CBELIER user guide

CBELIER calculates the transient flows (water hammer) of pressurised water networks: you draw the network, you define the operations, you run the calculation and you obtain the pressure envelopes, the risks of cavitation and a technical report in PDF.

1. Overview

1.1 What CBELIER is for

Water hammer is a pressure wave caused by a sudden change in flow: closure of a valve, stop of a pump, start-up, rupture of a pipe. It can produce overpressures above the nominal pressure (PN) of the pipes, or underpressures down to cavitation and air entry. CBELIER makes it possible to:

• check that a gravity main, a pumping main or a looped network withstands the planned operations;
• size and compare the protections: air valves / air inlet valves, pressure relief valve, air vessel (ASA), one-way surge tank;
• compare several scenarios and deduce the design envelope from them;
• produce a technical calculation report in the name of your design office.

1.2 Two ways to use CBELIER

1.3 The approach in six steps

1. Create the account (online version) and check the credit balance.
2. Draw the network: reservoirs, junctions, pipes, then devices (valves, check valves, pumps).
3. Enter the characteristics: lengths, diameters, wave speed, PN, elevations, heads. If possible, import the real longitudinal profile.
4. Fit the protections: air valves, relief valve, ASA, one-way surge tank.
5. Define the scenarios (valve closure, power failure, pump start, pipe break…).
6. Calculate, analyse, produce the technical report; adjust the protections until the criteria are met.

2. Quick start

The shortest way to understand the tool: open an example supplied and calculate it.

1. Open the menu File › Examples and choose Pumping main with pump and air vessel.
2. The schematic is shown in the Design view. Click a pipe, a node or the pump: the right-hand panel shows its characteristics.
3. Click Steady state in the toolbar. The calculation is free and checks that the initial state (flows, heads) is consistent.
4. Click Run (F5). The transient is calculated; the view switches to Results.
5. Look at the longitudinal profile: the curves Hmax envelope and Hmin envelope frame the initial head. The verdict banner shows whether there is cavitation or the PN is exceeded.
6. The profile starts upstream of the steady state. To plot another profile, choose Custom: choose the pipes… in the list of paths, then add the pipes one by one: each pipe must have a node in common with the end of the path (buttons Reverse and Clear). The window View › Results in a separate window offers the same choice, with Print / PDF and a PNG button to save the figure as an image. The profile chosen is kept during the session and offered in the dialog of the technical report (box "Include the selected longitudinal profile", ticked by default), where it becomes the first figure; Clear removes it.
7. Return to Design, delete the air vessel (selection tool then Del) and run again: compare the envelopes.
8. After an up-to-date calculation, Run › Create the technical report (PDF)… (Ctrl+P) produces the report.

The Examples menu (File › Examples) is organised in four submenus:

• Design templates: Gravity main with high point and air inlet valve, Gravity main with pressure relief valve, Pumping main with pump and air vessel, Pumping main with one-way surge tank, Gravity main with surge tank, High point described by a detailed profile, Dual-orifice air valve at the outlet, Two-node relief valve (return to sump), Swing check valve (torque balance), Montgolfier hydraulic ram, Time-delayed pressure-reducing valve and guard valve, Two-compartment tank with weir wall, Gravity main, two-compartment tank, submerged weir, 'Muela scheme (Lesotho): tunnel, surge tanks, Francis turbines, 'Muela scheme: 600 s variant for online calculation, El Borj scheme (Morocco): tunnel, throttled surge tank, full load rejection, El Borj scheme: load acceptance at minimum level, 206 km water transfer (Xue 2022): initial solution, surge tank, 206 km water transfer (Xue 2022): three two-shaft towers.
• Devices in parallel without pipes (device groups): Twin valves in parallel, Station with two pumps in parallel, Booster pump with bypass check valve, Pressure-reducing valve with bypass valve (see 5.3).
• Validation on measurements and published maxima: HDPE Y-shaped system (Perugia), measured data and HDPE looped network (Perugia), thesis layout (17 nodes, numbering and distances of Maietta's thesis), whose laboratory measurements are superimposed on the calculation with Run › Calibrate on measurements › Measurements attached to the project; Steel + HDPE in series (Warsaw), published maxima and Additional HDPE pipe (Warsaw), published maxima (test rigs of the Warsaw University of Technology, Water 2022 and Energies 2021; only the published maximum overpressures are compared); Free-discharge test rig, to be calibrated on a test (described below).
• Book validation (reference curves attached): thirteen projects (seven from the CBELIER validation book and six taken from Wylie & Streeter), each with its reference curve (see 2.2).

Long lists scroll without the menu closing: mouse wheel, or the arrows ▲ and ▼ at the top and bottom of the list (hovering over an arrow scrolls continuously, a click scrolls by about a page). In a window of small height, the list is limited to the height of the window.

Show the results in a separate window, print, save as PDF. After a calculation, View › Results in a separate window (or the button "Separate window" of the Results view) opens a second window that you can drag onto a second screen; it is updated at each new calculation. It contains four tabs: Summary (verdict, indicators, warnings), Tables (extremes at the nodes and characteristics of the pipes, sortable by clicking the header, with CSV export and copy to Excel), Hmax / Hmin envelopes (longitudinal profile of each path between reservoirs, in heads or in pressures) and Curves over time (pressure, head or flow rate of the chosen nodes and pipes, with a time window and extreme values). The button Print / PDF opens the print dialog of the browser: choose your printer, or "Save as PDF"; the section "Printed content" makes it possible to keep only some tabs. The layout is A4, on a white background, with a header (project, scenario, date). The flow over time is followed for the pipes adjacent to the monitored nodes; if the window is blocked, allow pop-up windows for CBELIER.

Compare the calculation with the attached measurements (without recalibration). For the Perugia validation examples and those of the validation book (see 2.2), the Results view shows, after the transient, a card "Measurements attached to the project": the measurement of the chosen sensor and the CBELIER calculation are plotted on the same graph (head variation ΔH or head), with the root-mean-square deviation and the measured amplitude. No recalibration is done: the calculation is plotted as it is, the measurement being placed in the time of the model (start of the operation at t = 0). This comparison works in both versions; the automatic recalibration is done with Run › Calibrate on measurements (see 7.10), which is also available in both versions.

Validate and calibrate a free-discharge test rig. The example Free-discharge test rig, to be calibrated on a test describes a typical laboratory set-up: pressurised reservoir of 40 m, steel pipe DN 50 of 62.5 m (wave speed 1,100 m/s), pressure sensor at node C at 3 m from the end, nozzle of 5.5 mm (Cd 0.90) closed in 30 ms by an end valve. The values are orders of magnitude to be replaced by those of your installation. No measurement is attached. To validate the model on your test: (1) adapt the data of the rig (length, diameter, wave speed, head, nozzle diameter, closure time); (2) run the transient and note the overpressure calculated at the sensor; (3) open Run › Calibrate on measurements… (version installed on the computer), choose node C, paste or upload your pressure time series (template exemples/banc_sortie_libre_gabarit_mesures.csv: time in seconds; pressure in m H₂O, the closure at t = 0, a few points before for the reference pressure); (4) tick the parameters to be calibrated: discharge coefficient Cd of the outlet, closure time of the outlet, wave speed factor, coefficient k of the unsteady friction, time shift; (5) run the calibration, examine the superposition measurement / initial model / calibrated model, then Apply to the model. Tick only what your measurements make it possible to distinguish: the Cd and the closure time are identified well only if the steady flow and the shape of the pressure front are measured. The calibration compares the variations of head: the elevation difference of the sensor has no effect. Check that the calibrated values remain physical (Cd between 0.6 and 1, closure time close to the real time of the valve) and that none reaches its bound: a parameter at its bound reveals a data error or a phenomenon that is not modelled (air pocket, viscoelasticity).

2.1 Your first project from scratch

1. Ctrl+Alt+N (or File › New project) opens an empty project. Give it a title in the right-hand panel (with nothing selected, it shows the properties of the project).
2. Reservoir tool (R): place the upstream reservoir, then a second, downstream reservoir.
3. Junction tool (J): place at least two intermediate junctions (high points, low points, branches).
4. Pipe tool (T): click the start node then the end node.
5. Select each element and enter its values (see chapter 5).
6. For a simple operation: place a Valve between two junctions and set its closure law.
7. Watch the Checks tab of the side panel and the log at the bottom of the screen: any element in red must be corrected before the calculation.
8. Save with Ctrl+S (file .cbelier.json); File › Save as… (Ctrl+Shift+S) creates a variant under another name.

2.2 Validation examples of the book (reference curves attached)

The submenu File › Examples › Book validation opens thirteen projects: seven from the CBELIER validation book (table below) and six taken from the work of E. Benjamin Wylie and Victor L. Streeter, Fluid Transients (McGraw-Hill, 1978), described further on. Each is an ordinary project (file .cbelier.json, which can be saved under another name) that contains, in addition to the network, the reference curve (laboratory measurement or digitised published curve) in the field "attached measurements". They serve two purposes: compare the calculation with a reference without adjusting anything, then, if you wish, calibrate the model on this reference.

The initial deviations are values calculated by CBELIER with the projects supplied (head variations, in m of water); they change if you modify the project. The amplitude is that of the reference curve.

Cases taken from Wylie & Streeter

Source: E. Benjamin Wylie and Victor L. Streeter, Fluid Transients, McGraw-Hill, 1978. The six projects use the data published in the work (examples 3-1, 3-7, 5-2, figure 9-7, Propson's tests, §8-5 with its programs of the appendix) and, when the book gives only a curve, the curve is read from the figure (reading uncertainty stated in the description of each project). The deviations below are those of the CBELIER calculation from the book, as measured with the projects supplied.

