temperature, density, and viscosity. These properties control friction loss and Reynolds number, which determine friction factors for pipe and fitting losses. Water at 20°C is the default reference; systems handling hot water, glycol solutions, or hydrocarbon liquids require property adjustments. Confirm whether the system operates at a single flow rate or cycles between minimum and maximum flows, because TDH changes with flow.
Static Elevation and Liquid-Level Range
Static head is the vertical distance between suction liquid surface and discharge liquid surface. If the pump draws from a tank at elevation zero and discharges into a tank at elevation 15 meters, static head is 15 meters. If both tanks are at the same elevation, static head is zero regardless of pipe length. Static head is measured opposite to gravity; pumping downhill produces negative static head, which reduces TDH.
Liquid levels change during operation. A booster pump filling a roof tank starts with the tank empty and finishes full; static head increases by the tank height during the fill cycle. A well pump operates across a range of dynamic water levels as the aquifer responds to pumping rate and recharge. Calculate TDH at both minimum and maximum static head to confirm the pump curve provides adequate pressure throughout the cycle. Maximum static head defines the pump shutoff pressure requirement. Minimum static head combined with peak flow establishes the highest power draw and confirms the motor is not overloaded.
In a closed-loop system such as heating circulation or cooling-tower piping, suction and discharge liquid surfaces are at the same elevation. Static head is zero. TDH consists entirely of friction loss, equipment pressure drop, and pressure head differences if portions of the loop are pressurized differently. Contractors who add building height to a closed-loop TDH calculation oversize the pump and waste energy.
Pressure Head at the Suction and Discharge Boundaries
Pressure head accounts for the difference in absolute pressure between suction and discharge boundaries. If the suction source is an atmospheric tank and the discharge destination is also atmospheric, pressure head is zero. If the suction tank is pressurized to 1.5 bar gauge and the discharge tank is atmospheric, the pump starts with a pressure advantage; subtract the suction pressure head from TDH. If discharge pressure is 3.0 bar gauge and suction is atmospheric, add the discharge pressure head to TDH.
Convert gauge pressure to head using:
Pressure Head (m) = Pressure (Pa) / (ρ × g)
where ρ is liquid density in kg/m³ and g is gravitational acceleration, 9.81 m/s². For water with density 1000 kg/m³, 1 bar (100,000 Pa) equals 10.2 meters of head. For liquids with specific gravity different from 1.0, adjust the conversion proportionally. A pressure of 2.0 bar gauge in a glycol solution with specific gravity 1.05 produces 2.0 × 10.2 / 1.05 = 19.4 meters of head.
When the discharge point is a spray nozzle, pressure head equals the nozzle’s required operating pressure. Irrigation and fire protection systems specify minimum nozzle pressures; that pressure converts directly to head and adds to static and friction components. In a chemical dosing application, discharge pressure is the vessel or pipeline pressure at the injection point. Obtain the pressure from the process and instrumentation diagram or measure it with a calibrated gauge.
Pipe, Fitting, Valve, and Equipment Losses
Friction loss in piping is calculated using the Darcy-Weisbach equation:
h_f = f × (L / D) × (V² / 2g)
where h_f is head loss in meters, f is the Darcy friction factor (dimensionless), L is pipe length in meters, D is inside diameter in meters, V is average velocity in m/s, and g is 9.81 m/s². The friction factor depends on Reynolds number and pipe relative roughness. Use the Moody diagram or Colebrook-White equation to determine f for actual flow conditions, or apply friction-loss tables from pipe manufacturers.
Velocity is flow rate divided by cross-sectional area:
V = Q / A = Q / (π D² / 4)
where Q is volumetric flow rate in m³/s. For a flow of 50 m³/h (0.0139 m³/s) in a 100-mm (0.1-m) pipe, velocity is 0.0139 / (π × 0.1² / 4) = 1.77 m/s. Friction loss is proportional to velocity squared, so doubling flow rate quadruples friction head. This nonlinear relationship defines the parabolic shape of the system curve.
Fittings, valves, and equipment add discrete losses expressed as equivalent length or as a loss coefficient K. A 90-degree elbow in a 100-mm pipe might add 3 meters of equivalent length or represent a K value of 0.9. Sum the equivalent lengths of all fittings, add them to straight pipe length, and calculate total friction loss. Alternatively, calculate fitting losses separately using:
h_fitting = K × (V² / 2g)
and add each loss to the straight-pipe friction total. Gate valves, check valves, filters, heat exchangers, and control valves all contribute; obtain K values or pressure-drop curves from equipment datasheets. Partially closed valves increase K dramatically; calculate losses with valves in their normal operating position.
Velocity Head and When It Matters
Velocity head is the kinetic energy per unit weight of liquid, equal to V² / 2g. If suction and discharge piping are the same size, velocity does not change across the pump and velocity head cancels out of the TDH equation. If pipe sizes differ, calculate the velocity head at each boundary and take the difference. For typical systems with similar suction and discharge pipe sizes, velocity head is less than 0.5 meters and is often neglected. In systems with a large reducer or increaser immediately downstream of the pump, or where discharge velocity is high, include velocity head in the TDH calculation.
