Library / Fluid Mechanics / FLU-14
Fluid Mechanics
Pump power after a speed change
Approximate shaft power of a given pump when its speed changes, assuming roughly equal efficiency.
- Ref
- FLU-14
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- P2 [kW]
The power absorbed by a centrifugal pump rises with the cube of the speed, P₂/P₁ ≈ (N₂/N₁)³, because both the flow and the head change with speed (power is proportional to flow times head). The relation is approximate since efficiency changes slightly with speed, and it holds at corresponding operating points of the pump curve.
Approximate shaft power of a given pump when its speed changes, assuming roughly equal efficiency. Power rises with the cube of the speed.
Calculator
- Speed ratio, N₂/N₁1.207
- Power ratio, (N₂/N₁)³1.758
- Extra power needed15.16 kW
- Energy per litre pumped relative to before, (N₂/N₁)²1.457
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 raises the shaft power from 20 to 35.16 kW: a 20.7 % speed increase costs 75.8 % more power.
- Going the other way, cutting the speed by 20 % saves about 49 % of the power, which is the reason variable-speed drives pay back so quickly on pumps and fans.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kW) | Local step | Change in result |
|---|---|---|---|---|---|---|
| P1 Original power | 0.1 to 1,000 kW | 0.1758 | 1,758 | 1,758 | +10% | +10 % |
| N1 Original speed | 500 to 4,000 rpm | 1.675 | 857.5 | 855.8 | +10% | −24.9 % |
| N2 New speed | 500 to 4,000 rpm | 0.82 | 419.9 | 419 | +10% | +33.1 % |
Sweep of New speed
| New speed (rpm) | New power (kW) |
|---|---|
| 500 | 0.82 |
| 937.5 | 5.406 |
| 1,375 | 17.05 |
| 1,813 | 39.06 |
| 2,250 | 74.73 |
| 2,688 | 127.3 |
| 3,125 | 200.2 |
| 3,563 | 296.6 |
| 4,000 | 419.9 |
Sweep one variable
Variables and how each one contributes
New power
What the equation gives you. Everything else feeds it.
Original power
The original shaft power, in kW. Raises the new power in direct proportion. Raising it by 2 kW (to 22 kW) moves the result by +10 %, from 35.16 to 38.68 kW.
Original speed
The original speed, in rpm. Lowers the new power with the cube of the speed ratio. Raising it by 50 rpm (to 1,500 rpm) moves the result by −9.67 %, from 35.16 to 31.76 kW.
New speed
The new speed, in rpm. Raises the new power with the cube of the speed ratio. Raising it by 50 rpm (to 1,800 rpm) moves the result by +8.82 %, from 35.16 to 38.26 kW.
Worked example with the values above
- Speed ratio: N₂/N₁ = 1,750 / 1,450 = 1.207.
- Cube it: 1.207³ = 1.758.
- P₂ = 20 × 1.758 = 35.16 kW.
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).
- The relation is approximate, since efficiency changes slightly with speed.
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.
- Expecting the full cubic saving when the system has a large static head.
Statistics and uncertainty
Because power rises with the cube of speed, a 1 % error in the speed gives about a 3 % error in the power. The relation is approximate: efficiency usually falls at lower speed, so the saving from slowing a pump is slightly less than the cube law predicts.
Where it is used
- Estimating the energy saving of a variable-speed drive on a pump or fan.
- Checking motor size when a pump is run faster.
Maths you need
- Pump curve: head against flow at a fixed speed
- Similarity: flows scale with speed, heads with speed squared