- 2075 Baisakh · 6 marks
Steady state work vs steady flow; turbine, nozzle
Short answer
Work devices (turbine, compressor) exchange shaft work; flow devices (nozzle, throttle) do not. Adiabatic turbine: Ẇ_out = ṁ(h₁ − h₂) neglecting KE. Adiabatic nozzle: h₁ + V₁²/2 = h₂ + V₂²/2, so exit velocity V₂ ≈ √[2(h₁ − h₂)] for low inlet speed.
Differentiate between steady state work applications and steady state flow applications with examples. Also write the functions and governing equations for an adiabatic turbine and adiabatic nozzle.
In steady flow, the mass flow and the properties at each point do not vary with time (dm_cv/dt = 0, dE_cv/dt = 0), so Σṁ_i = Σṁ_e and Q̇ − Ẇ = ṁ[Δh + ΔKE + ΔPE]. Devices are grouped by whether they exchange shaft work.
| Basis | Steady state work devices | Steady state flow devices (no work) |
|---|---|---|
| Main purpose | Produce or absorb shaft work | Change velocity, pressure or temperature of the stream |
| Work term | Ẇ ≠ 0 | Ẇ = 0 |
| Examples | Turbine, compressor, pump, fan | Nozzle, diffuser, throttle valve, heat exchanger, mixing chamber |
| Heat transfer | Usually negligible (adiabatic) | Nozzle, throttle: negligible; heat exchanger: key effect |
| Governing equation | w = (h₁ − h₂) for turbine (ΔKE, ΔPE neglected) | Nozzle: h₁ + V₁²/2 = h₂ + V₂²/2 |
Adiabatic turbine
Function: expands high-pressure, high-temperature gas or steam to produce shaft work. Q = 0 and ΔPE ≈ 0:
Ẇ_out = ṁ [ (h₁ − h₂) + (V₁² − V₂²)/2 ]
The kinetic energy change is usually small, so w = h₁ − h₂.
Adiabatic nozzle
Function: accelerates the fluid by decreasing its pressure (increases its kinetic energy). Q = 0, W = 0, ΔPE = 0:
h₁ + V₁²/2 = h₂ + V₂²/2
V₂ = √[ V₁² + 2 (h₁ − h₂) ]; for inlet velocity ≈ 0, V₂ = √(2 Δh).
Mass balance for both: ṁ₁ = ṁ₂, ṁ = A V / v.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Functions and energy equations of steady-flow devices · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Adiabatic air turbine: mass flow and areas · Fundamental of Thermodynamics & Heat Transfer, chapter 4 · asked 2×
- Adiabatic steam turbine 50 MW: mass flow, isentropic efficiency · Fundamental of Thermodynamics & Heat Transfer, chapter 5
- Mass and energy equations for CV; nozzle, condenser · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Adiabatic steam turbine 70% isentropic efficiency · Fundamental of Thermodynamics & Heat Transfer, chapter 5
- Steam nozzle 4 MPa: mass flow, exit velocity, area · Fundamental of Thermodynamics & Heat Transfer, chapter 4
- Governing equations; forward, backward, central differencing · Computational Techniques in Civil Engineering, chapter 5
- Governing equations, kinematic wave, Courant number · Computational Techniques in Civil Engineering, chapter 5
- Complete governing equations of fluid movement · Computational Techniques in Civil Engineering, chapter 5
- Turbine selection method and governing factors · Power Plant Design, chapter 3 · asked 3×
All Fundamental of Thermodynamics & Heat Transfer chapter 4 questions →