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Open resourceIt calculates segment flow, velocity, friction loss and node pressure, then identifies the critical low-pressure path. Branched tree networks and looped/ring networks use different solving logic, so the calculator must declare the selected network mode.
1. Purpose and Engineering Decision
A distribution network does not carry the same flow in every pipe. Trunk flow falls after each take-off, parallel paths share flow according to resistance, and the pressure at a remote user depends on every upstream segment.
The tool is intended for engineering screening, troubleshooting and scenario comparison. It should show where pressure is being consumed, which node is critical, and whether a proposed pipe change, branch addition or ring closure materially improves the pressure profile.
Network mode | Calculation approach | Primary output |
|---|---|---|
Branched tree | Aggregate downstream node demand into each upstream segment | Segment dP and pressure at every node |
Ring / loop | Iteratively split flow until node mass balance and loop pressure residuals converge | Balanced path flows and node pressures |
Scenario compare | Re-solve same topology with changed demand or segment properties | Before / after pressure profile |
Measured calibration | Optional measured source/node pressure used to compare model vs field | Model residual / investigation flag |
2. Network Data Model
The network should be stored as a graph. Nodes represent sources, junctions and demand points. Segments represent physical pipe runs between two nodes. Each segment needs its own actual internal diameter, length and roughness because one undersized branch can dominate a remote pressure problem even when the main header is adequate.
Object | Required fields |
|---|---|
Source node | Source pressure, pressure reference, atmosphere, temperature, available source identifier |
Demand node | Reference demand, flow basis, optional scenario multiplier, minimum required pressure |
Junction node | Node ID, connected segments; zero local demand unless entered |
Pipe segment | From-node, to-node, actual ID, straight length, fitting equivalent length or loss data, roughness |
Scenario | Demand multipliers, source pressure, open/closed segment state, changed diameters |
3. Flow Basis and Mass Conservation
Node demands should enter the model on one common reference-flow basis. Converting node demands to dry-air mass flow makes continuity straightforward because mass flow is conserved through a segment even though actual volumetric flow changes with pressure.
m_dot_node = rho_ref x Q_ref,node
At each node: sum(m_dot_in) - sum(m_dot_out) - m_dot_demand = 0
For a tree network, segment mass flow can be determined directly by summing all downstream demands. For a looped network, the flow split is unknown and must be solved iteratively.
4. Segment Pressure-Loss Engine
For ordinary plant-air screening with modest pressure loss per segment, an iterative mean-pressure calculation is practical and transparent.
dP = f x (L_eq / D) x (rho_mean x v_mean^2 / 2)
v_mean = (m_dot / rho_mean) / A
P_out = P_in - dP
The segment solver should iterate mean pressure, density, velocity, Reynolds number and friction factor until outlet pressure changes by less than the configured tolerance.
5. Branched Tree Solver
A tree network has one defined upstream path to each demand node. Solve demand first, then pressure:
Normalize every demand to the common reference basis and convert to mass flow.
Work from terminal nodes back toward the source and sum downstream mass flow into each parent segment.
Start at the source pressure and work downstream, solving each segment dP at its actual segment flow.
Store pressure at every junction and terminal node.
Compare each terminal node against its minimum required pressure.
Rank the path with the lowest margin as the critical path.
Pressure margin at node i = P_node,i - P_min,i
6. Ring / Loop Solver
In a ring or parallel-path network, flow distribution cannot be assigned only from downstream demand. Parallel routes share flow according to their hydraulic resistance. The solver therefore needs an iterative loop or nodal method.
A practical developer implementation may use Hardy-Cross style loop correction for compact ring mains, or a nonlinear nodal-pressure solver for general graphs. The acceptance criteria should be based on residuals, not a fixed number of iterations.
