Library / Fluid Mechanics / FLU-12
Fluid Mechanics
Pump flow rate after a speed change
Flow of a given pump when its speed changes, at corresponding operating points with the same impeller diameter.
- Ref
- FLU-12
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- Q2 [L/s]
For a centrifugal pump the flow rate is proportional to the speed: Q₂/Q₁ = N₂/N₁ (the first of the affinity laws). Doubling the speed doubles the flow, but the head rises four times and the power eight times, which is why speed control is so effective at saving energy. The speed unit does not matter as long as both are the same.
Flow of a given pump when its speed changes, at corresponding operating points with the same impeller diameter. Flow is directly proportional to speed.
Calculator
- Speed ratio, N₂/N₁1.207
- Change in flow10.34 L/s
- New flow in m³/h217.2 m³/h
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.
- Raising the speed from 1,450 to 1,750 rpm (20.7 % faster) raises the flow from 50 to 60.34 L/s.
- At the same time the head would rise by 45.7 % and the power by 75.8 %, so a modest increase in flow costs much more energy.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (L/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Q1 Original flow rate | 1 to 1,000 L/s | 1.207 | 1,207 | 1,206 | +10% | +10 % |
| N1 Original speed | 500 to 4,000 rpm | 21.88 | 175 | 153.1 | +10% | −9.09 % |
| N2 New speed | 500 to 4,000 rpm | 17.24 | 137.9 | 120.7 | +10% | +10 % |
Sweep of New speed
| New speed (rpm) | New flow rate (L/s) |
|---|---|
| 500 | 17.24 |
| 937.5 | 32.33 |
| 1,375 | 47.41 |
| 1,813 | 62.5 |
| 2,250 | 77.59 |
| 2,688 | 92.67 |
| 3,125 | 107.8 |
| 3,563 | 122.8 |
| 4,000 | 137.9 |
Sweep one variable
Variables and how each one contributes
New flow rate
What the equation gives you. Everything else feeds it.
Original flow rate
The original flow rate, in litres per second. Raises the new flow in direct proportion. Raising it by 5 L/s (to 55 L/s) moves the result by +10 %, from 60.34 to 66.38 L/s.
Original speed
The original speed, in rpm. Lowers the new flow, because the speed ratio N₂/N₁ becomes smaller. Raising it by 50 rpm (to 1,500 rpm) moves the result by −3.33 %, from 60.34 to 58.33 L/s.
New speed
The new speed, in rpm. Raises the new flow in direct proportion. Raising it by 50 rpm (to 1,800 rpm) moves the result by +2.86 %, from 60.34 to 62.07 L/s.
Worked example with the values above
- Speed ratio: N₂/N₁ = 1,750 / 1,450 = 1.207.
- Multiply the original flow: 50 × 1.207.
- Q₂ = 60.34 L/s.
Assumptions and limits
- The same pump and fluid at two speeds, with the operating point moving to a dynamically similar point on the pump curve.
- The impeller diameter is unchanged and the efficiency is the same at both points (a good approximation for modest speed changes).
Common mistakes
- Applying the laws to a system with a large static head: the new operating point is where the new pump curve meets the system curve, not on the affinity parabola.
- Using them for large speed changes, where the efficiency changes.
Statistics and uncertainty
The flow is in direct proportion to speed, so a 1 % error in the speed gives a 1 % error in the flow. In practice, slip in the drive can make the actual speed a little different from the nameplate value; use a measured speed.
Where it is used
- Setting a variable-speed pump to a required flow.
- Estimating the flow when a pump is changed to a different motor speed or pulley.
Maths you need
- Pump curve: head against flow at a fixed speed
- Similarity: flows scale with speed, heads with speed squared