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System curve calculation walkthrough

Published 2026-05-13

What a system curve is

A system curve plots the hydraulic head a piping system requires to push a given flow through it. Plot flow on the x-axis, head on the y-axis, and the curve climbs as flow increases — friction grows with the square of velocity, so even small flow increases push head requirements up significantly.

The system curve doesn't depend on the pump. It's a property of the pipe + fittings + elevation alone. Once you have the system curve, you overlay manufacturer pump curves on top — the intersection (the duty point) tells you what the pump will actually deliver in this specific system.

Without a system curve, picking a pump is guessing. A pump rated for "300 GPM at 80 ft" only delivers 300 GPM if the system happens to require exactly 80 ft of head at 300 GPM. Off the curve, you get something else.

The equation

Total Dynamic Head (TDH) at any flow Q is:

TDH(Q) = H_static + K · Q^n

Where:

  • H_static — static head. Vertical elevation difference between suction and discharge free surfaces. Independent of flow.
  • K · Q^n — friction + minor losses. The exponent n depends on which equation you use:

- Hazen-Williams: n = 1.852 - Darcy-Weisbach: n = 2 (technically: f varies with Re so n drifts slightly, but ≈2 in turbulent flow)

For most municipal water work, n = 1.852 is the standard.

K is computed once from a single design point: the design flow + design TDH. Solve for K, then use it to evaluate TDH at any other Q.

Step-by-step example

A wastewater force main:

  • Pumping 300 GPM (design) of 60 °F water.
  • 6" ductile iron pipe, 2,000 ft long, C = 130 (aged conservative).
  • 12 ft of static lift from wet well to discharge manhole.
  • Minor losses: 1 entrance (K=0.5), 4 90° elbows (K=0.3 each), 1 swing check valve (K=2.5), 1 gate valve fully open (K=0.15), 1 exit (K=1.0). Total ΣK = 0.5 + 4×0.3 + 2.5 + 0.15 + 1.0 = 5.35.

Step 1 — friction loss at design flow

Hazen-Williams (US units):

h_major = 0.2083 · (100/130)^1.852 · 300^1.852 / 6^4.8655 · (2000/100)
        ≈ 0.2083 · 0.610 · 38,899 / 6,113 · 20
        ≈ 16.13 ft

Step 2 — minor losses at design flow

Velocity at design flow: v = 0.4085 · Q / d² = 0.4085 · 300 / 36 = 3.40 ft/s. Velocity head: v²/2g = 3.40² / 64.4 = 0.180 ft.

h_minor = ΣK · v²/2g = 5.35 · 0.180 = 0.96 ft

Step 3 — total dynamic head at design

TDH_design = H_static + h_major + h_minor
           = 12 + 16.13 + 0.96
           = 29.1 ft

Step 4 — solve for K

Friction term at design = 16.13 + 0.96 = 17.09 ft.

K · 300^1.852 = 17.09
K = 17.09 / 38,899 = 4.39×10⁻⁴

Step 5 — evaluate the curve at other flows

Now we have TDH(Q) = 12 + 4.39×10⁻⁴ · Q^1.852. Build the table:

| Q (GPM) | Q^1.852 | Friction (ft) | TDH (ft) | |--------:|--------:|--------------:|---------:| | 0 | 0 | 0.0 | 12.0 | | 100 | 4,898 | 2.15 | 14.1 | | 200 | 16,948 | 7.44 | 19.4 | | 300 | 38,899 | 17.08 | 29.1 | | 400 | 65,797 | 28.88 | 40.9 | | 500 | 101,124 | 44.39 | 56.4 |

The curve starts at H_static when Q=0 and climbs steeply as flow increases.

Try this calculation →

Reading the curve

A few things the system curve tells you immediately:

  • Static-vs-friction split. At design flow, 12 ft of 29.1 ft TDH (41%) is static. If static dominated more (say, an irrigation system pumping 200 ft uphill with little friction), the curve would be nearly flat — VFDs would have less leverage. Friction-heavy systems have steeper curves and benefit more from VFDs.
  • Off-design flow behavior. If the operator dials this pump back to 200 GPM (say, because a downstream lift station is throttled), TDH falls to 19.4 ft. The pump must operate at that point — check that 19.4 ft, 200 GPM is still inside the AOR for your selected pump.
  • Worst-case head requirement. If a downstream blockage forces the pump to push 400 GPM (because of an alarm-driven peak event), required TDH jumps to 40.9 ft. Does the pump have head capacity at 400 GPM? Check the pump curve.

Overlaying the pump curve

A pump curve is "head delivered as a function of flow" at a given speed. Overlay it on the same axes as the system curve. The intersection is the operating point — the unique (Q, H) where pump output exactly equals system requirement.

If the intersection is:

  • Inside the pump's BEP region (within ±10% of BEP flow per HI 9.6.1). Best case. Highest efficiency, longest pump life.
  • Inside the pump's POR (Preferred Operating Region, ~70-120% of BEP). Good. Occasional excursions outside POR are tolerable.
  • Inside the AOR (Allowable Operating Region, ~50-130% of BEP) but outside POR. Acceptable for short runs only. Consider resizing the pump or trimming the impeller.
  • Outside AOR. Pump life suffers, NPSH margin shrinks, and warranty terms may be voided.

The point of building the system curve is to verify your selected pump intersects it inside POR — not just to confirm "yes there's a number where they meet".

When the system curve is wrong

A few common ways the calc misleads:

  • Aged C-factor not used. Designing with new-pipe C and operating with 20-year-old pipe means real-world TDH is higher than the curve predicts. The pump operates further left (lower flow) than designed.
  • Static head varies with tank level. A wet well that fluctuates 4 ft between fill cycles has a system curve that *moves vertically* with level. Pick the worst case (highest static) for sizing.
  • Suction strainer or filter clogging. Friction loss grows over service life. Some designs include a "fouled suction" case in the curve set.
  • Parallel paths ignored. Two pumps drawing from a common header into a common discharge see a different curve from one pump. Each pump's individual K isn't simply additive — the parallel-flow split matters.

What to do next

1. Compute H_static from your free-surface elevations. 2. Compute friction + minor losses at design flow. 3. Solve for K, build the curve at multiple flows. 4. Plot it on the same axes as candidate pump curves. 5. Verify the intersection point lands inside POR for the selected pump. 6. Check off-design points (lower / higher flow) so you know what happens when the system runs off-design.

Build the curve in the calculator →

References

  • Hydraulic Institute. *ANSI/HI 9.6.1 — Allowable Operating Region.*
  • Karassik, I. J., et al. *Pump Handbook,* 4th ed. — Chapter 8 on system analysis.
  • AWWA M11, *Steel Pipe — A Guide for Design and Installation,* hydraulic design chapter.