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Hydraulics, open channels and fluid power
Combined flow of two dissimilar parallel pumps
Total flow of two pumps with curves Hi = H₀i − aiQi² discharging into the same header at a common head H.
- Ref
- HYD-38
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- Qt [m³/s]
Pumps connected in parallel to a common header deliver the same head H, and their flows add. For a pump with Hi = H₀i − ai Qi², the flow at head H is Qi = √[(H₀i − H)/ai]. The total is Qt = Q₁ + Q₂. A pump whose shut-off head is below the header head delivers nothing, and a check valve stops it running backwards, so that case needs a separate state.
Total flow of two pumps with curves Hi = H₀i − aiQi² discharging into the same header at a common head H. Each pump must run forward, so H must be below both shut-off heads.
Calculator
- Flow of pump 10.03 m³/s
- Flow of pump 20.02 m³/s
- Share of the total from pump 160 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 16 m of head the pumps deliver 0.03 and 0.02 m³/s, 0.05 m³/s together.
- The stronger pump carries more of the flow, and as the head approaches the weaker pump’s shut-off head it contributes less and less.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m³/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| a1 Curve coefficient of pump 1 | 1 to 1,000,000 s²/m⁵ | 0.023 | 3.02 | 2.997 | +10% | −2.79 % |
| a2 Curve coefficient of pump 2 | 1 to 1,000,000 s²/m⁵ | 0.032 | 2.03 | 1.998 | +10% | −1.86 % |
| H01 Shut-off head of pump 1 | 17 to 500 m | 0.03 | 0.24 | 0.21 | +10% | +7.82 % |
| H02 Shut-off head of pump 2 | 17 to 500 m | 0.04 | 0.25 | 0.21 | +10% | +8.99 % |
| H Common operating head | 0 to 16 m | 0.05 | 0.09472 | 0.04472 | +10% | −14.6 % |
Sweep of Common operating head
| Common operating head (m) | Total flow (m³/s) |
|---|---|
| 0 | 0.09472 |
| 2 | 0.09038 |
| 4 | 0.08583 |
| 6 | 0.08101 |
| 8 | 0.07587 |
| 10 | 0.07035 |
| 12 | 0.06434 |
| 14 | 0.05766 |
| 16 | 0.05 |
Sweep one variable
Variables and how each one contributes
Total flow
What the equation gives you. Everything else feeds it.
Shut-off head of pump 1
The shut-off head of pump 1, in m. A stronger pump 1 raises its flow. Raising it by 10 % (to 27.5) moves the result by +7.82 %, from 0.05 to 0.05391 m³/s.
Shut-off head of pump 2
The shut-off head of pump 2, in m. A stronger pump 2 raises its flow. Raising it by 10 % (to 22) moves the result by +8.99 %, from 0.05 to 0.05449 m³/s.
Common operating head
The common operating head at the header, in m. A higher head cuts the flow of both pumps. Raising it by 10 % (to 17.6) moves the result by −14.6 %, from 0.05 to 0.04269 m³/s.
Curve coefficient of pump 1
The curve coefficient of pump 1, in s²/m⁵. A steeper curve cuts the flow of pump 1. Raising it by 10 % (to 11,000) moves the result by −2.79 %, from 0.05 to 0.0486 m³/s.
Curve coefficient of pump 2
The curve coefficient of pump 2, in s²/m⁵. A steeper curve cuts the flow of pump 2. Raising it by 10 % (to 11,000) moves the result by −1.86 %, from 0.05 to 0.04907 m³/s.
Worked example with the values above
- Pump 1: √((25 − 16) / 10,000) = 0.03 m³/s.
- Pump 2: √((20 − 16) / 10,000) = 0.02 m³/s.
- Qt = 0.05 m³/s.
Assumptions and limits
- Steady incompressible flow with the pump curve and system curve both of quadratic form.
- Ideal blade-guided flow for the velocity-triangle results, so the real head is lower.
Common mistakes
- Using gauge pressure where absolute pressure is needed for NPSH.
- Forgetting that pump curves in different units, such as litres per second, need converting to m³/s.
- Adding the flows of parallel pumps at different heads.
Statistics and uncertainty
Pump curves are known only to within a few percent and wear them down in service, and available suction head changes with the level, temperature and flow, so use a safety margin on the requirement.
Where it is used
- Choosing pumps and finding the duty point on a pipe system.
- Checking cavitation margin and estimating head from impeller geometry.
Maths you need
- Pump curve: head against flow for a pump at a fixed speed
- System curve: head needed by the pipe system against flow
- Velocity triangle: the vector diagram of blade and fluid velocities