A pump with 150-mm suction piping and 100-mm discharge piping handling 80 m³/h sees velocity increase from 1.26 m/s at suction to 2.83 m/s at discharge. Suction velocity head is 1.26² / (2 × 9.81) = 0.08 m; discharge velocity head is 2.83² / (2 × 9.81) = 0.41 m. The difference, 0.33 m, adds to TDH. For fire pumps and jockey pumps where discharge piping is often smaller than suction piping and velocities are high, velocity head becomes significant.
In systems discharging to a free-falling stream, spray, or atmosphere, the full discharge velocity head is lost and must be included in TDH. A center-pivot irrigation system spraying water into the air does not recover velocity head. An open-channel discharge similarly loses velocity energy. In these cases, add the discharge velocity head V² / 2g to static, friction, and pressure components without subtracting suction velocity head.
Worked Open-Tank Transfer Example
A process plant transfers water from a ground-level storage tank to an elevated day tank. The suction tank surface is at elevation 0 meters, and the discharge tank surface is at elevation 22 meters. Suction pipe is 150 mm diameter and 5 meters long. Discharge pipe is 100 mm diameter and 60 meters long. The system includes a suction strainer (K = 1.5), four 90-degree elbows (K = 0.9 each), two gate valves fully open (K = 0.2 each), and one check valve (K = 2.0). Design flow rate is 80 m³/h (0.0222 m³/s). Water density is 1000 kg/m³. Calculate TDH.
Step 1: Static head. Discharge surface at 22 m, suction surface at 0 m. Static head = 22 m.
Step 2: Suction piping friction loss. Pipe diameter = 0.15 m, length = 5 m, flow = 0.0222 m³/s. Velocity = 0.0222 / (π × 0.15² / 4) = 1.26 m/s. Assume friction factor f = 0.020. h_f = 0.020 × (5 / 0.15) × (1.26² / 19.62) = 0.05 m.
Step 3: Discharge piping friction loss. Pipe diameter = 0.10 m, length = 60 m, flow = 0.0222 m³/s. Velocity = 0.0222 / (π × 0.10² / 4) = 2.83 m/s. Assume f = 0.020. h_f = 0.020 × (60 / 0.10) × (2.83² / 19.62) = 4.89 m.
Step 4: Fitting and valve losses. All components on discharge side at 2.83 m/s. Strainer: 1.5 × (2.83² / 19.62) = 0.61 m. Four elbows: 4 × 0.9 × (2.83² / 19.62) = 1.47 m. Two gate valves: 2 × 0.2 × (2.83² / 19.62) = 0.16 m. Check valve: 2.0 × (2.83² / 19.62) = 0.82 m. Total fitting loss = 3.06 m.
Step 5: Pressure head. Both tanks open to atmosphere. Pressure head = 0 m.
Step 6: Velocity head. Suction velocity 1.26 m/s, discharge velocity 2.83 m/s. Velocity head difference = (2.83² – 1.26²) / 19.62 = 0.33 m.
Step 7: Total dynamic head. TDH = 22 + 0.05 + 4.89 + 3.06 + 0 + 0.33 = 30.33 m. Round to 31 m for pump selection. Select a pump whose curve delivers 80 m³/h at 31 m of head. Verify that the pump curve at shutoff does not exceed the pressure rating of system piping and tank.
Repeat the calculation at minimum flow (50 m³/h) and maximum flow (100 m³/h) to confirm the selected pump operates stably across the range. At 50 m³/h, velocity drops, friction decreases, and TDH may fall to 24 m. At 100 m³/h, TDH may rise to 40 m. The pump curve must span this range without running off the end or into an unstable operating region.
TDH for Closed Loops and Pressurized Vessels
In a closed-loop circulation system such as chilled water or heating hot water, static head is zero because suction and discharge points are at the same elevation in the loop. TDH equals the sum of friction losses and equipment pressure drops around the entire loop. A heating system with a boiler, piping, radiators, and expansion tank requires a circulator pump that overcomes pressure drop through the boiler, supply and return piping, control valves, and radiators. Building elevation does not appear in the TDH equation.
When pumping into a pressurized vessel, convert vessel pressure to head and add it to TDH. A boiler feed pump delivering water into a steam drum at 10 bar gauge produces 10.2 × 10 = 102 meters of pressure head. If the steam drum is 15 meters above the deaerator from which the pump takes suction, static head is 15 m. If piping and equipment losses total 8 m, TDH = 15 + 102 + 8 = 125 m. The pump must develop 125 meters at design flow and withstand vessel pressure at shutoff.
Pumping from a pressurized suction source reduces TDH. A pump taking suction from a pressurized tank at 2 bar gauge and discharging to atmosphere gains 20.4 meters of pressure assistance. Subtract suction pressure head from TDH: if static head is 10 m and friction is 5 m, net TDH = 10 + 5 – 20.4 = -5.4 m. The system can gravity-flow without a pump. A pump is still installed for flow control or to ensure positive flow during pressure transients, but required head is minimal.
