BIZOMAT MAKEOS · Hydraulics
Two-Pump Arrangement Check (Parallel or Series Operating Point, Flow Gain, Each Pump’s Duty)
If I run two identical pumps in parallel or in series on this system, what flow and head do I get compared with one pump, and where does each pump run on its curve?
Operating point of two identical centrifugal pumps in parallel (heads equal, flows add) or in series (flows equal, heads add) on a system curve: the single-pump operating point (as the pump operating point tool), the combined pump curve and its intersection with the system curve, the flow gain over one pump, the flow, head, share of best-efficiency flow and efficiency of each pump, and the total power, against the flow needed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Arrangement | choice | Parallel pumps share the flow at the same head; series pumps pass the same flow and add their heads. |
| Each pump at rated speed | ||
| Shut-off head | m | Head of each pump at zero flow. |
| Best-efficiency flow | L/min | Flow of each pump at its best efficiency. |
| Head at best efficiency | m | Head of each pump at best efficiency. |
| Best efficiency | % | Best efficiency of each pump. |
| System | ||
| Static head | m | Static head of the system. |
| Known system flow | L/min | A known flow on the system curve. |
| System head at that flow | m | System head at that flow. |
| Liquid density | kg/m³ | Liquid density. |
| Flow needed | L/min | Flow the duty needs. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Arrangement
- What it is
- How the two identical pumps are connected. In parallel they share the flow at the same head; in series the same flow passes through both and their heads add.
- Units and format
- Choose one of 2 options from the list: Parallel (flows add); Series (heads add).
- Example
- The form opens with “Parallel (flows add)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Pick the arrangement you want to check; the tool treats the two pumps as identical, each with the curve entered below.
Each pump at rated speed
What this means: Shut-off head
- What it is
- The head one pump produces at zero flow, against a closed valve, at rated speed.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Read it from the pump curve at the flow axis zero point.
What this means: Best-efficiency flow
- What it is
- The flow of one pump at its best efficiency point on the curve.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Read it from the pump curve at the efficiency peak; enter L/min.
What this means: Head at best efficiency
- What it is
- The head of one pump at its best efficiency flow. With the shut-off head it defines the parabolic pump curve the tool uses.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be below the shut-off head.
What this means: Best efficiency
- What it is
- The peak efficiency of one pump, at its best efficiency point. It is used only for the power estimate.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 5% to 95%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself, read from the pump curve.
System
What this means: Static head
- What it is
- The static head of the system: the height difference and pressure difference the pumps must overcome at zero flow.
- Units and format
- Enter a number in m: metres. The form accepts 0 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Include any pressure difference between the suction and discharge vessels, converted to head.
What this means: Known system flow
- What it is
- A flow at which the system head is known, used with the static head to fit the system curve.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use a measured or calculated duty point for the existing system.
What this means: System head at that flow
- What it is
- The total system head at the known flow, including static head and pipe friction.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 5000 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must exceed the static head.
What this means: Liquid density
- What it is
- The density of the pumped liquid, used only for the power estimate.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the density at the pumping temperature.
What this means: Flow needed
- What it is
- The flow the duty needs, compared with the combined flow of the two pumps.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 10000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 420 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter L/min, the same unit as the pump and system flows.
Method and formulas
- Pump curve H = H₀ − a Q² through the best-efficiency point; system curve H = H_s + k Q² (as the pump operating point tool).
- Parallel: H₀ − a (Q ÷ 2)² = H_s + k Q². Series: 2 (H₀ − a Q²) = H_s + k Q².
- Each pump’s efficiency from the parabola through its best-efficiency point; power = ρ g Q H ÷ η per pump.
- Example: one pump gives 390.8 L/min; two give 438.18 L/min (12.122% more).
Limitations
- Identical pumps with simple parabolic curves; real curves and unequal pumps need the makers’ data.
- Parallel pumps need check valves; series pumps need the second casing rated for the higher pressure.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- See how much a second pump really adds
- Choose parallel or series for a duty
- Check each pump stays near its best efficiency
Who it is for
- Process engineers
- Building services engineers
- Maintenance engineers
What you get
- One pump alone
- Both pumps together and the gain
- Each pump’s flow, head and efficiency
Interpreting the result
- On a steep (friction-dominated) system a second pump in parallel adds little flow; series suits high static head.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3021–3026. Topic reference; no source tables or recommended settings are reproduced.
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