Specific Energy Calculator

This calculator uses the Bernoulli-style specific energy (energy per unit mass) expression:

Units are converted internally to SI base units, then converted back to your selected display units.

1. Select a Mode to calculate e or solve for one variable.
2. Enter the known values and choose correct units for each field.
3. For solve modes, provide a Target specific energy value.
4. Click Submit to view results above the form.
5. Use Download CSV or Download PDF to export.

Sample cases help verify your inputs and units.

1) What “specific energy” means

Specific energy is energy per unit mass, reported in J/kg (or equivalent units). In steady flow, it combines pressure energy (p/ρ), kinetic energy (v²/2), and potential energy (g·z). Engineers use it to compare states without multiplying by mass flow rate, which keeps interpretations clean and scalable.

2) Why the pressure term can dominate

The pressure contribution p/ρ grows large when density is small. For air near sea level, 101325 Pa and ρ≈1.225 kg/m³ gives p/ρ≈82673 J/kg, often larger than moderate kinetic terms. For water, the same pressure with ρ≈1000 kg/m³ gives only 101.3 J/kg, so motion and elevation can become more visible.

3) Interpreting the kinetic term

The kinetic term v²/2 increases quadratically with speed. At 10 m/s, v²/2 is 50 J/kg; at 30 m/s it is 450 J/kg; at 100 m/s it reaches 5000 J/kg. This scaling explains why high-speed jets, nozzles, and wind tunnels are highly sensitive to velocity changes.

4) Elevation changes and the g·z term

Potential energy depends linearly on height. With g≈9.80665 m/s², a 10 m rise adds about 98.07 J/kg. A 100 m rise adds about 980.67 J/kg. In pipelines over terrain, this term helps quantify lift demands and the energy impact of vertical routing.

5) Using solve modes for quick design checks

This calculator can solve for v, p, or z when a target specific energy is known. That supports “what-if” evaluation: estimate how much pressure is required for a planned velocity and elevation, or find the maximum velocity allowed before the energy budget is exceeded. Negative results flag inconsistent inputs.

6) Data quality: units and reference states

Enter pressure consistent with your reference (often gauge or absolute). Mixing reference types can distort p/ρ. Density should match the fluid state (temperature and composition matter for gases). Elevation should be measured from a consistent datum. These details typically explain outliers.

7) Common ranges for engineering context

Typical water distributions may show total specific energy in the hundreds to thousands of J/kg when velocities are a few m/s and elevation changes are tens of meters. Airflows at modest pressures can show tens of thousands of J/kg because p/ρ is large. Always compare terms, not only totals.

8) Reporting and documentation

Exporting results supports reviews and lab notes. The CSV is ideal for spreadsheets, while the PDF print view is useful for project files. For traceability, record your chosen units, the mode used, and the normalized SI inputs shown in the results block.

1) Is this the same as “specific mechanical energy”?

Yes. The expression e = p/ρ + v²/2 + g·z is commonly called specific mechanical energy or Bernoulli specific energy. It excludes internal energy and heat transfer effects.

2) Should I use gauge or absolute pressure?

Use one consistently. Many comparisons work with gauge pressure if all states share the same reference. If you mix gauge and absolute values, p/ρ may be shifted and results can mislead.

3) What density should I enter for gases?

Use the density at the same temperature and pressure as the flow state you’re analyzing. For air, density changes noticeably with altitude and temperature, so avoid assuming a constant value.

4) Why does solving for velocity sometimes fail?

A real velocity requires e − p/ρ − g·z ≥ 0. If your target energy is too low for the given pressure and elevation, the remaining kinetic term becomes negative and no real solution exists.

5) Can the solved pressure be negative?

Mathematically, yes, if the target energy is below v²/2 + g·z. In practice, that usually indicates inconsistent inputs, a different pressure reference, or a situation outside the model’s assumptions.

6) How accurate are the non-SI energy units?

They are approximate conversions for convenience. For critical work, report SI (J/kg) and convert with your project standard. The calculator is best used for consistent comparisons and checks.

7) Does this account for pumps, losses, or viscosity?

No. This is a specific-energy balance at a point. If you need pumps or head losses, you would extend the model with added energy and dissipation terms using a full system energy equation.