Reservations. In the project "Pump and condenser", the pump is represented as in the book by a head imposed as a function of time (upstream reservoir with a head law, and a loss in series), not by a pump with its characteristic and its inertia; the friction of the condenser (f = 0.415 in the book) is limited by the maximum roughness accepted by the interface (0.05 m), hence the shift reported; the degassing of the book (Henry's law) is not modelled, only the case without air is comparable.

Using an example

1. Open the project, then Run (F5). The calculation is done on the server in the online version.
2. In the Results view, the card "Measurements attached to the project" plots the reference curve and the calculation on the same graph, with the root-mean-square deviation and the amplitude. The calculation is plotted as it is; the curve is placed in the time of the model.
3. Calibration (both versions; online, the calculation is done on the CBELIER server and it is included in the study, see 7.10): Run › Calibrate on measurements… › Measurements attached to the project offers the calibration of the wave speed (factor), of the coefficient k of the unsteady friction and of the time shift; tick only what the curve makes it possible to distinguish, examine the superposition, then Apply to the model if the result remains physical.
4. Save the calibrated project under another name: the original project, without calibration, remains the reference for comparison.

Cases of the book not available in the interface: case 3 of the same suite (pump table specific to the original software) remains outside the project format. Cases 5, 6, 7 and 15 (variable-flow inflow) and 9 (variable-head reservoir) are not yet included: the project format can now describe an inflow and a reservoir head that vary with time (see 5.1 and 5.1 bis), but these cases have not been ported; they remain calculable with the scripts of the book. Cases CV-012 (calibrated model) and CV-014 (Perugia network) also exist in the form of the two Perugia examples of the submenu "Validation on measurements and published maxima".

3. Account, credits and prices

3.1 Access to the service

On registration, 2 credits are offered. Account › My account and credits shows the balance and the movements.

3.2 How much a study costs

A study corresponds to a pipe layout. Its cost depends on its complexity class, which is the highest of three measures: number of physical pipelines, number of devices and attached devices, total length.

• A physical pipeline is a sequence of pipes without branching, without a device, an attached device or a demand: dividing a pipeline into several pipes (to place a profile on it, for example) does not make it count several times.
• Before the run, the interface shows for example "Complexity C2 · new study · 2 credits · balance 18".
• The steady state is free. A calculation that fails costs nothing (the credit is returned).
• Upgrade. A calculation that is exceptionally heavy for its class (long simulated duration, very short pipes that impose a very fine time step) can be charged in the higher class that covers it. The interface proposes it before any charge, for example "Complexity C4 → C5 (upgrade) · 16 credits": accept, or reduce the simulated duration. For a variant of a study already paid for, only the difference is charged (C4 paid 8 credits, variant in C5: complement of 8 credits); the study then remains open at this level. Beyond class C5, the calculation is on quotation.
• The technical report is included in the study: no additional credit.

3.3 Credit packs and payment

Menu Account › Buy credits…. Bank transfer: VAT of 20 % in addition, a reference is generated, the credits are added on receipt of the funds and an invoice is sent to you. Bank card and PayPal: payment in euros. Institutions and large volumes: on quotation from ALFA WAMANE.

3.4 My studies and credits

Account › My studies and credits… (online account) shows, read-only, your open or completed studies, your latest calculations, the credit movements and your purchases by bank transfer. Only the data of your account are visible. Account › Company profile… makes it possible to enter the header and the signatories of the technical reports without producing a report.

4. The interface

4.1 The areas of the screen

4.1 bis The symbols of the schematic

Since interface 4.9.0, the toolbox and the schematic use the same pictograms, drawn on a grid of 24 × 24 px (solid shapes, details in reserve). The family is read from the shape and the colour:

Status markers. An element carries at most one round marker, at its top right corner, chosen in order of priority; each marker has its sign and a tooltip, so it can also be read without the colour:

Connection points. With the Pipe tool or a device tool, each node shows a hollow blue circle where the link can be attached; the start node chosen turns solid green.

Results on the schematic. After a transient, the box "Results on the schematic" colours the network according to the maximum pressure, the minimum pressure or the ratio Maximum pressure / PN of the pipes. This last mode puts each pipe in one of three classes: compliant (≤ 0.8 PN), to be watched (0.8 to 1 PN) and exceeded (> 1 PN); a pipe that exceeds is also drawn thicker, and its tooltip gives the ratio. Out-of-date results no longer colour the schematic.

4.2 The menus

Touch screens (tablets, Android). The submenus open as a drop-down list in the menu: tap a submenu (for example Examples, then Book validation) to expand it, scroll the list with your finger, tap the project you want. Opening another submenu of the same level closes the previous one, without closing the one that contains it.

Menus with the keyboard. Reach a menu with the Tab key, then Enter or Space to open it; ↓ ↑ choose a command, → opens a submenu (or moves to the next menu), ← closes the submenu (or moves to the previous menu), Enter runs, Esc closes.

Scrolling submenus (desktop computer). When a list exceeds the height of the window, it stops at the edge of the window and scrolls without the menu closing: mouse wheel, or arrows ▲ ▼ at the top and bottom of the list (hover for continuous scrolling, click to move by a page).

4.3 Keyboard shortcuts

4.4 Units and conventions

CBELIER offers four unit systems, chosen project by project. They change the display and the input; they change neither the saved data nor the calculations (g = 9.81 m/s² in all cases).

• Choosing the system. Click in an empty area of the schematic so that nothing is selected: the "Properties" panel then shows the setting Unit system. The choice is saved with the project.
• Existing projects. A project saved before this feature, or left in AEP, opens and is saved again exactly as before: the file adds the field "units" only if you leave AEP.
• What follows the system of the project. The input fields and their labels, the tables, the Results view (indicators, cavitation, profiles, attached devices), the scenarios, the sensitivity, the closure optimisation, the calculation log, the validation messages, the help, the imports (longitudinal profile, calibration measurements, EPANET) and the technical report (PDF).
• Default import value. Imported files are read in the unit of the system of the project, unless another choice is made in the import dialog.
• Priority. If your account imposes a display preference other than m H₂O / L/s (see below), it prevails over the system of the project for the pressures and flow rates of the results.
• Angular velocities in rad/s, inertia in kg·m²; numbers follow the notation of the interface language (a decimal comma is also accepted on input).
• Account › Display preferences makes it possible to show the pressures in bar and the flow rates in m³/h, with additional decimals. This choice applies to the indicators, the verdict and the table of extremes of the Results view; it changes neither the inputs nor the technical report, which follow the unit system of the project. With bar, the pressure graphs remain in m H₂O. The CSV exports always remain in the units of the engine (m H₂O, L/s, m), whatever the system.

4.5 The properties dialog

Each node, pipe or device has its properties dialog, in the manner of the transient software on the market: a window in the centre of the screen, organised in tabs, that you confirm with OK or discard with Cancel. The "Properties" side panel remains available: it shows the same fields, and the two remain synchronised.

Opening the dialog. Double-click the element in the schematic, or select it and press Enter, or right-click then "Properties…". A double-click on a row of the bottom tables (on the name of the element) also opens it.

OK and Cancel. The entries apply at once to the schematic, the panel and the checks, so that you see their effect. OK (or Ctrl+Enter) saves them as a single action "Modify <element>": a single Ctrl+Z undoes them all. Cancel (or Esc, or the cross) restores the element, the history and the state of the results exactly as at the opening. While the dialog is open, Ctrl+Z, F5 and the file commands wait for OK or Cancel. Esc while typing in a field only restores that field.

Header. At the top of the dialog, always visible: the identifier, for a pipe or a device its upstream and downstream nodes (button "Open…": confirms the dialog then opens that of the node), the list "Copy from", and a red banner when the element has a model error.

A "✓" in the name of a tab shows an option in service (attached device fitted, viscoelastic wall, longitudinal profile, pump control…). The tab shown is kept after each entry.

Pipes (nodes): pipes and devices connected, with their direction, length and diameter; "Open…" confirms the dialog and opens that of the connected element. A node without a connection has this tab in red.

Preview of the characteristic (pump, Curves tab): it plots only the data entered — rated point, H(Q) curve and efficiency η(Q) of the manufacturer. With the Suter polynomials or the tables of the book, only the rated point is plotted: the complete four-quadrant curves are calculated by the engine.

Copy from. Takes all the characteristics of another element of the same type (attached device and its settings, section and wave speed of a pipe, operating law, pump curves…). Never copied: the identifier, the position, the ends, the notes, and for a node the elevation, the head and the demand or inflow flow rates, for a pipe the length and the longitudinal profile. Cancel undoes the copy.

Notes. Free text saved in the project (origin of the data, assumptions, drawing reference…). It is never sent to the engine or to the server: it changes neither the results nor the cost of a study.

Status. The model checks that concern this element (the same messages as the Checks tab), the steady state (head and pressure, or flow rate and velocity) and, after an up-to-date transient, the pressure envelope (p₀, p max, p min and their times; at both ends for a pipe or a device). The name of the tab summarises: "Status ✓", "Status ⚠ n" (warnings) or "Status ✕ n" (errors).

Help. The "?" button to the right of the tab bar opens this guide at the section of the tab shown (Minor losses, Alerts, Viscoelastic wall, Longitudinal profile…).

Tablet. On a touch screen, the dialog takes up the whole screen, its tabs scroll with the finger and its buttons are enlarged; a double tap opens the dialog, a long press opens the element menu.

5. Modelling the network

The units given in this chapter are those of the AEP system (by default). With another system, the fields, labels and tables follow the system of the project (see 4.4).

