Calculator · Thermal Engineering
Turbine Power Calculator
Shaft power a turbine delivers from the steady-flow energy balance. A positive power output means useful power produced. Heat transfer is either stated as zero (adiabatic) or entered — it is never assumed silently.
Inputs
q − ws = Δh + ΔV²/2 + gΔz (rate form × ṁ). q, Q̇ > 0 is heat into the control volume; ws, Ẇs > 0 is shaft work done by the fluid on the surroundings.
Results
Shaft power output Ẇs (produced)
Specific shaft work ws = 490 kJ/kg. Positive = useful power produced.
| Term | Per mass | Rate |
|---|---|---|
| Heat in q / Q̇ | 0 J/kg | 0 W |
| Shaft work out ws / Ẇs | 490 kJ/kg | 980 kW |
| Δh contribution | -500 kJ/kg | -1 MW |
| ΔKE contribution ΔV²/2 | 10 kJ/kg | 20 kW |
| ΔPE contribution gΔz | 0 J/kg | 0 W |
| Residual q − ws − (Δh + ΔKE + ΔPE) | 0 J/kg | 0 W |
| Property | Inlet 1 | Outlet 2 |
|---|---|---|
| Enthalpy h | 3000 kJ/kg | 2500 kJ/kg |
| Speed V | 50 m/s | 150 m/s |
| Elevation z | 0 m | 0 m |
| Mass flow ṁ (steady, in = out) | 2 kg/s |
|---|
Assumptions
- · steady flow
- · single inlet and outlet
- · q > 0 into the fluid
- · w_s > 0 done by the fluid
- · adiabatic: Q̇ = 0 stated explicitly
Explore in the Lab
The full control-volume state travels; the Lab adds the energy-flow schematic.
Technical reference
Ẇs = Q̇ − ṁ[(h2 − h1) + (V2² − V1²)/2 + g(z2 − z1)]
ws = Ẇs / ṁ
- h
- specific enthalpy[J/kg]
- V
- stream speed[m/s]
- z
- elevation[m]
- ṁ
- mass flow rate[kg/s]
- Q̇
- heat rate into the control volume[W]
- Ẇs
- shaft power out of the control volume[W]
q − ws = Δh + ΔV²/2 + gΔz (rate form × ṁ). q, Q̇ > 0 is heat into the control volume; ws, Ẇs > 0 is shaft work done by the fluid on the surroundings.
A negative result means the device absorbs work and is flagged.
A positive mass flow is required.