Where should the calculation begin and end?

Choose two physical boundaries that describe the transfer duty. For tank-to-tank service, the liquid surfaces are often convenient. For a supply line feeding equipment, the destination may be a specified connection where a minimum pressure is required. The boundary choice determines which terms belong in the calculation.

Draw the source, destination, pump, and intervening components. Mark surface elevations, pressures, pipe dimensions, and the required flow. If the flow splits into branches, identify which path and operating combination are being evaluated. A single series-pipe equation cannot fully represent every network.

For large tanks, liquid-surface velocities can often be treated as negligible. If both tanks are open to the same atmosphere, their pressure difference is zero. If the receiving vessel is pressurized, include its pressure relative to the source. The pressure reference must be consistent.

The highest point in a pipeline is not automatically the destination elevation used for steady tank-to-tank TDH. The entire pressure profile, filling behavior, air management, and minimum-pressure conditions may still require separate analysis. Net endpoint elevation alone does not resolve those installation questions.

What does each term mean?

Elevation difference is based on the endpoints

The elevation term is z₂ − z₁. A destination surface 25 m above the source surface contributes 25 m. If the source level falls by 2 m while the destination remains fixed, that term becomes 27 m. Use liquid levels, not merely the elevations of tank foundations.

A horizontal section can still create friction loss even though it adds no elevation head. Conversely, a vertical rise contributes both geometric elevation and pipe friction. Keeping those effects separate makes the calculation easier to inspect.

Pressure difference must be converted using density

The pressure term is (p₂ − p₁)/(ρg). For an incompressible liquid, either absolute pressures or consistently referenced gauge pressures can be used for the difference. Do not mix the two. Record density at the assessed operating condition.

For the assumed density of 1,000 kg/m³, a 200 kPa pressure difference contributes 20.39 m using g = 9.81 m/s². A denser mixture gives a different pressure-head conversion, but that does not imply unchanged friction or unchanged pump performance on the mixture.

Velocity head belongs to the endpoint definition

Velocity head is v²/(2g). Between large tank surfaces, its difference is usually negligible under the stated assumption. At pipe connections with different inside diameters, it may need to be included. Determine average velocity from volumetric flow divided by actual flow area.

Do not add an outlet velocity term twice. For example, a reservoir-boundary calculation that includes an exit loss must remain consistent with that boundary. An alternative calculation ending at a free jet or pipe section uses a different energy accounting arrangement.

How are pipe and fitting losses calculated?

For a suitable single-phase liquid model, Darcy–Weisbach pipe loss is hf = f(L/D) × v²/(2g). Here f is the Darcy friction factor, L is pipe length, D is inside diameter, and v is average velocity. The factor depends on flow regime and relative roughness.

Do not interchange Darcy and Fanning friction factors. Their numerical values differ by a factor of four. A calculation sheet should name the convention and identify the method or data source used to obtain the factor.

Losses through fittings and valves may be represented as hK = ΣK × v²/(2g), using coefficients appropriate to the component and reference velocity. If the system has several diameters, apply each coefficient on its stated basis rather than using one velocity for every component.

Equipment such as filters, heat exchangers, and process devices may have manufacturer-supplied pressure-loss data. Convert those values consistently and account for condition: clean, fouled, operating, or bypassed. A generic allowance cannot replace equipment data when that item dominates the duty.

Define the worked example before calculating

The example transfers a water-like incompressible liquid from a large open source tank to a large receiving vessel. The destination liquid surface is 25 m higher, and its gas-space pressure is 200 kPa gauge. The source is at 0 kPa gauge using the same atmospheric reference.

Required flow is 100 m³/h. Assume density 1,000 kg/m³, g = 9.81 m/s², and negligible velocity at both liquid surfaces. The entire series path has 250 m of pipe with a uniform 0.150 m inside diameter. These dimensions include the suction and discharge sections within the chosen boundary.

Assume a Darcy friction factor of 0.025 for this teaching case. It is supplied as an input, not calculated from an unspecified viscosity or roughness. Assume the total fitting coefficient is 12 on the pipe-velocity basis, including the inlet and exit effects appropriate to the reservoir boundaries.

Finally, assume a process component contributes 4.0 m of head loss at 100 m³/h. For the later sensitivity example only, its loss is assumed to vary with flow squared. An actual project would use the component's applicable performance data.

Calculate velocity and each head contribution

Convert flow first: 100 m³/h divided by 3,600 gives 0.02778 m³/s. Pipe area is πD²/4 = 0.01767 m². Dividing flow by area gives an average velocity of approximately 1.572 m/s.

The velocity-head quantity used for losses is v²/(2g) = 1.572²/19.62 = approximately 0.1259 m. This is not an additional endpoint velocity difference because the boundaries are the large tank surfaces. It is the reference quantity in the loss calculations.