Convergence check | Recommended criterion |
|---|---|
Node continuity residual | Absolute flow imbalance below user/system tolerance |
Loop pressure residual | Algebraic sum of segment dP around each independent loop approaches zero |
Node pressure change | Maximum pressure change between iterations below pressure tolerance |
Iteration limit | If exceeded, return non-converged status rather than a normal result |
7. Segment Flow Direction and Sign
Flow direction in a loop may change during iteration. Pressure loss always opposes the current flow direction. The displayed result can show an arrow from higher-pressure node to lower-pressure node after convergence.
dP_signed = sign(m_dot) x |dP(m_dot)|
If the solved flow direction is opposite to the user-drawn segment direction, that is not automatically an error; the UI should show the reversed direction clearly.
8. Input Model
Input group | Field | Validation / note |
|---|---|---|
Source | Pressure, temperature, atmosphere | |
Demands | All demands normalized before solving | |
Topology | Node and segment connectivity | No orphan segment; source must reach every solved demand |
Segment | Actual ID, length, fitting equivalent length, roughness | Actual ID required, not nominal label only |
Node | Minimum required pressure | Optional for junction, recommended for users |
Solver | Tree / Loop / Auto detect | Auto detect may identify cycles but must report chosen mode |
Tolerance | Flow and pressure convergence | Visible engineering defaults may be provided |
Scenario | Open/closed segment, demand multiplier, changed ID | Preserve baseline for comparison |
9. Required Network Node and Segment Register
ID | Type | Connection / demand | Engineering output |
|---|---|---|---|
S | Source | Defined source pressure | Solved reference node |
J1 | Junction | No local demand | Pressure at branch point |
A | Demand node | Demand A + minimum pressure | Delivered pressure and margin |
B | Demand node | Demand B + minimum pressure | Delivered pressure and margin |
S-J1 | Segment | ID / Leq / roughness | Flow, velocity, Re, f, dP |
J1-A | Segment | ID / Leq / roughness | Flow, velocity, Re, f, dP |
J1-B | Segment | ID / Leq / roughness | Flow, velocity, Re, f, dP |
10. Reference Test Case A - Branched Network
Source pressure is 7.0 bar(g), atmosphere 1.01325 bar(a), line temperature 25 C. Total reference demand is 15 m3/min FAD at 1.01325 bar(a), 20 C. The source-to-junction trunk carries both branches. Branch A demands 9 m3/min; Branch B demands 6 m3/min. Roughness is 0.045 mm and the line is treated as isothermal for the screening calculation.
Segment | Flow basis | ID / Leq | Velocity | dP | Outlet pressure |
|---|---|---|---|---|---|
S-J1 | 15 m3/min FAD | 75 mm / 100 m | 7.31 m/s | 0.063 bar | 6.937 bar(g) |
J1-A | 9 m3/min FAD | 63 mm / 75 m | 6.25 m/s | 0.043 bar | 6.894 bar(g) |
J1-B | 6 m3/min FAD | 50 mm / 120 m | 6.64 m/s | 0.103 bar | 6.834 bar(g) |
The model predicts about 0.106 bar total pipe loss from source to A and 0.166 bar from source to B. Branch B is the critical path in this example because its smaller diameter and longer equivalent length consume more of the pressure budget.
11. Reference Test Case B - Targeted Branch Upsize
Keep the same network but increase Branch B internal diameter from 50 mm to 63 mm. The trunk and Branch A remain unchanged.
Branch B option | Velocity | Branch dP | Node B pressure | Source-to-B pipe loss |
|---|---|---|---|---|
50 mm ID | 6.64 m/s | 0.103 bar | 6.834 bar(g) | 0.166 bar |
63 mm ID | 4.17 m/s | 0.032 bar | 6.905 bar(g) | 0.095 bar |
The scenario comparison shows the value of locating the dominant loss before increasing plant header pressure. A targeted branch change can recover remote pressure without imposing a higher pressure setpoint on the entire system.
12. Reference Test Case C - Parallel / Ring Flow Split
A 12 m3/min FAD demand is supplied from the same source through two parallel routes that reconnect at one demand node. Path 1 is 63 mm ID with 100 m equivalent length. Path 2 is 75 mm ID with 140 m equivalent length. The loop solver must find a split where the pressure drop through both paths is equal while their flows sum to 12 m3/min.