5.1 The nodes

5.1 bis Demands and inflows at junctions

A junction can carry a demand point and/or an inflow point. Input: Properties panel of the junction (section "Demand and inflow"), columns "Demand" and "Inflow" of the node table (in L/s), or EPANET import (positive demands = demands, negative demands = inflows). The schematic shows them with an outgoing arrow (demand) or an incoming arrow (inflow) with the flow rate.

Constraints: junction connected only to pipes, without an air valve or a break. For a node touching a valve, a check valve or a pump, place the flow on a neighbouring junction (the EPANET import does this automatically). The net balance (demands − inflows) is taken from the reservoirs.

5.1 ter Variable-level tank

The Variable-level tank tool (key N) represents a sump or a reservoir whose level rises and falls during the transient, instead of imposing a constant head. In the Properties panel:

• initial, minimum and maximum levels, and overflow;
• height / area curve: table of pairs (h, A); the area is interpolated linearly between the points;
• asymmetric head losses: filling ζ (inflow) and emptying ζ (outflow), referred to the velocity in the connected pipe (loss = ζ·V²/2g).

External weir (tab "External weir" of the properties dialog, interface 4.10.9, engine 3c.15): "None (overflow at the maximum level)" or "Yes (weir law)", with the crest elevation Z_x, the crest length, the crest shape (sharp-crested, broad-crested or custom) and μ. The flow discharged to the outside follows the weir law, Q = μ·L·√(2g)·(z − Z_x)^3/2: the level rises above the crest by the head needed to discharge the flow, and the maximum level becomes the height of the wall (warning "wall overtopped" beyond). The results give the spilled volume and the maximum flow rate. μ must be justified as for the weir wall (see 5.3 ter).

Emptying and draining front (interface 4.10.12, engine 3c.18). When the tank empties and the flow goes out, the air that has entered occupies the upper part of the descending pipes: a draining front moves down reach by reach and stops at the level held downstream; it moves back if the water returns. The results give the drained length, the minimum level of the front, the air volume and the time. Before, the descending pipe emptied endlessly.

The checks report missing or inconsistent data, and the technical report includes these characteristics. The variable-level tanks of an EPANET model (TANK) are taken over on import.

5.1 quater Surge tank

The Surge tank tool (key E) places a tank open to the atmosphere, to be connected to the pipe by a pipe. Fields: elevation of the base Z, area A_c, height of the crest h_max and ζ of the connecting orifice. Two lists specify how it works:

• Type of surge tank: Ordinary (the water enters and leaves in both directions) or One-way (tank with a check valve: it empties into the pipe when the head falls, but is not filled by the pipe; its filling by a separate line is not modelled).
• Shape: Column only, or Differential (Johnson): the central column spills over its crest into an annular tank (area A_t, height h_t) that communicates with the base through an orifice (filling CdAs, optional emptying CdAs). The column reacts quickly to small variations, the tank absorbs the large ones. If the level of the tank exceeds the crest of the column, a warning invites you to review A_t or h_t.

Variable area A(z) (interface 4.10.15, engine 3c.20). List "Area": Constant (A_c) or Variable with height A(z), entered in rows "height above the base; area". The area is interpolated linearly between the points and extended as a constant beyond; a step (expansion chamber, upper tank) is described by two very close points. The volume and the level are calculated exactly from the curve. The curve must cover the whole height, from the base to the crest (warning otherwise).

Throttle (interface 4.10.15, engine 3c.20). List "Connection to the pipe": Orifice (single ζ) or Throttle (asymmetric losses): diameter D of the throttle, ζ at the inlet (the water rises in the surge tank) and ζ at the outlet (it falls), referred to the velocity in the throttle. Variable area and throttle do not apply to a differential surge tank.

Layout. Place the surge tank on the route, between the supply pipe and the downstream pipe (the surge tank serves as a through node, as in the example). A surge tank at a dead end, connected by a single pipe to an intermediate junction, does not always make it possible to establish the initial steady state: the calculation then starts out of equilibrium and the alert "Approximate initial state" is shown.

Examples: File › Examples › Design templates › "Gravity main with surge tank"; "'Muela scheme (Lesotho)" for the variable area and the throttle; "El Borj scheme (Morocco)" for the role of the throttle (without it, the surge tank overflows at the full load rejection and empties at the load acceptance at the minimum level: remove the throttle in the dialog of the surge tank to see it).

5.2 The pipes

5.2 ter Minor losses distributed on a pipe

The Minor losses tab of a pipe (or the section "Minor losses" of the panel) lists the singularities spread along the pipe: bends, tees, tapers, open valves… Each row gives a description, a number and a unit K, referred to the velocity in this pipe (loss ΔH = K·V²/2g). The sum ΣK = Σ n·K is shown and sent to the engine.

Model (engine 3c.9). ΣK is distributed over the whole length of the pipe and added to the friction: equivalent coefficient f + ΣK·D/L, that is ΔH = (f·L/D + ΣK)·V²/2g in the steady state, and the same term in the transient (method of characteristics, boundary conditions, rigid columns, finite-volume fallback). A distributed loss does not reflect the waves: for a localised and strong singularity (partly open valve, orifice plate), use the device "Minor loss", which concentrates it at one point.

Values of K. The input is free: CBELIER proposes no default value. Use those of the manufacturer or of a reference handbook, and cite them in the notes of the pipe. ΣK appears in the pipe table of the technical report, with the details of the singularities.

Verification. A pipe without a singularity gives exactly the same results as before version 3c.9. The model has been checked in the steady state with the analytical formula, and in the transient by comparison with the same loss split into more and more "Minor loss" devices, whose results converge towards those of the distributed loss.

5.2 bis Plastic pipes: the viscoelastic behaviour

In an HDPE or PVC pipe, the wall does not deform instantaneously under the overpressure: part of the deformation is delayed (creep). This delayed deformation damps the oscillations and lowers the peaks, whereas a purely elastic calculation overestimates them. CBELIER represents it with a generalised Kelvin–Voigt model (Covas et al., 2004 and 2005), optional and specific to each pipe. Without it, the pipe remains elastic and the results are unchanged.

Where to enter it. In the pipe inspector, block "Viscoelastic wall (PE, PVC… optional)": tick "Viscoelastic pipe", then enter:

A table of elements (one row τ; J per element) makes it possible to describe several time scales; two elements are usually enough. At least one row is required.

The wave speed to enter. With viscoelasticity, the wave speed a of the pipe must be the instantaneous elastic wave speed of the wall, that is that of the wave before the creep acts. It is higher than the "apparent" wave speed that one would choose for a purely elastic calculation. On the Perugia HDPE measurements, the best calibration gives an instantaneous wave speed of 390 to 400 m/s, above the 200 to 350 m/s of the table in 5.8. The interface warns if the wave speed exceeds 700 m/s on a viscoelastic pipe. The Young's modulus of the catalogue for HDPE (1 GPa) is marked "to be validated": check it.

Where J and τ come from. Three sources, in order of confidence: transient measurements on the pipe concerned (calibration; see 9.2), published values for the same material and the same type of pipe, or failing that the values of the manufacturer. Values from the literature cannot be transposed without precaution: they depend on the precise material, the temperature and the age of the pipe. The model is linear and has no temperature dependence: J and τ are those of the temperature and of the stress level at which they were determined.

Rules for good use.

• Calibrate the viscoelasticity (J, τ) before the unsteady friction (Brunone's coefficient k). On the Perugia measurements, the damping attributed to k is explained at least as well by a stronger creep; k then absorbs what J and τ have not described.
• Keep τ ≥ 2·Δt: the scheme is explicit and becomes unreliable below this (a warning is shown). Aim rather for τ ≥ 3 to 4·Δt. An element with τ = 7.5 ms therefore imposes a step of about 2 ms or less.
• Provide at least 8 reaches on the pipe; below that, the damping is poorly resolved (warning).
• The model is not applicable with very large compliances (γ = a²·ρ·D·J/e of the order of 1 or more). In this case, refine the step or increase τ.
• The finite-volume cross-check ignores the viscoelasticity: on a network with a viscoelastic pipe, its deviation is only indicative and triggers no alert.

5.3 The devices

Valve

Defined by its maximum effective area Cd·As (m²) and its operating law. Five laws are available:

The two-stage closure is the classic strategy to limit the overpressure: a fast closure at the start, slower afterwards.

Check valve

Non-return valve: effective area Cd·As (m²) and initial state open. It closes when the flow reverses, which can produce a second pressure peak.

Swing check valve (torque balance)

The check valve above closes instantaneously when the flow reverses ("ideal" check valve), or follows a simplified disc law (dynamic model). The swing check valve with torque balance ("Swing check valve" tool of the toolbox, Links section) describes the real hinged disc: you give its mass, its lever arm, the inclination of the seat, an optional counterweight or torsion spring, and the engine calculates at each step the opening angle, the reverse flow before closure and the impact velocity on the seat. It is the way to know whether a given check valve slams or not, and to compare a light disc, a heavy disc, a counterweight and a spring. It connects two junctions, like an ordinary check valve, and can be placed at the discharge of a pump.

Physical principle. The disc rotates about a hinge. In normal flow, the thrust of the water lifts it: it settles at the equilibrium angle where the torque of the hydraulic thrust equals the torque that returns it to its seat (its weight, plus the counterweight and the spring if any). The larger the flow, the more the disc opens, up to the stop. When the pump stops, the flow decreases, the thrust decreases and the disc falls under its weight while the water column slows down then moves back in the opposite direction. If the disc is slow (high inertia, braked by its hinge, or with a large lever arm), it is still open when the reverse flow develops: the reverse water then pushes it violently onto its seat (slam) and the sudden stop of the reverse flow creates an overpressure. A disc that closes before the reversal, thanks to a sufficient weight or counterweight, avoids the reverse flow and the slam; at the extreme, it closes with the flow still positive and cuts off the moving column, which can also create an overpressure on a long pipe (the guide of the spring check valve points this out).

