Library / Fluid Mechanics / FLU-03
Fluid Mechanics
Pump head from the extended head balance
Head a pump must add between two points of a piping system.
- Ref
- FLU-03
- Rev
- v1
- Field
- Fluid Mechanics
- Result
- hp [m]
Steady incompressible flow. Pump head adds energy, turbine head removes it and hL accounts for losses. Solving for pump head gives hp = H₂ − H₁ + ht + hL.
The pump must supply the head difference between the end points plus whatever is lost to friction and fittings or taken by a turbine.
Calculator
- Pressure rise equivalent (water)308.9 kPa
- Share of head lost14.29 %
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.
- Friction losses grow with the square of flow rate, so doubling the flow quadruples hL.
- Pump head, not pressure, is the quantity on pump curves and does not depend on fluid density.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| H₂ Head at point 2 | −10 to 200 m | −10.5 | 199.5 | 210 | +10% | +10.2 % |
| H₁ Head at point 1 | −10 to 100 m | −63.5 | 46.5 | 110 | +10% | −1.59 % |
| hL Head loss | 0.1 to 100 m | 27.1 | 127 | 99.9 | +10% | +1.43 % |
| ht Turbine head | 0 to 50 m | 31.5 | 81.5 | 50 | +10% | 0 % |
Sweep of Head loss
| Head loss (m) | Pump head (m) |
|---|---|
| 0.1 | 27.1 |
| 12.59 | 39.59 |
| 25.08 | 52.08 |
| 37.56 | 64.56 |
| 50.05 | 77.05 |
| 62.54 | 89.54 |
| 75.03 | 102 |
| 87.51 | 114.5 |
| 100 | 127 |
Sweep one variable
Variables and how each one contributes
Pump head
What the equation gives you. Everything else feeds it.
Head at point 1
Total head at the start. Lowers the head needed.
Head at point 2
Total head at the end. Raises the head needed.
Turbine head
Head removed by a turbine. Adds directly.
Head loss
Friction and fitting losses. Adds directly.
Worked example with the values above
- Head difference: H₂ − H₁ = 32 − 5 = 27 m.
- Add turbine head 0 m and losses 4.5 m.
- hp = 31.5 m.
Assumptions and limits
- Steady incompressible flow.
- One pump between the two points.
Common mistakes
- Forgetting minor losses.
- Using pressure units where head is needed.
Statistics and uncertainty
Head losses are usually the least certain part (friction factors are good to ±10–20%), so add a margin to the selected pump.
Where it is used
- Pump selection and duty points.
- Cooling-water and fire-main design.
Maths you need
- Total head: p/ρg + V²/2g + z
- Head loss: hf and hm