Formula Used
Total head is the energy per unit weight of a flowing fluid, expressed as an equivalent fluid column height:
H = z + p/(ρg) + v²/(2g)
- z is elevation head (m or ft).
- p/(ρg) is pressure head (m or ft).
- v²/(2g) is velocity head (m or ft).
This calculator rearranges the same relationship to solve for pressure, velocity, or elevation.
How to Use This Calculator
- Select what you want to solve for (H, p, v, or z).
- Enter the remaining values and choose their units.
- Keep pressure type consistent (gauge or absolute).
- Click Calculate to view results above the form.
- Use Download CSV or Download PDF from the results.
Example Data Table
| Scenario | z (m) | p (kPa) | ρ (kg/m³) | v (m/s) | g (m/s²) | H (m) |
|---|---|---|---|---|---|---|
| Water line, moderate pressure | 8 | 250 | 1000 | 3.5 | 9.80665 | 34.058 |
| Low pressure, higher velocity | 2 | 80 | 998 | 8 | 9.80665 | 12.529 |
| Air flow, small density | 5 | 3 | 1.2 | 15 | 9.80665 | 273.297 |
Values are illustrative; verify against your system conditions.
Total head in practical fluid systems
Total head expresses the mechanical energy available in a moving fluid as an equivalent height. Because it is normalized by weight, engineers can compare very different pipelines and fluids using one consistent unit: meters or feet of fluid.
Why the head form is useful
Pressure alone does not capture motion or elevation. Head combines elevation, pressure, and velocity into a single energy balance. This helps identify whether a pump is adding energy, whether valves are dissipating it, or whether elevation changes dominate system behavior.
Typical ranges you may encounter
In water distribution, total head commonly spans 10–60 m depending on terrain and service pressure. Industrial recirculation loops may exceed 100 m when long runs, filters, or heat exchangers add resistance. For air, the same pressure produces very large head because density is low.
Interpreting elevation, pressure, and velocity heads
Elevation head is purely geometric and changes with height. Pressure head reflects static pressure relative to the fluid weight, while velocity head depends on speed and grows with the square of velocity. High-speed flows can have modest pressure but significant velocity head.
Choosing density and gravity carefully
Density varies with temperature and composition; water near room temperature is close to 998–1000 kg/m³, while oils can be 800–950 kg/m³. Gravity is often 9.80665 m/s² for standard calculations, but local values can differ slightly for precision work.
Unit consistency and common pitfalls
Convert inputs to a consistent unit set before computing. Mixing gauge and absolute pressure can shift results by an offset head. Another frequent issue is entering kPa as Pa, which changes pressure head by a factor of 1000. This tool’s unit selectors reduce those mistakes.
Using total head for diagnostics
If total head drops between two points in a real pipeline, the difference is often head loss from friction, fittings, or equipment. Comparing component heads reveals whether loss is mostly from pressure reduction, velocity changes, or elevation. This supports faster troubleshooting and sizing decisions.
When to extend beyond the basic model
The formula here assumes steady, incompressible flow and focuses on energy terms at a point. For full system analysis, include head loss, pump head, and minor losses. In rapidly varying or compressible cases, use time-dependent methods or compressible flow relations.
FAQs
1) Is pressure head based on gauge or absolute pressure?
Either works, but stay consistent across points. Gauge pressure is common for pipelines. Absolute pressure is required when vapor pressure, cavitation checks, or compressibility considerations matter.
2) Why does air produce such large head values?
Head divides pressure by ρg. Air density is about 1.2 kg/m³, far smaller than water. The same pressure therefore corresponds to a much taller equivalent column height.
3) Can I solve for velocity if the result is negative under the square root?
No. A negative value indicates the specified total head is too small for the given elevation and pressure. Reduce z or pressure head, increase total head, or recheck units.
4) What is a reasonable velocity head in pipes?
For water at 1–3 m/s, velocity head is roughly 0.05–0.46 m. It becomes significant in high-speed systems, nozzles, and jets where velocity is much higher.
5) Does this include friction losses?
No. This computes the energy terms at a point. To compare two locations, subtract heads to estimate losses, or add a separate loss model using friction factors and minor-loss coefficients.
6) How do I pick density for mixtures or hot liquids?
Use a property table or supplier data at the operating temperature and concentration. Small density changes can noticeably shift pressure head in tall systems.
7) What unit should I use for elevation?
Use meters or feet, matching your project standard. Elevation head is a direct length term, so incorrect length units will shift total head by the same amount.