Mathematical principle. We write φ for the opening angle (0 = closed, φ_max = stop), ω = dφ/dt, ΔH = H_upstream − H_downstream the head loss through the check valve, A = πD²/4 the area of the seat, l_p the lever arm of the thrust (by default, that of the weight), l_g the arm of the weight, m the mass of the disc, g = 9.81 m/s². The balance of torques about the hinge is written:

• Equation of motion. I_tot·dω/dt = M_hyd − M_f(φ) − c·ω, with M_hyd = ρ·g·ΔH·A·l_p (torque of the hydraulic thrust) and c the viscous damping of the hinge (N·m·s/rad).
• Closing torque. M_f(φ) = m·g·l_g·sin(θ_s + φ) + m_cp·g·l_cp·sin(θ_s + φ + β) + T₀ + k·φ, where θ_s is the inclination of the seat from the vertical (0°: vertical seat, horizontal pipe, 90°: horizontal seat, vertical pipe), m_cp, l_cp and β the mass, the arm and the setting angle of the counterweight, T₀ the preload and k the stiffness of the torsion spring. The sine terms are the moment of the weight about the hinge: it increases with the opening as long as θ_s + φ remains below 90°.
• Inertia. I_tot = I_disc + m_cp·l_cp² + f·ρ·(π/6)·D³·l_p². I_disc is m·l_g² by default; the last term is the inertia of the mass of water entrained with the disc (that of a sphere of diameter D, at l_p from the hinge, multiplied by the coefficient f, 1 by default). This mass of water is of the same order as that of the disc: ignoring it would distort the closure time.
• Head loss. ΔH = Q·|Q| / (2g·(Cd·A · a(φ))²), where Cd·A is the effective area of the fully open check valve and a(φ) ∈ [0; 1] the relative flow area: proportional to the angle up to the stop by default (a = φ/φ_max), or given by a table "angle; a" (Cv curve against angle of the manufacturer). As long as the disc has not touched its seat, reverse flow is possible (Q < 0, ΔH < 0, negative thrust torque: it helps closing).
• Equilibrium and steady state. At the steady flow Q, the equilibrium angle φ* is the root of ρ·g·ΔH(φ, Q)·A·l_p = M_f(φ), searched by bisection; if the hydraulic torque exceeds M_f at the stop, the disc is against the stop. The head loss of the check valve in the steady state is then M_f(φ*) / (ρ·g·A·l_p): it is calculated with the network, so that the initial state is consistent with the first step of the transient.
• Closure. The disc touches its seat when φ reaches 0: the flow is then zero (as for a closed check valve), the impact velocity ω_imp (rad/s) and the velocity at the thrust arm ω_imp·l_p (m/s) are recorded, the impact is inelastic (no rebound). Impacts slower than 0.05 rad/s are contacts without a slam and are not counted.
• Opening. With the disc closed, it lifts as soon as the torque of the differential pressure exceeds the closing torque at rest: ρ·g·ΔH·A·l_p > M_f(0), that is ΔH > M_f(0) / (ρ·g·A·l_p) (the "cracking head", shown in the form).
• Coupling with the method of characteristics. At each step, the node is solved with the angle of the previous step (loss law above, implicit solution with the pipes), then the disc is advanced over this step by sub-steps, with the flow and the area of the step. As the loss at frozen flow grows like 1/a² when the disc settles, the area cannot decrease by more than half during one step: the slam torque remains bounded and the flow collapses at the next step under the effect of the overpressure.

Results. The Results view adds a card "Swing check valve": curve of the opening angle, initial angle, number of impacts, maximum impact velocity (rad/s and m/s) with its time and the flow at that time, maximum reverse flow. An impact velocity of more than a few m/s at the thrust arm is the sign of a severe slam: the comparison between variants is made on the overpressure at the downstream node and on this velocity.

Example: File › Examples › Design templates › "Swing check valve (torque balance)". Pumping main of 120 m in DN 500 to a reservoir at 80 m, without protection, pump tripped at 1 s, disc of 90 kg with an arm of 0.30 m on a seat inclined at 7°. In the steady state (218 L/s) the disc is open at 37.3° (head loss of the check valve 0.32 m); at closure, the reverse flow reaches 5.1 L/s and the impact velocity 2.1 rad/s (0.64 m/s at the thrust arm), for a maximum pressure of 83.2 m H₂O downstream, against 80.8 m H₂O with an ideal check valve. A disc of 300 kg closes before the flow reversal (reverse flow below 1 L/s, 80.7 m H₂O); a counterweight of 40 kg at 0.5 m gives 82.4 m H₂O; a torsion spring (30 N·m of preload, 60 N·m/rad) 80.8 m H₂O; a damping of 60 N·m·s/rad, which brakes the closure, 86.7 m H₂O. These orders of magnitude are confirmed by the verification tests of the engine: torque equilibrium within 3·10⁻⁸, free-fall closure identical to a reference Runge–Kutta integration, impact velocity consistent with the conservation of energy (½·I·ω² = ∫M_fdφ).

Minor loss

The Minor loss tool (Links section) connects two junctions and represents a bend, a tee, a reducer, a strainer or a meter: ΔH = K·V²/2g, V being the velocity in the reference diameter D. Fields: coefficient K, reference diameter D and, optionally, K in reverse flow for an asymmetric device (diffuser, nozzle); empty, the loss is the same in both directions. The engine treats it as a fixed orifice that is always open.

Pump

The engine uses the pump curves in 4 quadrants (normal operation, flow reversal, turbining). A station of pumps in parallel is possible: place several pumps between the same junctions.

Devices in parallel or in branch without a pipe (device groups)

Devices can be connected directly to one another, without an intermediate pipe, in series (pump then check valve, valve then check valve) as well as in parallel: two twin valves between the same two nodes, two pumps with their check valves between a suction header and a discharge header, a bypass check valve between the suction and the discharge of a pump, a bypass valve around a pressure-reducing valve. To place a second device between the same two nodes, draw it like the first: the schematic moves it aside as a curve.

Calculation principle. The devices that share a node (other than a reservoir) form a group. A group reduced to a simple chain follows the historical method, with unchanged results. An arrangement in parallel, in branch or in a loop is solved as a block at each time step: the unknowns are the head of each node of the group and the flow of each device; each open device gives its law (valve, check valve, pump, pressure-reducing valve, flow control valve, return relief valve), each closed device a zero flow, and each node the continuity (with, at the nodes that carry pipes, the characteristic relation). The system is solved by Newton's method; continuity is exact at the nodes.

Steady state. It is calculated by the global gradient method. A pressure-reducing valve takes one of three states: regulating (downstream head at the set point), fully open, or closed, according to the rules of EPANET; the state found is checked again with the law of the transient calculation. Two pressure-reducing valves in parallel with different set points share the demand as in a "low flow / high flow" station.

Examples: File › Examples › Devices in parallel without pipes (twin valves, station of two pumps, booster pump with bypass check valve, pressure-reducing valve with bypass valve).

5.3 bis Pressure-reducing valve and flow control valve: response time

By default, the pressure-reducing valve and the flow control valve are ideal: at each time step, the pressure-reducing valve holds the downstream set point (the flow control valve, the maximum flow) as if it could open or close in an instant. A real device, with a main valve controlled by a pilot, takes several seconds to travel its stroke; the speed is set by the needle valve of the pilot circuit and often differs on opening and on closing.

In the properties dialog, tab Response time, choose "Valve response: Time-delayed" and enter:

The values entered when "Time-delayed" is chosen (2 s, 30 s and 30 s) are only an example: replace them with those of the manufacturer's data sheet or of measurements (operation test). A zero value removes the corresponding limit; all three at zero give back the ideal device (results identical to the previous versions). The opening χ is plotted in Results › Devices › Link analysis. During an operation, the downstream head of a time-delayed pressure-reducing valve can depart from the set point: check the PN of the downstream section, in particular between a pressure-reducing valve and a guard valve that closes. Example: File › Examples › Design templates › Time-delayed pressure-reducing valve and guard valve (illustrative values).

5.3 quater Francis turbine

The Francis turbine tool (Links group) is placed between two junctions: the inlet (penstock or branch of the trifurcation), then the outlet (draft tube). Interface 4.10.15, engine 3c.21.

Model. Head and torque from the Euler equation (swirl imposed by the wicket gates, friction losses and outlet swirl losses). The shape is fitted to the published points of the Francis-99 model turbine (NTNU) then scaled to the rated point. Before the disconnection, the electrical grid imposes the speed n_R; after, the unit is free: J·dω/dt = M_hydraulic − M_losses.

Results. Results › Devices: card "Francis turbines" (maximum speed, time, overspeed, final state) and "Link analysis" (heads, flow, speed and wicket gate opening over time). The technical report includes the description of the turbine and its maximum speed.

Example: File › Examples › Design templates › "'Muela scheme (Lesotho)" (full load rejection of the three units); "El Borj scheme (Morocco)" (full load rejection of two units and load acceptance; calculation speed transposed to the Francis-99 similarity, explained in the notes of the turbines).

5.3 ter Two-compartment tank with weir wall

The Two-compartment tank (weir wall) tool, in the Links group of the toolbox, represents a tank whose two compartments are separated by a wall whose crest acts as a weir. It is a device placed between two junctions: the start junction (J1) carries compartment 1 (upstream), the end junction (J2) compartment 2 (downstream). Each compartment has its own free level; the water passes from one to the other over the wall, in either direction.