Pipe friction is 0.025 × (250/0.150) × 0.1259 = approximately 5.25 m. Fitting and valve loss is 12 × 0.1259 = approximately 1.51 m. Adding the stated equipment loss gives approximately 10.76 m of total flow-dependent losses at this duty.

Pressure head is 200,000/(1,000 × 9.81) = 20.39 m. The elevation term is 25 m, and the endpoint velocity-head difference is taken as zero. Therefore, TDH = 25 + 20.39 + 5.25 + 1.51 + 4.00 = 56.15 m, subject to rounding.

The resulting preliminary duty is 100 m³/h at approximately 56.15 m TDH. It is not a selected pump. The next steps include a pump-curve comparison, suction assessment, power calculation, operating-range review, and confirmation of the application's materials and installation needs.

How does the result change at a different flow?

For this simplified example, keep endpoint pressures and levels fixed and assume all loss terms retain a quadratic relationship with flow. The static component is 25 + 20.39 = 45.39 m, and the loss component at 100 m³/h is approximately 10.76 m.

The illustrative system relationship is Hₛ(Q) = 45.39 + 10.76 × (Q/100)², with Q in m³/h. At 80 m³/h, the result is approximately 52.27 m. At 120 m³/h, it is approximately 60.88 m, allowing for rounding of intermediate values.

The calculation shows why one TDH value belongs to one flow and condition. Increasing flow does not merely move the same liquid faster at unchanged head. It changes the losses. An actual friction factor or equipment characteristic may also vary, so the quadratic model must be checked rather than assumed universally.

The source-level case also affects suction conditions. It is possible for a change to increase required system head while reducing available NPSH. A complete selection review therefore uses the same operating cases across the discharge-duty and suction calculations.

Which losses are easy to miss or double count?

Check whether pipe lengths already include equivalent lengths for fittings. If they do, adding separate K losses for the same fittings can count them twice. Choose a consistent method and document exceptions, especially when data comes from several calculation sheets.

Confirm whether a process vendor's required inlet pressure already includes downstream equipment loss. If the chosen destination boundary is that vendor's inlet connection, adding the internal loss again may overstate the pump duty. Ask what the pressure requirement is intended to cover.

Control valves need a clear operating basis. A valve may deliberately dissipate excess head at one condition and be nearly open at another. Do not combine a fully open valve loss with an unrelated throttled operating assumption without describing the control case.

Include actual inside diameters rather than nominal labels. Pipe schedule, lining thickness, deposits, and wear can change the flow area. Because velocity and friction are sensitive to diameter, a modest dimensional misunderstanding can materially alter the result.

For suction and discharge branches, trace the flow in each segment. The common header may carry the combined flow of several pumps or users, while individual branches carry only part of it. Applying total flow to every branch exaggerates losses; applying branch flow to the common header understates them.

How should TDH be handled for slurry pipelines?

The energy-balance framework still helps organize the calculation, but the loss model must match the slurry. Solids concentration, particle distribution, carrier liquid, rheology, settling, and gas can influence the relationship between flow and loss. A clean-water Darcy factor is not automatically a slurry model.

State concentration by mass or volume and provide the density basis. If the mixture density changes, the pressure-head conversion changes as well. At the same time, pipe loss and pump performance may change for reasons that density alone does not describe.

For a settling slurry, evaluate transport requirements and the consequences of low flow or shutdown. The line may need a minimum operating condition, flushing provision, or restart assessment specific to the material and route. This article does not prescribe a universal minimum velocity.

Long-distance routes need more than a single endpoint head number. Review the pressure profile, local high points, component ratings, air management, and credible transients with the project designer. A steady TDH calculation does not predict every pressure during starting, stopping, or a rapid valve movement.

Longteng's horizontal slurry pump range provides a relevant starting point for a pipeline-duty inquiry. Submit the calculation assumptions and slurry description so the proposed curve and drive can be reviewed on a consistent basis.

Should you add a safety factor to the calculated head?

Treat uncertainty explicitly before adding a general allowance. Identify which inputs are uncertain and how they might vary: pipe roughness, equipment fouling, destination pressure, level, or future flow. Calculate credible cases rather than increasing every term independently without a reason.

An unexplained allowance can lead to a pump that operates at excessive flow or dissipates unnecessary head through a control valve. It can also hide an underestimated suction limitation. More head capability is not a substitute for understanding the system.

Where the project requires a contingency or design margin, state its value and where it is applied. Keep the base calculation visible. The supplier should be able to distinguish current duty, future duty, uncertainty allowance, and contractual acceptance requirements.

If an input is missing and dominates the result, obtain it before final selection. For example, an unknown process-equipment pressure loss cannot be resolved by a small arbitrary percentage on the pipe friction. Request the equipment data or define a documented provisional range.

How do you turn the calculation into a pump specification?

