Topic 5 of 10 — free theory
Pumps & System Curves
Operating point, affinity laws, pump power, NPSH, and cavitation.
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The system curve and the operating point
A pump does not deliver a fixed flow — it delivers whatever flow makes its head match the system's head. The system curve has two parts: the static lift (elevation difference plus any pressure difference, independent of flow) and the friction loss (which grows with Q²):
Hsys = Hstatic + KQ²
| Hsys | total head the system demands at flow Q |
| Hstatic | static head: elevation lift + (pdischarge − psuction)/γ |
| KQ² | friction + minor losses, which scale with the square of flow |
Operating point: the (Q, H) where the pump curve crosses the system curve.
Steepen the system curve (smaller pipe, more fittings) and the operating point slides left: less flow, more head. That is the logic behind throttling with a valve.
Affinity laws — what changes with speed or impeller size
For the same pump at a different speed N (or a trimmed impeller of diameter D), performance scales as follows — exact near the best-efficiency point:
Q2Q1 = N2N1 H2H1 = (N2N1)² P2P1 = (N2N1)³
| Q | discharge |
| H | head |
| P | power |
| N | rotational speed (or impeller diameter D) |
Water power: P = γQHη English shortcut: bhp = Q(gpm) × H(ft)3960 × η
| η | pump efficiency as a decimal |
| The 3960 shortcut already includes unit conversions for water — do not multiply by γ again. |
Power scales with the cube of speed: a 10% speed cut saves roughly 27% of the power. That cubic is why variable-speed drives pay for themselves.
NPSH and cavitation
Cavitation — vapour bubbles forming and collapsing in the impeller — destroys pumps. It is avoided by keeping the available net positive suction head above what the pump requires:
NPSHA = patm/γ − pv/γ ± hs − hL,suction > NPSHR
| NPSHA | net positive suction head available from the system |
| NPSHR | net positive suction head required by the pump (from its curve) |
| pv | vapour pressure of the liquid at its temperature |
| hs | static suction head: + if the supply sits above the pump, − if the pump must lift (suction lift) |
| hL,suction | head loss in the suction piping |
Hot liquids and high suction lifts are the danger combination: vapour pressure rises with temperature while the lift eats into NPSHA.
PE depth: multiple pumps and distribution storage
Pumps in series: add head at the same discharge. Pumps in parallel: add discharge at the same head. The combined pump curve must still be intersected with the system curve; two identical parallel pumps rarely deliver exactly twice one-pump flow because system losses rise with Q².
Distribution storage balances time-varying demand against a steadier supply. Over each time interval, track the signed volume:
ΔV = (Qsupply − Qdemand)Δt
The required equalisation volume is the range between the maximum and minimum cumulative ΣΔV. Keep Q and Δt in compatible units before accumulating.
Operating judgement: check the selected duty point against efficiency, NPSHR, motor power, minimum stable flow, and the full range of static water levels — not just the average condition.
Worked example Pump speed change via affinity laws
Given:
- A pump at 1,750 rpm delivers 500 gpm at 100 ft of head, drawing 20 bhp.
- Speed is reduced to 1,450 rpm. Assume efficiency stays roughly constant.
Solution:
- Speed ratio: N2/N1 = 1450/1750 = 0.8286.
- Flow: Q2 = 500 × 0.8286 = 414 gpm.
- Head: H2 = 100 × (0.8286)² = 100 × 0.6866 = 68.7 ft.
- Power: P2 = 20 × (0.8286)³ = 20 × 0.5689 = 11.4 bhp.
Answer: At 1,450 rpm: ≈ 414 gpm at 68.7 ft, drawing ≈ 11.4 bhp — a 17% speed cut saves 43% of the power.