Library / Fluid Mechanics / FLU-13
Fluid Mechanics
Pump head after a speed change
Head developed by a given pump when its speed changes, at corresponding operating points.
- Ref
- FLU-13
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- H2 [m]
The head produced by a centrifugal pump rises with the square of the speed: H₂/H₁ = (N₂/N₁)². Head is the energy per unit weight, set by the speed at the impeller tip, which explains the square. It applies at corresponding operating points, so flow must change in proportion to speed at the same time.
Head developed by a given pump when its speed changes, at corresponding operating points. Head rises with the square of the speed.
Calculator
- Speed ratio, N₂/N₁1.207
- Head ratio, (N₂/N₁)²1.457
- New head in bar of water4.285 bar
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 head from 30 to 43.7 m, which is 45.7 % more for 20.7 % more speed.
- Cutting the speed to 80 % of the original would drop the head to 64 % of its value: a pump too slow cannot lift fluid to a given height at all.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| H1 Original head | 1 to 500 m | 1.457 | 728.3 | 726.8 | +10% | +10 % |
| N1 Original speed | 500 to 4,000 rpm | 5.742 | 367.5 | 361.8 | +10% | −17.4 % |
| N2 New speed | 500 to 4,000 rpm | 3.567 | 228.3 | 224.7 | +10% | +21 % |
Sweep of New speed
| New speed (rpm) | New head (m) |
|---|---|
| 500 | 3.567 |
| 937.5 | 12.54 |
| 1,375 | 26.98 |
| 1,813 | 46.88 |
| 2,250 | 72.24 |
| 2,688 | 103.1 |
| 3,125 | 139.3 |
| 3,563 | 181.1 |
| 4,000 | 228.3 |
Sweep one variable
Variables and how each one contributes
New head
What the equation gives you. Everything else feeds it.
Original head
The original head, in metres. Raises the new head in direct proportion. Raising it by 2 m (to 32 m) moves the result by +6.67 %, from 43.7 to 46.61 m.
Original speed
The original speed, in rpm. Lowers the new head with the square of the speed ratio. Raising it by 50 rpm (to 1,500 rpm) moves the result by −6.56 %, from 43.7 to 40.83 m.
New speed
The new speed, in rpm. Raises the new head with the square of the speed ratio. Raising it by 50 rpm (to 1,800 rpm) moves the result by +5.8 %, from 43.7 to 46.23 m.
Worked example with the values above
- Speed ratio: N₂/N₁ = 1,750 / 1,450 = 1.207.
- Square it: 1.207² = 1.457.
- H₂ = 30 × 1.457 = 43.7 m.
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
Head depends on speed squared, so a 1 % error in speed gives a 2 % error in head. For a system with a static lift, check that the new head still exceeds the static head, since flow stops when the head falls below it.
Where it is used
- Checking whether a pump at a new speed can reach a given pressure or elevation.
- Estimating the shut-off head of a pump at a different speed.
Maths you need
- Pump curve: head against flow at a fixed speed
- Similarity: flows scale with speed, heads with speed squared