Weir law. Free weir (downstream compartment below the crest): Poleni's law, Q_s = μ·L·√(2g)·h^3/2, h being the head on the crest. Submerged weir (downstream above the crest): Villemonte correction (1947), Q_s = Q_free·[1 − (h_d/h_u)ⁿ]^0.385. When compartment 2 is higher than compartment 1, the direction reverses. Over a band of 1 mm around equal levels, the law is connected without a jump in slope for the stability of the calculation. The two compartments and the weir are solved together at each time step, conserving the volume exactly.

Broad-crested weir (interface 4.10.4, engine 3c.14). When the crest is long in the flow direction, the water passes over it in critical flow. As long as the downstream head stays below 2/3 of the upstream head, the weir is free: Q_s = μ·L·√(2g)·h_u^3/2. Beyond, it is submerged: Q_s = (3√3/2)·μ·L·√(2g)·h_d·√(h_u − h_d). The two laws connect in value and in slope. μ = 0.385 by default, theoretical value without losses ((2/3)^3/2/√2), to be justified. Source: C. Ancey, Hydraulique à surface libre, EPFL course, chap. 1. If the crest thickness e is entered, CBELIER compares it with the maximum head h calculated on the crest: thin crest if e < h/2, broad if e > 2h/3 (Cassiopée documentation, INRAE, § 4.4.1.2). A warning reports a shape that does not match; the calculation is not changed.

Input rules. The junctions J1 and J2 connect only pipes (at least one each), without an attached device. A demand or an inflow can be carried by J1 or J2 (branch connected directly to a shaft, interface 4.10.10, engine 3c.16): its flow enters the balance of the compartment, the demand following the orifice law set on the level of the compartment; the results give the volumes taken and injected per compartment. The crest must be above both floors and below the maximum level of compartment 1. The structure is not available with the finite-volume calculation or with the EPANET import.

External weir of each compartment (interface 4.10.9, engine 3c.15): section "External weir" of compartment 1 and compartment 2, the same fields and the same law as for the variable-level tank (see 5.1 ter); volume spilled per compartment in the results card.

Structures in series and imposed level (interface 4.10.11, engine 3c.17). With several two-compartment tanks in the mode "levels derived from the weir, both compartments" (towers of a transfer main), the levels of all the compartments are searched together in the steady state, the mass being conserved in each compartment. Each compartment then has the choice "Steady-state level: Derived (balance of the compartment) / Imposed (initial level entered)": a compartment that supplies only demands has an undetermined level and must be imposed; the imbalance of an imposed compartment is quantified (adjust the head valve). The two compartments of the same structure cannot both be imposed.

Empty compartment. If a compartment empties, the draining front described in 5.1 ter applies to the descending pipes that leave it (interface 4.10.12, engine 3c.18).

Results. Results › Devices, card "Two-compartment tank": levels of the two compartments with the crest, flow over the weir Q_s, supply to compartment 1 and outflow from compartment 2, regime (closed, free, submerged, reversed) and volume passed over the weir. The technical report includes these data, the weir law with its sources and the balance of the structure.

Examples with several structures: "206 km water transfer (Xue 2022): three two-shaft towers" (towers in series, external weirs, branch on a shaft) and its "initial solution" with a surge tank.

Example: File › Examples › Design templates › "Two-compartment tank with weir wall" (closure then reopening of the downstream valve; scenario "Withdrawal on J1"). As long as compartment 2 stays below the crest, compartment 1 does not see the waves coming from downstream: this is the hydraulic purpose of the weir wall. Second example: "Gravity main, two-compartment tank, submerged weir" (upper reservoir, HDPE DN 250, compartments of 1.5 and 1 m² with different initial levels, ductile iron DN 250, valve closed in 30 s or in 120 s): compartment 2 fills and submerges the weir around t ≈ 47 s, then compartment 1 rises with it up to the overflow and the flow slows down in the HDPE pipe. In the third scenario, the valve is opened again in 30 s as soon as the maximum level is reached: the weir becomes free again around t ≈ 2,400 s and compartment 1 returns to its initial regime.

5.4 The protection devices

Choose the tool in Attached devices then click the junction. The right-hand panel then makes it possible to set the attached device. Only one attached device per junction.

Air valve / air inlet valve

An air valve lets air in when the pressure falls (it limits the underpressure) and lets it out slowly when the pipe fills. The air pressure is not released instantaneously: the engine calculates the flow of air through the inlet and outlet orifices.

• Catalogue device: manufacturer / model / DN. At present, only the RAMUS CEAI DN 150, 200, 250, 300, 400, 500 have complete data. The TRIFON and SNH 3F models appear in the catalogue but remain not simulable as long as the manufacturer's data sheets are missing (critical message).
• Parametric air valve: inlet orifice D and inlet Cd (mandatory), outlet D and Cd, opening threshold (m H₂O).
• Dual-orifice outlet (optional): a second outlet orifice (D and Cd) smaller than the first. It replaces the first orifice as soon as the overpressure in the pipe reaches the head difference threshold (m H₂O) or the expelled air flow reaches the flow threshold (m³/s of air at atmospheric pressure); at least one of the two thresholds is mandatory. The final expulsion of the air is thus slowed down, which limits the overpressure on reclosing. The same compressible orifice law as the other stages. Example: Design templates › Dual-orifice air valve at the outlet.

Pressure relief valve

The results show the discharged flow (L/s) over time.

Dynamic pressure relief valve

Chosen in the form of a junction (Attached device › Type), it uses the fields of the relief valve and adds a plug with mass, spring and damping: response time, damping ζ and reclosing difference (blowdown). The lift follows the head with a delay and closes again below the set pressure minus the blowdown. A response time that is too long lets the overpressure through; too short, the relief valve can chatter.

Surge anticipating valve

Chosen in the form of a junction (Attached device › Type). It opens on the underpressure that follows a pump stop to discharge water before the wave returns, then closes slowly. Trigger: low pressure threshold, stop of a monitored pump, or the first of the two. Fields: trigger pressure, monitored pump, effective area, pilot delay, opening time, hold-open time, closing time, discharge elevation. A closure that is too fast recreates an overpressure; the anticipating valve can also lower the minimum pressure: to be checked.

Bursting disc

Chosen in the form of a junction (Attached device › Type). Single-use device: it bursts at the first head above the threshold, then remains open. Fields: bursting pressure, effective area after bursting, opening time, discharge elevation.

Two-node pressure relief valve (return to sump)

The relief valve above discharges to the atmosphere from a single node. The two-node relief valve ("Relief valve with return to sump" tool of the toolbox, Links section) is a device that connects two junctions, like a valve or a check valve: the upstream node is the protected pipe, where the pressure is measured; the downstream node receives the discharged water, which the return pipe brings back to the sump or to a reservoir. The discharged water is therefore not lost and the volume balance remains closed. It is an internal pressure relief valve, with return to the sump (passive version).

Physical principle. Closed below the set pressure, the relief valve has no leakage. When the upstream pressure reaches the set pressure, the valve lifts; its lift increases with the pressure up to full opening (set pressure + overpressure band). Part of the flow then goes downstream, which clips the pressure peak instead of letting it propagate. When the pressure falls again, the relief valve recloses at the set pressure reduced by the blowdown (reclosing difference): the difference between opening and reclosing is a hysteresis that prevents chattering around the set pressure. The operating speeds (opening time and closing time) represent the inertia of the valve; at zero, they give an instantaneous reaction. Reverse flow from downstream to upstream is prevented.

Mathematical principle. We write H₁ for the head at the upstream node, H₂ the head at the downstream node, Q the discharged flow (from 1 to 2), H_t the set head (elevation of the upstream node + set pressure), ΔP the overpressure band and H_f = H_t − blowdown the reclosing head.

• Opening. The relative opening area τ ∈ [0; 1] is τ = (H₁ − H_t) / ΔP, bounded at 0 and 1. A relief valve already open keeps, between H_t and H_f, a residual lift (5 % at the set pressure) that decreases linearly to 0 at H_f: the law remains continuous, without a jump at opening. The opening and closing times limit the change in τ per time step to Δt / T_o and Δt / T_f.
• Head loss. H₁ − H₂ = Q·|Q| / (2g · (Cd·A · τ)²), where Cd·A is the fully open effective area. With the relief valve closed or a negative flow, the engine applies an almost infinite resistance: Q ≈ 0.
• Coupling with the pipes. The method of characteristics gives, at the upstream node, H₁ = C_P1 − B₁·Q (C_P1 and B₁ come from the upstream pipe, B = a / (g·A)) and, at the downstream node, H₂ = C_M2 + B₂·Q. For a given opening τ, the balance K·Q² + (B₁ + B₂)·Q − (C_P1 − C_M2) = 0, with K = 1 / (2g·(Cd·A·τ)²), is solved for Q; as τ depends on H₁, the engine solves the whole at the current time step (Newton's method, with fallback on more robust solvers).
• Volume balance. The relief valve stores nothing: the flow that leaves the upstream node enters the downstream node, and the discharged volume is the sum of Q·Δt.

Example: File › Examples › Design templates › "Two-node relief valve (return to sump)". Pipe of 1,400 m, valve closed in 3 s, relief valve set at 110 m H₂O at node J1 (100 m upstream of the valve). Calculation on this computer (engine 3c.8): at J1, the maximum pressure goes from about 393.6 m H₂O without a relief valve to 124.3 m H₂O with the relief valve; just upstream of the valve (JV), from 401.7 to 237.4 m H₂O. Downstream of the valve (J2), the relief valve does not act: 354.8 m H₂O and cavitation (−10 m H₂O), hence the verdict "Cavitation and PN exceeded" of the summary. The relief valve therefore protects the upstream pipe, not the downstream section. In the established regime, the discharged flow satisfies the orifice law within 0.5 %, and the discharged volume is equal to the volume received by the return pipe within 0.02 % (verification tests of the engine). Current version: passive relief valve; the pilot-operated, remote-sensing and unbalanced variants are not yet modelled. Results: the balance of the relief valve (openings, maximum lift, maximum flow, discharged volume) appears in the results file.

