Flow Devices & Isentropic Efficiency流動裝置與等熵效率

What you'll be able to do本章學習成果

• Reduce the steady-flow energy equation for each common device by dropping negligible terms.
• Size nozzles, turbines, compressors, throttles, and heat exchangers from inlet/exit states.
• Define and evaluate isentropic efficiency for turbines, compressors, pumps, and nozzles.
• Locate the ideal (isentropic) exit state and quantify the loss to irreversibility.

Builds directly on the general balance from Control-Volume Analysis.

Key equations重要公式

Nozzles & diffusers噴嘴與擴散器

A nozzle speeds a flow up at the expense of pressure; a diffuser does the reverse. Both have no work and usually negligible heat transfer and potential-energy change, so the SFEE reduces to a trade between enthalpy and kinetic energy:

A drop in enthalpy appears as a rise in velocity. (Subsonic nozzles narrow in the flow direction; supersonic ones widen — the reverse for diffusers.)

Turbines

A turbine develops shaft work as fluid expands through its blades. With negligible heat transfer and KE/PE changes, the enthalpy drop becomes work:

Compressors & pumps

A compressor (gas) or pump (liquid) does work on the fluid to raise its pressure. Same reduced equation as the turbine, with the work input sign reversed:

For a pump handling a nearly incompressible liquid, $w_p \approx v(p_2 - p_1)$ — much smaller than equivalent gas-compression work.

Throttling devices

A throttle (valve or porous plug) drops pressure with no work and negligible heat or KE change, so enthalpy is conserved:

For an ideal gas $h = h(T)$, so $T$ is unchanged; for real fluids the temperature usually drops sharply — the basis of refrigeration and of the throttling calorimeter used to measure steam quality.

Mixing chambers & heat exchangers

In a mixing chamber streams combine directly; in a heat exchanger they exchange heat through a wall without mixing. With no work and no external heat loss, the energy carried in by the streams equals that carried out:

Mass balances on each stream close the problem — e.g. a condenser relates the cooling-water flow to the steam flow.

SFEE device explorerSFEE 裝置探索器

Pick a device and the schematic grays out the energy terms that drop, leaving the reduced equation. Then drive the sliders (air as ideal gas) to compute the headline result — exit velocity, power, or the throttle's constant-enthalpy outcome.

Air as ideal gas, $c_p = 1.005$ kJ/kg·K. Each device keeps only its essential terms.

Isentropic efficiency等熵效率

Adiabatic devices can only reach exit states with $s_2 \ge s_1$, so the best possible exit is the isentropic one (state 2s) at the same exit pressure. Isentropic efficiency measures how close a real device comes. For a turbine it is the actual work as a fraction of the ideal:

For a compressor or pump the ideal is the minimum work, so the ratio inverts:

A nozzle efficiency compares actual to isentropic exit kinetic energy. In every case the irreversibility shows up as the actual state lying to the right of 2s on a T–s or Mollier diagram. (The entropy basis for $s_2 \ge s_1$ is developed in Entropy.)

Isentropic-efficiency lab

Expand or compress air between two pressures at a chosen isentropic efficiency. The ideal path (1→2s) is vertical — constant entropy; the actual path (1→2) leans right by exactly the entropy generated. Lower the efficiency and watch the work and exit temperature respond.

Air as ideal gas, $c_p = 1.005$ kJ/kg·K, $k = 1.4$.

Isentropic turbine efficiency渦輪機等熵效率