A pipeline with two takeoffs needs a separate head-versus-flow curve for each operating case; one curve cannot represent changing withdrawals unless the flow distribution and delivery requirements stay the same. First establish what 200,000 m³/day represents and whether 25,000 and 50,000 m³/day are takeoff totals or total pipeline flows. Then calculate the losses along each active flow path.
Define the three operating cases
Take the first reading from the flow basis in the design brief: is 200,000 m³/day the inlet flow, the pipeline design capacity, or a required flow at a delivery point? Next, identify whether 25,000 m³/day is the flow from one takeoff and whether 50,000 m³/day is the combined flow from both takeoffs. The wording does not say whether the 50,000 m³/day is split equally, so do not assign 25,000 m³/day to each without confirming it.
| Case | Reading to confirm | What it changes |
|---|---|---|
| Main line only | Required inlet and end-of-line flows | Establishes the baseline curve and any minimum main-line flow. |
| One takeoff active | Which takeoff is active and its 25,000 m³/day flow | Changes flow in every upstream and downstream segment differently. |
| Two takeoffs active | Whether 50,000 m³/day is their combined withdrawal, plus each individual flow | Sets the segment flows and delivery-point losses for the two-takeoff case. |
If 200,000 m³/day is the inlet flow, use it as the upstream flow only if that is the intended operating condition. If it is merely the pipeline capacity, do not treat it as the inlet flow for every curve point. If the values describe only takeoff demand, obtain the main-line flow or minimum flow separately. A system curve plots head against a range of flow; it is not just one fixed operating point.
Map each takeoff and segment flow
Draw the line from inlet to final endpoint and mark both takeoff locations, pipe diameters, elevations, and delivery requirements. Split the main line at each diameter change and takeoff. For each operating case, use continuity at every takeoff: flow downstream equals flow upstream minus the withdrawal at that junction. Use the actual specified withdrawal at each point; do not subtract the combined 50,000 m³/day before the first takeoff unless both withdrawals occur there.
Calculate the pressure drop for each relevant path: inlet to the end of the main line, inlet to the first takeoff, and inlet to the second takeoff. For example, a path ending at the first takeoff does not include losses in downstream pipe. A path to a later takeoff includes upstream segments carrying the flow remaining after earlier withdrawals. This is why takeoff position matters: a withdrawal near the start changes flow through more of the pipeline than the same withdrawal near the far end.
Where the active flow split, required endpoint pressure, or minimum main flow is unknown, stop the curve calculation and obtain that design input. Guessing these values can change which path controls pump head.
Calculate friction and local losses by segment
Use Darcy-Weisbach for each segment, with the actual segment flow and diameter. The friction head loss is h_f = f (L/D) (v²/(2g)), where f is the Darcy friction factor, L is segment length, D is internal diameter, v is mean fluid velocity, and g is gravitational acceleration. Derive velocity from segment flow and internal area, keeping units consistent.
Determine the friction factor for the fluid and pipe conditions, rather than presuming it is constant. Darcy-Weisbach with Colebrook is one calculation route; a network model or spreadsheet solver can iterate friction factor while applying continuity and Bernoulli energy balance. Include the pipe dimensions, fluid properties, elevations, and minor losses in the model. For fittings or other local restrictions represented by loss coefficients, calculate their losses using the flow in the segment where they are installed.
A constant-resistance approximation gives head loss proportional to flow squared, often written h = C Q². That relationship assumes a constant friction factor; the K-factor method makes a similar complete-turbulence assumption. Do not force a square-law curve if the friction factor varies materially with flow. The exponent can be closer to 1.82 than 2 in some conditions, so calculate the loss at each flow point instead of assuming an exponent.
Add static elevation and delivery pressure
Choose head or pressure for the vertical axis. Head is usually clearer for comparing a pump curve with a pipeline system curve. If you plot pressure, convert elevation rise into pressure consistently. The required pump head for a path includes the elevation difference between its inlet and delivery point, friction and local losses along that path, and the pressure head required at the delivery point.