Air vessel (ASA)

Pressurised tank with an air cushion, connected to the pipe. It supplies water during the underpressure and absorbs the overpressure on the return.

One-way surge tank and air-cushion tank

Two variants, chosen in the form:

Both variants require the floor elevation and the diameter of the connecting branch: the losses ζ are dimensionless and referred to the velocity in this branch (Δh = ζ·V²/2g). For the cushion, the form shows the air pressure calculated in the steady state.

Free discharge

It is placed, with the "Free discharge" tool of the toolbox, on the junction that ends a pipe (only one pipe must arrive there): the water flows to the atmosphere through a free jet, without a reservoir or an imposed head downstream. The flow follows the orifice law Q = τ(t) · Cd · A · √(2g (H − Z)), where Z is the elevation of the axis of the outlet (elevation of the node), A its area and Cd its discharge coefficient.

• Outlet diameter: empty = diameter of the pipe; a nozzle or a partly open end valve is represented by a reduced diameter or Cd.
• Opening law: the same laws as the valves (fixed opening, linear or power closure, two-stage, opening). Closing the outlet creates the closure overpressure of an end valve.
• Air entry: by default, air enters through the outlet when the head falls below its axis; with the outlet closed, the end of the pipe is closed and ordinary cavitation applies.
• Steady state: the outlet flow depends on the head at the outlet, therefore on the network; it is determined with it (several outlets allowed, for example a Y). If the outlet elevation is above the available head, the flow is zero and a warning is given.

Never reverse flow through the outlet. Not covered: free-surface flow in a pipe that empties, submerged jet (use a reservoir with an imposed head). The finite-volume cross-check is not available on a network with a free discharge.

Trapped air pocket

An air pocket often remains trapped after draining or refilling: at a high point without an air valve, at the top of a siphon, at a closed pipe end. It is placed with the "Trapped air pocket" tool of the toolbox, or with Attached device › Type of a junction connected to at least one pipe, without a demand or an inflow. The pocket is stationary; the water column compresses and expands it. Its absolute pressure p* is the head of the node minus the elevation of the water-air surface, plus the atmospheric pressure; the air follows the polytropic law p*·∀ⁿ = C·mⁿ, written per unit mass so that the air that leaves does not change the law of the air that remains.

• Initial volume: length of pipe full of air (the volume follows from it with the diameter of the largest connected pipe) or volume in m³.
• Polytropic exponent n: 1 (isothermal, slow compression) to 1.4 (adiabatic, fast compression); 1.2 by default.
• Elevation of the water-air surface: empty = elevation of the node plus half a diameter.
• Initial pressure: that of the steady state (pocket in place in service) or atmospheric (filling of an empty pipe). In the second case, a valve closed at the start must separate the pocket from the reservoir: the water between the valve and the pocket is then at rest, at the pressure of the pocket.
• Air release: none (closed pocket), orifice (diameter and discharge coefficient) or air valve (air inlet and outlet orifices, the same laws as the Air valve attached device). The air flow is compressible, subsonic or choked.

If all the air leaves, the pocket disappears: the node becomes an ordinary junction again until the end of the calculation, and the water column strikes the node. The engine reports it in its warnings, in the check "Reserves of storage devices" and in that of the maximum pressure. In the Results view, Devices tab, the curve gives the air volume; the summary, the minimum volume, the share of air that has left and the time of disappearance.

Validated range (validation sheet V2: 29 verifications, tests of Coronado-Hernández et al. 2019 and of Zhou 2000): the first compression peak and its time, when the water front advances little compared with the length of the column. Beyond the first cycle, the damping is underestimated (no heat exchange between the air and the wall): the following peaks are too high by 15 to 20 %, and a late shock after the complete release of the air through a small orifice can be overestimated. Outside the range: a pocket that moves, breaks up or reappears, air entrained as bubbles, free-surface flow. Examples: File › Examples › Design templates › "Filling against an air pocket at a dead end" and "Gravity main: air pocket at the high point with an air inlet valve".

Montgolfier hydraulic ram

The ram is modelled with three elements: a free discharge whose Control is "Autonomous waste valve (hydraulic ram)", placed at the end of a short pipe leaving the node of the ram; a delivery check valve connecting this node to the air chamber (one-way surge tank, air cushion variant); the delivery pipe. The waste valve is open at rest; it closes when the flow reaches the closing flow and opens again when the head falls back to the reopening head, after the minimum closure (adjustable closing and reopening durations). Kinematic model: thresholds and durations are calibrated on a test rig.

In the Results view, Devices tab, the attached device of the outlet gives the number of closures, the average cycle of the waste valve and the discharged volume; the link analysis of the delivery check valve plots the delivered flow at each cycle. Example: File › Examples › Design templates › "Montgolfier hydraulic ram"; its time step is very small (waste pipe of 0.5 m): the calculation over 60 s takes several minutes.

Pipe break

The break is not placed on the schematic and does not appear in the list Attached device › Type of a junction: it is modelled only by the event "Pipe break" of a scenario (see 6.4).

5.5 Detailed longitudinal profile of a pipe

A real profile (high and low points) governs the underpressures and the cavitation. In the form of a pipe, Upload the profile… imports a file .xls, .xlsx, .csv or .txt with three columns:

• Formats read without an external library: Excel 97-2003 and 2007+, CSV with semicolon, comma or tab, decimal comma, UTF-8 or Windows-1252. The columns are recognised by the header or by the order and remain editable.
• Check before acceptance: blocking errors (columns, non-numeric values, non-increasing distances, elevations out of range) and points to be checked (length difference, slopes > 100 %, elevations of the end nodes, duplicate stations, points too far apart). The direction of the survey is detected and a preview is shown.
• The axis of the pipe is calculated: CGII + D/2 (recalculated if the diameter changes). The developed length is proposed as the length L; the elevations of the end junctions can be aligned on request. Everything can be undone (Ctrl+Z).

5.6 Calculation options

5.7 Live checks

CBELIER checks the model continuously, before any calculation and before any charge of credit. Three levels:

Click a message to select the element concerned. A banner in the side panel summarises the four conditions of a calculation (geometry, fluid, initial state, scenario); each condition not met leads to the tab concerned.

5.8 Choosing the wave speed

The wave speed a governs the amplitude (Joukowsky) and the duration (2L/a) of the transient. Orders of magnitude for water:

The exact wave speed is calculated with Young's modulus of the material, the ratio D/e and the anchoring of the pipe: a = √(K/ρ) / √(1 + (K·D)/(E·e)·c₁) (K: bulk modulus of water ≈ 2.2 GPa). Since engine 3c.7.5, CBELIER makes this calculation: in the inspector of a pipe, choose the material, the DN and the series (or enter Dint and the thickness), then the wave speed mode "Calculated (Allievi)" and the anchoring (pipe anchored upstream, over its whole length or with expansion joints). Poisson's ratio and Young's modulus come from the catalogue and remain editable; for plastics, the modulus is corrected for the water temperature. In "Imposed" mode, you enter a yourself and a warning appears if it departs by more than 10 % from the calculated value. The values of the catalogue (marked with an asterisk) are indicative: justify them in the calculation report and test the sensitivity (±10 %) with the free variants of the study.

Fluid and site. With nothing selected, the "Fluid and site" panel of the project sets the water temperature and the altitude. They determine the density, the viscosity, the vapour pressure (IAPWS-IF97 formula, from 0 to 95 °C; therefore the vapour head, absolute floor of the calculated pressures) and the atmospheric pressure (air laws of the air valves and surge tanks). Earlier projects open in "historical" mode (ρ = 1,000 kg/m³, vapour at −10 m H₂O) and give exactly the same results; switch to "calculated" mode to apply the real properties of water. The server always recalculates these values.

Pressure tunnel (interface 4.10.15). Wave speed mode "Pressure tunnel (lining and rock mass)": lining layers from the inside to the outside, one per row "thickness; modulus E; ν; cracked or intact" (steel liner, intact concrete, radially cracked concrete), and rock mass (modulus E_r, ν_r) or free outer surface. Calculation in plane strain: a = √(K/ρ) / √(1 + K·χ), χ being the deformability of the section. The moduli of the concrete and of the rock mass are often poorly known: vary the wave speed before concluding (sensitivity study).

5.9 Importing an EPANET model

The menu File → Import → EPANET model (.inp)… converts an EPANET network into a CBELIER project. Select the .inp file and, preferably, the corresponding results file .rpt (both together, or add the .rpt in the window that opens). The .rpt provides the flows of the pipes, the demands and the steady state of the control valves.

Not taken over: demand patterns (without .rpt), emitters, fixed-power pumps, closed pipes. The import window lists each assumption and each element not taken over; it is up to you to enter the wave speed, the PN and the parameters of the pumps. A file that contains only the geometry (without diameters or reservoirs) opens with default values that are reported; the network must then be completed before calculating.

6. Transient scenarios

A scenario describes the timed events of a study. It is saved with the project. Without a scenario, the calculation relies on the laws carried by the devices (valves, pump trip).