Parallel path | Solved flow | Velocity | Path dP |
|---|---|---|---|
Path 1 - 63 mm / 100 m | 5.15 m3/min FAD | 3.55 m/s | 0.0196 bar |
Path 2 - 75 mm / 140 m | 6.85 m3/min FAD | 3.33 m/s | 0.0196 bar |
Network check | 12.00 m3/min total | - | Equal path dP at convergence |
The wider path carries more flow even though it is longer because the total hydraulic resistance is lower. This is why a looped network cannot be solved by simply dividing demand equally between parallel routes.
13. Critical Path and Pressure-Budget Reporting
The user should not have to inspect every row manually.
Critical-path output | Meaning |
|---|---|
Source pressure | Starting operating pressure for the scenario |
Cumulative pipe dP | Sum of solved segment losses along the path |
User-entry losses | Optional downstream allowance for filters/regulators/hoses outside the network model |
Delivered node pressure | Solved node pressure |
Minimum required pressure | User / OEM requirement |
Pressure margin | Delivered minus minimum |
Top loss contributors | Segments ranked by dP or share of path loss |
14. Scenario Analysis
Scenario change | |
|---|---|
Demand increase | Every affected upstream segment flow and all downstream node pressures |
Branch pipe upsize | Flow distribution and pressure profile; loops may redistribute flow |
Ring closure / new tie | Topology, path split and node pressure |
Segment isolated | Connectivity and alternate supply path; flag disconnected demand |
Lower source pressure | All node pressures and critical margins |
Leakage reduction | Demand at affected node/zone and upstream segment loading |
15. Validation and Guardrails
Condition | Required behaviour |
|---|---|
Disconnected demand node | Do not solve as normal; flag unreachable from source |
Multiple source nodes without source-control definition | Require explicit boundary/control rule |
Negative solved absolute pressure | Stop and flag invalid / nonphysical solution |
Large segment dP fraction | Warn that mean-density Darcy screen may be inadequate |
Non-converged loop | Return non-converged status and residuals |
Nominal size without actual ID | Request actual internal diameter |
Mixed flow reference bases | |
Gauge source pressure without atmosphere | |
Demand with no minimum pressure | Solve pressure but mark margin unavailable |
Calculators and worked examples
These tools give indicative figures for screening, comparison and for preparing an enquiry. They run in your browser and send nothing. Prices, tariffs and efficiencies shown are example values: replace them with your own. Results are not a performance guarantee or a design certificate; final selection is confirmed by an engineer against the machine data sheet and the site.
Pipe pressure drop and sizing
Check the pressure drop and air velocity in a compressed-air line, or find the smallest bore that keeps the drop within a target.
The worked example below shows the method with fixed numbers. Turn on JavaScript to change the inputs.
Worked example
Inputs
- Flow (m³/min free air): 12
- Inlet pressure (bar g): 7
- Pipe length (m): 150
- Inside diameter (mm): 80
- Roughness (mm): 0.046
- Fittings allowance (% extra length): 30
- Air temperature (°C): 30
- Target pressure drop (bar): 0.1
Result
- Pressure drop: 0.059 bar (0.839% of line pressure)
- Air velocity: 5.22 m/s
- Reynolds number: 2,06,066
- Smallest bore for the target drop: 72 mm inside diameter
- Velocity check: Within the common rule-of-thumb range for mains (roughly up to 15–20 m/s)
Method. Darcy–Weisbach: ΔP = f × (L/D) × ρv²/2, with the friction factor f from the Swamee–Jain relation and air density taken at mean line pressure. Fittings are allowed for as extra equivalent length. Typical commercial steel roughness is about 0.046 mm.
What to take from it. Pressure drop varies roughly with the fifth power of the bore at constant flow, so a larger main is a cheap way to hold pressure.