- 2073 Magh · 6 marks
Functions and energy equations of steady-flow devices
Short answer
Turbine: produces work from enthalpy drop, adiabatic w = h1 - h2. Compressor: uses work to raise pressure, adiabatic w_in = h2 - h1. Nozzle: converts enthalpy to kinetic energy, h1+V1²/2 = h2+V2²/2. Heat exchanger: transfers heat between streams, ṁ_h(h_h,in - h_h,out) = ṁ_c(h_c,out - h_c,in).
Write down the functions of turbine, compressor, nozzle and heat exchanger. Also write down energy equations for them.
All of these are steady flow devices: ṁ_in = ṁ_out, and the steady-flow energy equation is
Q̇ − Ẇ = Σṁ_e (h + V²/2 + gz)_e − Σṁ_i (h + V²/2 + gz)_i
| Device | Function | Energy equation (per unit mass, ΔPE ≈ 0) |
|---|---|---|
| Turbine | Expands steam/gas, converting enthalpy to shaft work output | w = (h₁ − h₂) + (V₁² − V₂²)/2 + q; adiabatic and ΔKE ≈ 0: w = h₁ − h₂ |
| Compressor (also pump, fan) | Raises the pressure of a gas using shaft work input | w_in = (h₂ − h₁) + (V₂² − V₁²)/2 − q; adiabatic: w_in = h₂ − h₁ |
| Nozzle | Increases the velocity of the fluid by decreasing its pressure | h₁ + V₁²/2 = h₂ + V₂²/2 (Q = W = 0), V₂ = √(V₁² + 2(h₁ − h₂)) |
| Heat exchanger | Transfers heat between two fluid streams without mixing (condenser, boiler, radiator) | ṁ_h (h_h,in − h_h,out) = ṁ_c (h_c,out − h_c,in) (W = 0, no loss to surroundings) |
Example: in a steam power plant, steam from the boiler expands in the turbine (work out), the exhaust is condensed in the condenser (a heat exchanger), and a pump raises the pressure of the liquid. Nozzles are used in jet engines and in steam turbines, where they direct high-velocity steam onto the blades.
✓ Answer checked by Claude Opus 5.5 (high effort)
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