An outlet above the inlet shifts the curve upward by the elevation contribution; an outlet below the inlet shifts it downward. The system curve therefore does not necessarily pass through the origin. Do not confuse this static component with flow-dependent friction loss: elevation and endpoint pressure requirements are not calculated by multiplying the flow-dependent loss by a fitted constant.
For each path and operating condition, sum the terms using an energy balance. Include control-valve loss when a valve is part of the required flow-control arrangement. If the main pipeline has little pressure drop, a takeoff may lack sufficient available back pressure to maintain its required flow even with a control valve. Check the delivery pressure and valve pressure drop; a back-pressure regulator may be needed to preserve that back pressure.
Compare paths and select the controlling curve
At each total flow point, calculate the head required for all paths that must meet delivery requirements. The path with the highest required head controls pump sizing for that operating condition. Do not choose a path solely by its length: its flow, diameter changes, elevation, endpoint pressure, and valve losses all contribute.
Use this branch sequence:
- Read the inlet flow and each takeoff flow for the operating case. If they do not reconcile by continuity, correct the flow basis before proceeding.
- Read the pressure or required head at each delivery point. If endpoint requirements differ, retain separate path calculations.
- Compare calculated head at each path endpoint. If one path requires more head, use it as the controlling path for pump sizing in that case; if the controlling path changes with flow, preserve that change in the curve data.
- Repeat for main line only, one active takeoff, and both active takeoffs. Treat each as a distinct operating curve, not as one curve with a label change.
Flow control valves can help maintain specified takeoff rates as system pressure changes, but include their pressure losses in the calculations. If calculated main-line pressure drop is too small to provide adequate takeoff back pressure, evaluate the back-pressure-regulator arrangement and recalculate the network. Do not size from an idealized curve that omits the pressure losses needed to achieve the required flow distribution.
Plot and verify the calculated curves
For each operating case, select a range of total flow values relevant to the intended operating range. At each point, recalculate segment flows, friction factors, friction and minor losses, and endpoint head. Plot the resulting total head against the corresponding total flow and connect the calculated points. A pressure-drop calculator can also be run at multiple flow values for each pipe diameter; for serial pipe sections carrying the same flow, their pressure drops can be added. For a pipeline with takeoffs, however, apply the different segment flows created by withdrawals before summing losses.
Verify the result before using it for pump selection:
- Check every takeoff and segment flow against continuity for each case.
- Check units, internal pipe diameters, fluid properties, elevations, minor losses, and delivery pressures used by the calculation.
- Confirm the curve includes the static elevation and endpoint pressure contribution, not friction alone.
- Confirm valve and regulator losses are included where those devices are required to control takeoff flow or maintain back pressure.
- Compare the calculated head at a selected flow with an independent energy-balance calculation or a second solver run.
If the calculation uses a simplified square-law fit, compare it with the point-by-point Darcy-Weisbach results across the operating range. If the deviations matter to the pump selection or control range, use the calculated points rather than the simplified parabola. The procedure resolves the curve only after the flow interpretation and delivery requirements are fixed; verify those inputs with the process design owner before releasing pump sizing.
Frequently asked questions
Why do I need three system curves for two takeoffs?
Main line only, one active takeoff, and two active takeoffs produce different segment flows and losses. Calculate a head-versus-flow curve for each case because each curve represents a different flow distribution and delivery condition.
Why does the curve change when a takeoff is closer to the pipeline inlet?
An upstream takeoff reduces flow through more downstream pipe. Recalculate flow and losses in every segment after each withdrawal; do not apply one flow value to the entire line.
Why doesn’t my system curve start at zero head?
An outlet above the inlet adds static elevation head, and a delivery point can also require pressure head. Include those terms with friction and local losses; an outlet below the inlet can shift the curve below the origin.
Why is head loss not always proportional to flow squared?
The square-law approximation assumes a constant friction factor. Use Darcy-Weisbach with a friction-factor calculation at each flow point when pipe conditions make that assumption unsuitable.
Stop pump selection if the 200,000 m³/day basis, takeoff split, endpoint pressure, or minimum main-line flow remains unresolved. Escalate the network calculation to the responsible process or hydraulic engineer, and contact the equipment manufacturer through its official support channel when pump selection or operating limits require product-specific confirmation.