Governing Formula
A pump must overcome four distinct energy additions: the static lift, the friction losses in the piping and fittings, and any residual pressure required at the delivery point (converted into metres of water column):
TDH = H_stat + h_f + h_m + h_res Where:
-
H_stat= Static lift from suction water level to discharge outlet [m] -
h_f= Suction and discharge pipe friction loss [m] -
h_m= Minor / fitting losses (valves, bends, tees) [m] -
h_res= Residual head required at the delivery point [m] -
TDH= Total dynamic head the pump must supply [m]
Derived Equations:
h_res = P_res × 10.1972 TDH = H_stat + h_f + h_m + h_res P_total = TDH / 10.1972 How the Calculation Works
Residual pressure is first converted to head of water using the standard conversion 1 bar = 10.1972 m H₂O (based on ρ = 1000 kg/m³ and g = 9.80665 m/s²):
h_res (m) = P_res (bar) × 10.1972
The four head components are summed to give the total dynamic head. Converting back to pressure by dividing by 10.1972 gives the equivalent total pressure, which is useful for checking against a pump curve in bar.
Worked Engineering Example
Design Scenario: Booster to a Roof Tank, 12 m Lift, 2 bar Residual
- Residual pressure to head:
h_res = 2.0 × 10.1972 = 20.39 m - Head components:
H_stat = 12.0 m · h_f = 4.0 m · h_m = 1.0 m - Total dynamic head:
TDH = 12.0 + 4.0 + 1.0 + 20.39 = 37.39 m - Equivalent total pressure:
P_total = 37.39 / 10.1972 = 3.67 bar
Engineering Notes & Design Benchmarks
| Application | Typical TDH Range | Residual Pressure |
|---|---|---|
| Roof tank booster | 20 – 40 m | 1 – 2 bar at the tank inlet |
| Borehole supply | 40 – 120 m | 1 – 3 bar at delivery |
| Utility transfer | 10 – 35 m | 1 – 2 bar at destination |
The residual pressure term is what keeps a booster from being undersized: a modest 2 bar discharge requirement adds over 20 m of head. Every major energy consumer must be captured or the pump curve duty point will be wrong.
Assumptions & Limitations
- Water density fixed at 1000 kg/m³ and g = 9.80665 m/s² for the bar-to-head conversion.
- Friction and minor losses must already be expressed in equivalent head of water.
- The calculator composes head only — it does not size the pump, select the motor, or check NPSH.
- Suction lift, flooding conditions, and variable-speed operation must be evaluated separately.
Frequently Asked Questions
What exactly counts as the "static lift"?
Static lift is the vertical distance between the free water surface on the suction side and the discharge outlet, regardless of the pipe path. Curved or diagonal runs still count only the vertical elevation difference.
Why does residual pressure add so much head?
Because 1 bar of pressure equals roughly 10.2 m of water column. A 2 bar residual at the delivery point is therefore equivalent to lifting the water over 20 m vertically — it must appear in the TDH or the pump will be badly undersized.
How do I get friction and minor losses to put in here?
Pipe friction can come from the Darcy–Weisbach or Hazen–Williams calculators on this site; minor losses are typically expressed as equivalent length of pipe or as K-factors (h = K·v²/2g) and must be converted to head before entry.
Engineering Disclaimer
Engineering Note: This calculator composes the total dynamic head for preliminary design and education. Final pump selection must check the duty point against the manufacturer’s curve, NPSH requirements, and suction conditions.
Technical References
- Hydraulic Institute, Pump Standards (ANSI/HI 1.1–1.6 for rotodynamic centrifugal pumps).
- Karassik, I., Messina, J., Cooper, P., & Heald, C., Pump Handbook, 4th ed., McGraw-Hill, 2008.
- Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe (TP 410), 2009.