Provide the normal and limiting flow-head pairs, not merely the largest head and largest flow from separate scenarios. Include the system curve or enough information to reproduce it. Specify whether a control valve, variable-speed drive, or another control method will regulate operation.

Submit a separate suction assessment with source pressure, level range, temperature, vapor pressure, and suction losses. TDH describes the energy the pump must add across the system; it does not by itself show whether the inlet condition is adequate.

Review shaft power using the proposed pump efficiency and actual liquid basis. For the teaching example, hydraulic power would be about 15.30 kW at 100 m³/h and 56.15 m for the assumed density. A motor cannot be selected from that value alone because pump, transmission, and motor characteristics remain relevant.

Ask the supplier to identify the offered speed, impeller configuration, operating range, and pressure limitations. For a replacement, provide connection dimensions and installation constraints as well. Hydraulic suitability and mechanical fit must both be confirmed before ordering.

Perform a short calculation review before issuing the duty

Have the reviewer follow the liquid path from the source boundary to the destination. Every included length, fitting, and equipment loss should be traceable to that path. Each endpoint pressure and elevation should describe the same operating case. This simple route check often reveals omissions that are difficult to see in a spreadsheet alone.

Check units independently of the formula. The flow conversion from hours to seconds, the conversion from kilopascals to pascals, and the distinction between radius and diameter are common places for large errors. Confirm that the friction factor convention matches the equation and that percentages have not been entered where decimal fractions are required.

Then perform a plausibility review. Does increasing flow increase the modeled losses? Does lowering the source level increase the elevation requirement? Does an open-tank pressure difference cancel as intended? These checks do not replace the calculation, but they can expose an incorrect sign or cell reference.

Review significant figures as well. A head result displayed to six decimals is not justified when pipe roughness or equipment loss is provisional. Retain sufficient precision for calculation, then report a sensible rounded duty with its uncertainty and design basis.

The issued calculation should include a revision and a list of unresolved inputs. If the pipeline route or equipment changes, update the calculation rather than adding an unexplained allowance to the old result. A traceable revision is easier for the supplier to evaluate and for the commissioning team to verify.

Frequently asked questions

Is TDH the same as vertical lift?

No. Vertical lift is the elevation component. TDH can also include pressure difference, velocity difference, and flow-dependent losses. For a long pipeline or pressurized destination, those other components may be substantial even when the physical elevation change is modest.

Do I include atmospheric pressure for two open tanks?

If both surfaces are exposed to the same atmospheric pressure, that pressure cancels in the difference. Do not add it as an extra discharge requirement. Atmospheric pressure still matters in the separate NPSH assessment at the pump inlet.

Can TDH be negative?

For some boundary conditions, gravity or source pressure can provide more driving energy than the specified losses require. A negative calculated pump-head requirement indicates that the system may not need added pump head at that condition. Flow control and pressure behavior still need engineering review.

Does the highest pipe elevation always determine TDH?

Not for a fully established steady tank-to-tank flow calculation. Net endpoint elevations enter the energy balance, while the route's pressure profile and filling behavior need separate attention. High points can remain important for minimum pressure, air accumulation, and startup.

Can I use the same friction factor at every flow?

Only if that approximation is appropriate over the assessed range. The factor depends on flow regime and roughness. For more accurate work, recalculate it with the relevant fluid properties and flow. Slurries may require a different loss model altogether.

How do I include a filter?

Use the filter's pressure-loss information at the relevant flow and condition, then convert it consistently to head. Evaluate clean and credible fouled states where needed. Clarify whether a vendor's stated downstream pressure requirement already includes the filter to avoid double counting.

Is a closed-loop system's building height added to TDH?

In a completely filled closed circulation loop, the net elevation change around the loop cancels. The pump primarily supplies losses and any other defined energy requirement. System pressurization and local pressure conditions still require separate checks.

What should I do when only discharge pressure is measured?

Obtain the suction condition, measurement locations, flow, density, and relevant velocity and elevation corrections before estimating total pump head. A single discharge reading is usually insufficient. Label any provisional result so it is not mistaken for a verified design duty.

Request a selection against a documented duty envelope

Keep the boundary sketch, input table, calculations, and operating cases together. Resolve the fluid and equipment-loss assumptions before treating the result as final. Then compare pump curves against the paired flow-head requirements and complete the suction and power checks.

Contact Longteng Pump with your TDH calculation, slurry data, and installation conditions. Request a proposed configuration that identifies the curve basis, expected operating range, and remaining information needed for the project.

Sources and What They Support

• Hydraulic Institute Data Tool: System Curves — Supports the separation of static and frictional head and the use of Darcy–Weisbach and fitting-loss methods on an appropriate liquid basis.
• KSB Centrifugal Pump Lexicon: Head — Supports the distinction between pump head, system head, and geometric elevation head.