Separate window. The button "Open in a window" of the Scenarios tab (or View › Scenarios in a separate window) shows the same editor in a second window, which you can place on a second screen next to the schematic. The side panel and the window remain synchronised: a change made in one appears at once in the other, and F5 (or Shift+F5) runs the calculation from it. If the window is blocked, allow pop-up windows for CBELIER.

6.1 Creating and managing scenarios

1. Open the Scenarios tab of the side panel.
2. Create a scenario (or From the devices to take over the existing operations automatically — the results are then identical to the calculation without a scenario). You can duplicate or delete.
3. Set the name and the simulated duration.
4. Set the initial opening of the valves and the initial state of the pumps (running, or stopped with the pipe under pressure).
5. Add events and set them. The timeline of operations shows their chronology.

6.2 Types of events

Laws of change: Linear, Parabolic (1 − t/T)^Em, Exponential, Instantaneous. A duration is required except for instantaneous laws.

6.3 Pumps: stop and start

• Pump trip: the pump decelerates freely according to the inertia of the unit; the check valve then closes. This is the most frequent case and the most unfavourable for a pumping main without protection.
• Stop by variable-speed drive: the speed decreases according to the law chosen over the duration given. A stopping time of several 2L/a strongly reduces the overpressure.
• Soft start: speed ramp from 0 to the final speed.
• Direct-on-line start: the speed rise results from the torque of the induction motor (Kloss formula, with Cd, Ck and slip from the pump form).
• In a station in parallel, the pumps already running keep their regime during the start of the added pump. Several successive trips and restarts are possible.

6.4 Pipe break

The full-bore break is modelled as a rupture boundary condition at an intermediate chainage of the pipe: the pipe is cut in two at the break and the water spills to the atmosphere (Q = τ·Cd·A·√(2g(H − Z))).

Limitations: one break per pipe, at t > 0. The results are merged under the original identifier of the pipe; a trace "Flow at the break" is added, as well as a break marker on the longitudinal profile. The report gives the opening law, the maximum flow, the spilled volume and the air admitted.

6.5 Running all scenarios

Run › Run all scenarios (Shift+F5) runs each scenario. The results include:

• a comparison table (click a row to show the details of the scenario);
• the design envelope: p max and p min over all the scenarios, superimposed longitudinal profile, governing scenario per pipe and per node.

7. Calculating and reading the results

7.1 Steady state

The Steady state button calculates the initial state (flows, head losses, heads at the nodes). It is free: do it systematically before the transient to check that the initial pressures, the flow directions and the operating point of the pumps are what you expect.

Robustness (5 October 2026). The steady-state calculation automatically chains several methods: pipe in series (1D Newton), global gradient (Todini–Pilati, sparse matrix up to 5,000 junctions), global gradient damped by continuation (head applied in stages), then nodal Newton (networks of 60 junctions at most). Each result is checked (finite values, head at least equal to the vapour pressure, continuity at the nodes, residual of the device laws). The log of the methods tried, with the cause of each abandonment, is shown in the Results screen. If no method succeeds, the initial state is marked "approximate, not reliable" with a warning banner, instead of being presented as a valid result. A preliminary diagnosis reports inconsistent data (network not connected, demands greater than what the supply can provide).

7.2 Transient

Run (F5) calculates the active scenario (or the project without a scenario). During the calculation, Esc interrupts it. The status bar shows the percentage and, for a calculation on this computer, the current step: initial steady state, transient, fallback attempt, cross-check. A calculation on the server shows only the percentage; a network interruption of less than a minute is tolerated, beyond that a message gives the reference of the calculation (to be given to ALFA WAMANE if the credit has been charged). A simple network incident does not sign you out; only the real expiry of the session does. In the online version, the launch screen recalls the complexity class and the cost before any charge.

7.2 bis Checks and automatic fallback of the calculation

CBELIER never returns a numerically doubtful result. Before and during the calculation:

When a fallback has been needed, a banner "Result obtained after numerical fallback" gives the method retained, the time step and the cause of the initial failure. A result obtained with the other cavity model or by finite volumes has an "alternative" fidelity: the peaks after cavitation, or on a viscoelastic network, can differ by a few percent. Confirm it with the chosen model if possible. The fallback is disabled when you impose the time step yourself.

Cross-check. When the option is enabled, the result remains that of the characteristics and a banner compares the two methods: in agreement (deviation below the threshold), deviation (beyond the threshold, with a warning), indicative (viscoelastic network or with unsteady friction: non-homogeneous comparison, no alert), or not performed (attached devices or surge tanks). A large deviation invites you to refine the mesh or to lengthen an operation that is too short.

7.3 Reading the Results view

The Results view is organised in sub-tabs, always accompanied by three status badges at the top right (verdict, checks, mesh): an orange or red badge remains visible whatever tab is open, and a click on it opens the section concerned.

The details of the blocks are given below. In the Results view, the side and bottom panels keep the state you gave them (View › Panels to collapse or expand them). In the bottom panel (Tables and log), a click on the title collapses or expands it, a double-click on a tab enlarges it (another double-click: original size), and the Log opens by itself when a calculation fails.

Each graph can be exported as CSV (with station, survey distance and CGII). The envelopes are read at the points of the detailed longitudinal profile of each pipe: the verdict takes them into account.

7.4 Usual acceptance criteria

The allowable values depend on your specifications and on the applicable regulations; CBELIER provides the results, the engineer decides on the acceptability.

7.4 bis Design alerts

The design alerts check, on each pipe, thresholds specific to your study. They are verified after the calculation, from the results already obtained: changing a threshold runs no calculation and uses no credit. The thresholds are never sent to the engine or to the server.

Where to enter them. In the properties of the project (no element selected), frame "Design alerts (all pipes)": these thresholds apply to all the pipes. A pipe can replace them with its own in the Alerts tab of its dialog (or the section of the same name in the panel). Threshold applied: that of the pipe, otherwise that of the project, otherwise the PN for the maximum pressure.

Where to read them. In the Alerts tab of the pipe (calculated value, threshold and origin; "Alerts ⚠ n" if there are exceedances), in the summary of the Results view (block "Design alerts") and in the compliance appendix of the technical report (one row per type of alert, table of exceedances). An exceedance is a warning ("to be assessed"): it does not change the verdict, which remains based on cavitation and the PN.

7.5 The technical report (PDF)

After an up-to-date transient calculation: Run › Create the technical report (PDF)… or Ctrl+P, or the button "Technical report (PDF)" of the Results view.

1. A dialog asks for your design office: company name, address, contact, logo, author, checker (stored on this computer; with an online account, CBELIER offers to save them on your account as well, and deletes them from this computer at sign-out).
2. It also asks for the project data: client, reference, revision, purpose, remarks (saved with the project).
3. The report opens first as an on-screen preview (nothing is printed automatically); read it through, then use the button "Print / save as PDF" or Ctrl+P and choose "Save as PDF".

Content: cover page, contents, 1. purpose and data (with annotated schematic of the network), 2. methodology, 3. steady state, 4. orders of magnitude (Joukowsky, 2L/a valve by valve, as in the sensitivity study, see 7.8), 5. results (envelopes per path, pressures over time, extremes, attached devices, warnings of the engine, table of the extreme pressures at the notable points), 6. sensitivity study, if an up-to-date study has been made and the box of the dialog is ticked (§ 7.8), 7. automatic conclusions and remarks. With several scenarios ticked, the report includes the summary per scenario and the chapter Design envelope. When the interface is in English, the report is in English.

The report is built in your browser from the results: nothing is sent to the server. It is included in the study (no credit charged).

7.6 Exporting the results, compliance check

File › Export (available after a calculation) offers:

• Hmax / Hmin envelopes along the profile (CSV), for the path shown;
• Pressures at monitored nodes (CSV) and Extremes at nodes (CSV);
• Results view figures in PNG or SVG (one image per graph, background of the current theme).

If the model has been changed since the calculation, the export uses the out-of-date results and a warning is shown. Run › Compliance check opens the Results view at the verdict: maximum pressure against the PN of each pipe and cavitation.

7.7 Quick preliminary sizing

Run › Quick preliminary sizing… is a calculator independent of the engine: from the wave speed a, the velocity V₀, the length L and the operation time T, it gives the round-trip time 2L/a, the Joukowsky pressure rise a·V₀/g and, for a slow operation (T > 2L/a), the Michaud pressure rise 2·L·V₀/(g·T). With the static head and the PN, it estimates the maximum pressure. These are orders of magnitude for checking: they do not replace the simulation.

7.8 Sensitivity study

Run › Sensitivity study… runs five transients (−20 %, −10 %, 0, +10 %, +20 %) varying only one parameter: operation time of the valves (all or a single one), wave speed, or roughness of the pipes. The model is not changed; the active scenario is used. The calculations are done where the current calculation is done: on this computer (desktop version, without credit) or on the CBELIER server (online version, account signed in). Online, the sensitivity study is included in the study: the five calculations are variants of the same layout; if no study is open for this layout, its opening is charged once, after confirmation, as for a transient. The five calculations count in the number of calculations of the study.

The result is a p max / p min graph, a table (deviation from the reference, cavitation, points above the PN) and a CSV export.

Operation time: sweep in multiples of 2L/a (default choice). A closure shorter than the wave round-trip time 2L/a is equivalent to an instantaneous closure: the ±20 % variation around a short duration therefore shows nothing. Choose a valve: CBELIER calculates 2L/a: on each side of the valve, twice the shortest travel time Σ L/a, through the pipes, to the nearest reservoir, variable-level tank, surge tank or compartment of a two-compartment tank; the longer of the two sides is retained (that of the main pipe, interface 4.10.2). The technical report uses the same value and runs the durations 0.5; 1; 1.5; 2; 3; 4 and 6 × 2L/a, plus the duration of the project (8 calculations at most). The simulated duration is raised if necessary to start of operation + T + 3 × 2L/a. The table gives, at the valve, the first-phase peak (during the operation and the first round trip) and the overall maximum with its time: a higher and later maximum, marked ⚠, comes from the collapse of the vapour cavities, which the Joukowsky and Michaud formulas do not predict. A box gives the verdict: the shortest duration calculated from which each calculation complies with the PN without cavitation (between two calculated durations, nothing is checked). The ±20 % sweep remains available.