In chemical dosing and metering pump applications, discharge pressure is often high. Convert that pressure to head in the dosing liquid and ensure the pump is rated for the pressure. A dosing pump injecting into a pipeline at 80 bar gauge sees 80 × 10.2 = 816 meters of pressure head. Static and friction losses are negligible compared to this value, so TDH is approximately 816 m. Positive displacement metering pumps handle this duty; centrifugal pumps do not.
Plot More Than One Point on the System Curve
A single TDH value at design flow defines one point on the system curve. To visualize how TDH changes with flow and confirm the pump curve intersects the system curve in a stable region, calculate TDH at three or more flow rates. Choose zero flow, 50 percent of design flow, design flow, and 120 percent of design flow. At zero flow, TDH equals static head plus pressure head because friction is zero. As flow increases, friction rises with the square of velocity, and TDH climbs along a parabola.
For the worked example, at 0 m³/h TDH = 22 m (static only). At 40 m³/h, recalculate velocities and friction: suction V = 0.63 m/s, discharge V = 1.41 m/s, suction friction = 0.01 m, discharge friction = 1.22 m, fitting losses = 0.77 m, velocity head difference = 0.08 m. TDH = 22 + 0.01 + 1.22 + 0.77 + 0.08 = 24.08 m. At 120 m³/h (0.0333 m³/s), discharge V = 4.24 m/s, discharge friction = 11.0 m, fitting losses = 6.89 m, TDH rises to approximately 41 m.
Plot these points on a graph with flow rate on the horizontal axis and TDH on the vertical axis. Draw a smooth curve through the points. Overlay the pump curve on the same axes. The intersection is the operating duty point. If the pump curve is too flat, the system will operate at higher flow than intended. If the pump curve is too steep, flow will be restricted. Match the pump curve to system curve shape and confirm that the duty point is near the pump’s best efficiency point for longest bearing and seal life.
When multiple pumps operate in parallel or series, construct a combined pump curve and confirm the new duty point. For pumps in series, add the heads at each flow rate to produce a steeper combined curve. For pumps in parallel, add the flow rates at each head. Recalculate TDH for the new operating flow because friction losses change, and verify the combined duty point remains in the stable range of each pump.
よくある質問
Does TDH include the pressure inside the pump casing?
No. TDH is the energy the pump must add to move liquid through the external system, not the pressure measured inside the pump. Pressure at the pump discharge flange equals the sum of suction pressure plus the head the pump adds, converted to pressure units. TDH describes the system requirement; the pump adds head equal to TDH to satisfy that requirement at the duty point.
How do I calculate TDH when suction is below the pump centerline?
Static head is the vertical distance from suction liquid surface to discharge liquid surface. If the suction source is below the pump—a sump, well, or basement tank—measure the vertical distance from the suction surface down to the pump and then up to the discharge. The total remains the difference between discharge and suction elevations. Alternatively, break static head into suction lift plus discharge head. A pump with 3 meters of suction lift and 20 meters of discharge head has static head of 20 – (-3) = 23 m.
Can TDH be negative?
Yes, when suction pressure head exceeds the sum of static head, friction, and discharge pressure head. This occurs in gravity-flow systems or when pumping from a high-pressure source to a lower-pressure destination with the discharge point below the suction. Negative TDH means liquid will flow without a pump. A control valve or throttle maintains the desired flow rate. A pump installed in a negative-TDH system must be selected for low head and high flow, and may require special construction to avoid overload.
What is the difference between TDH and total head?
Total head and total dynamic head are the same value in most engineering practice. Some sources distinguish between "static" systems where flow is zero and "dynamic" systems where liquid is moving, but TDH is defined to include all components at the operating flow rate. The pump curve shows total head or simply head; that value is what the pump adds to the liquid. When system requirement equals what the pump supplies, the pump operates at its duty point on both curves.
How often should I recalculate TDH for an existing system?
Recalculate when flow rate changes, when pipe or fittings are added or modified, when valves are repositioned, when liquid properties change (temperature, viscosity, density), or when liquid levels shift. Fouling and corrosion increase friction over time; if pump discharge pressure rises or flow rate drops at constant speed, friction has increased and TDH is higher. An annual review of operating data against the original calculation identifies trends and prompts maintenance before performance degrades to system failure.
結論
Total dynamic head calculation assembles static elevation, pressure head differences, friction losses, and velocity head into a single value that defines the pump requirement. Draw the system boundaries, measure or calculate each component at design flow, and verify the sum against the pump curve to confirm the duty point falls near best efficiency. Calculate TDH at minimum and maximum expected flows to ensure the pump operates stably across the full range. Gather the certified pump curve, verify calculated TDH against actual installation conditions, and record suction and discharge pressures during commissioning to confirm the pump delivers the predicted head. When selecting a new pump, provide the TDH calculation, system diagram, and liquid properties to the pump supplier so they can recommend a model whose curve matches your system curve and whose construction suits the service.