Calculator · Thermal Engineering
Nozzle & Diffuser Calculator
A nozzle trades enthalpy for speed; a diffuser trades speed for enthalpy. Neither has shaft work. The nozzle solves the outlet speed from h1 and h2; the diffuser solves the outlet enthalpy from V1 and V2. Adiabatic operation is a stated choice, not a hidden default.
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
Outlet speed V2
| Term | Per mass | Rate |
|---|---|---|
| Heat in q / Q̇ | 0 J/kg | 0 W |
| Shaft work out ws / Ẇs | 0 J/kg | 0 W |
| Δh contribution | -50 kJ/kg | -50 kW |
| ΔKE contribution ΔV²/2 | 50 kJ/kg | 50 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 | 2950 kJ/kg |
| Speed V | 10 m/s | 316.39 m/s |
| Elevation z | 0 m | 0 m |
| Mass flow ṁ (steady, in = out) | 1 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
- · no shaft work (Ẇs = 0)
Explore in the Lab
The full control-volume state travels; the Lab adds the energy-flow schematic.
Technical reference
V2 = √(V1² + 2[q − (h2 − h1) − g(z2 − z1)]), nozzle
h2 = h1 + q − (V2² − V1²)/2 − g(z2 − z1), diffuser
q = Q̇ / ṁ, ws = 0
- 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 nozzle balance that would need a negative outlet kinetic energy is refused, not clipped.
A diffuser whose outlet is faster than its inlet is flagged: it acts as a nozzle.