Inclusion in the technical report. A completed study is saved with the project (one per parameter and per scenario). As long as the model is not changed, the dialog of the report offers to include it: chapter "Sensitivity study" (method, table, figure, comment, verdict, limitations) and finding in the conclusions, without a new calculation or credit. After a change to the model, run the study again.

7.9 Optimising a valve closure

Run › Optimise a valve closure… searches for the two-slope closure law (end of the first slope t₁, opening τ₁) of given duration that minimises the maximum pressure of the network, at all the points of all the pipes, without falling below the allowable minimum pressure. Fields: valve, closure time, allowable minimum pressure (empty = no limit), criterion (maximum pressure, or overpressure above the steady state), precision of the search (fast, standard or fine: 60 to 150 calculations). The complete network is simulated at each trial, first on a coarse mesh, then the three laws compared (current law, linear closure, optimised law) are recalculated with the mesh of the project.

The model is changed only with Apply the law to the valve, which enters it as a "two-stage" law (or, for a valve linked to a pump, as a two-slope closure). No law is proposed, and the button remains disabled, if the law found makes the network cavitate (the maximum pressure then depends on the collapse of the vapour pockets and is not reliable) or if it worsens the maximum pressure compared with the linear closure or the current law: first remove the cavitation (slower closure, protection), or lengthen the duration. The optimum remains numerical: check it with a complete transient calculation and with the sensitivity study.

Online version. The search is done on the CBELIER server (account signed in) and is included in the study: if no study is open for this layout, its opening is charged once, after confirmation, as for a transient. The number of optimisations is limited per study (10 by default); an optimisation that fails is not counted, and the log shows the number already run. Closing the window during the search does not stop the calculation on the server: the run remains counted.

7.10 Calibrating on measurements

Run › Calibrate on measurements… superimposes a time series measured at a node and the calculation of the project, then adjusts the coefficient k of the unsteady friction, a wave speed factor common to all the pipes and a time shift; with a free discharge, also its discharge coefficient Cd and the closure time of its law. It is the head variations that are compared; the time series must start in the steady state, before the operation, and the active scenario provides the operation.

1. Choose the measurement node, the quantity (head, or gauge pressure) and the units; paste the time series (time; value), load a CSV or text file with two columns, or choose one of the Measurements attached to the project.
2. Adjust if necessary the start of the operation in the time series (detected automatically), the duration compared and the maximum shift; tick the parameters to be calibrated (k and wave speed are ticked by default).
3. Run the calibration, examine the superposition and the deviation, then Apply to the model if the values remain physical. Save the calibrated project under another name.

Calibrating is not validating: see 9.2.

Online version. The calibration is done on the CBELIER server and is included in the study, like the optimisation. It is limited to 3 calibrations per study (default value); a calibration that fails is not counted, and the log shows the number already run. A calibration often lasts 10 to 20 minutes: it does not block ordinary calculations. The time series is reduced to 6,000 points at most before sending. Closing the window during the calibration does not stop the calculation on the server: the run remains counted.

8. Theory, assumptions and limitations

8.1 Water hammer basics

When the velocity of the water in an elastic pipe is changed suddenly, the kinetic energy is converted into pressure that propagates as a wave at the wave speed a. The maximum pressure rise of a "rapid" operation is given by Joukowsky's formula:

An operation is said to be rapid when its duration is shorter than the round-trip time of the wave:

Beyond that, the reflections at the ends attenuate the peak. Example: a = 1,000 m/s and ΔV = 1 m/s give ΔH ≈ 102 m of pressure rise. This is why the operation time, the inertia of the pumps and the protections are decisive.

8.2 The method of characteristics (MOC)

CBELIER solves the water hammer equations (momentum and continuity in an elastic pipe) by the method of characteristics: along two families of lines C⁺ and C⁻ of the (x, t) plane, the partial differential equations reduce to ordinary differential equations. Each pipe is divided into reaches, with a time step Δt = Δx / a. At the ends and at the nodes, the boundary conditions (reservoir, junction, valve, check valve, pump, air valve, ASA, one-way surge tank, relief valve, break) are solved by a Newton–Raphson method; if it does not converge at a time step, fallback solvers take over (damped Newton, Illinois false position, bisection) and the result is kept only if the residual decreases.

• Friction is taken into account with Darcy–Weisbach at each step (quasi-steady friction).
• The wave speed is adjusted to the common time step with a tolerance of 5 %.
• Very short pipes (travel time L/a shorter than half the target step) are treated as a rigid column, which bounds the calculation cost.

8.3 Cavitation: the DGCM model

When the pressure falls to the vapour pressure, the water vaporises and a cavity forms; its later collapse can generate large pressure peaks. The DGCM (Discrete Gas Cavity Model) places free-gas cavities at the calculation points, including at the internal points of a pipe, to represent the separation of the water column and its rejoining.

Node without a pipe between two devices. Between two consecutive devices (for example a pump and a check valve), the junction has no pipe and therefore no volume: its head is not bounded and, at the vapour pressure, the integrity check rejects the calculation. Then insert a real short pipe between the devices.

8.4 Pumps in 4 quadrants

The transient behaviour of the pump is described by its complete curves (Suter) in reduced variables: normal operation, dissipation (reversed flow), turbining. The equation of motion of the unit, I·dω/dt = −C_hydraulic + C_motor, gives the speed. The specific speed N_S selects the typical curves. Without a manufacturer's catalogue, the curves are reconstructed from the rated point (Q, H, ω, η) and the inertia.

8.5 Principle of the protections

8.6 Assumptions of the model

• One-dimensional flow of water, compressibility of the water and elasticity of the pipe summarised by the wave speed a, constant per pipe.
• Quasi-steady Darcy–Weisbach friction, with Brunone's unsteady friction as an option (form of Vítkovský et al., 2000).
• Elastic pipes by default; viscoelastic behaviour (HDPE, PVC) available in the pipe form, with parameters J and τ to be justified (see 5.2 bis).
• Dissolved and free gas represented by the DGCM model; air entry of the air valves according to an orifice law.
• Variable-speed pumps described by their curves in 4 quadrants.
• Francis turbine: head and torque from the Euler equation, fitted to the published points of the Francis-99 model turbine (NTNU) and scaled to the rated point by similarity; Pelton, Kaplan and pump-turbine models not available.
• Pressure tunnel: wave speed calculated in plane strain (lining in layers, radially cracked concrete, infinite rock mass or free surface).
• Check valves without inertia (closure at flow reversal), except the dynamic check valve and the swing check valve with torque balance (disc, weight, spring, inertia); quasi-static relief valve, except the dynamic relief valve.
• A single network in one piece, with at least one reservoir with an imposed head.

8.7 Known limitations

The dynamic pressure relief valve (form of a junction, Attached device › Type) and the manufacturer's H(Q) curve of the pumps (pump form, characteristic) are available.

9. Good study practice

1. First get the steady state right. A transient calculated from a wrong initial state has no meaning.
2. Calculate the case without protection. It sets the need: maximum overpressure, minimum underpressure, cavitation zones.
3. Add the protections one by one and compare the envelopes; keep only what is necessary.
4. Test several scenarios: total pump trip, pump trip + check valve failing to close (degraded case), fast valve closure, direct-on-line start, break. Retain the envelope.
5. Vary the wave speed (±10 %) and the roughness to check the robustness.
6. Check the mesh: double the number of reaches per pipe; the extremes must hardly change.
7. Compare the model with measurements when they exist (see 9.2).
8. Document: produce the technical report, keep the .cbelier.json file with the report.

9.1 Typical cases and associated protections

9.2 Comparing with measurements and calibrating without getting it wrong

1. Attach the measurement to the project (field "measurements": node, start time in the time of the model, constant time step, head in m). Place the start of the operation at t = 0 and keep a few points before, which serve as the reference pressure: only the variations of head are compared.
2. Start by comparing without adjusting anything. Note the initial root-mean-square deviation in the report: it is the result of the model built from the known data alone.
3. Calibrate few parameters (wave speed, Brunone's coefficient k, shift, closure time), those that the curve makes it possible to distinguish; on a plastic pipe, calibrate J and τ first, then only k, and reject a result one of whose parameters reaches its bound or becomes non-physical: it is the sign of wrong data or of a phenomenon that is not modelled.
4. Keep part of the measurement for checking: calibrate on one window or one sensor, check on the other. Only this check has the value of a validation.
5. Always present both results: without calibration, then with calibration, stating what has been adjusted; never present a calibrated result as a result obtained without adjustment.
6. State the origin of each piece of data: published, measured, read from a figure, calculated, assumed. A missing piece of data remains "not available".

10. Troubleshooting and FAQ

10.1 Frequent messages

10.2 Frequently asked questions

10.3 Contact

ALFA WAMANE SARL AU — hydraulic engineering consultancy, Rabat / Marrakech. Support and quotations: alfawamane@gmail.com. Presentation of the consultancy and of the software: www.alfawamane.ma.

Legal notice · Privacy policy (account, calculation and payment data; CBELIER sets no cookie).

11. Appendices

11.1 Glossary

11.2 Nomenclature of the fields

11.3 Version history