Thermal Engineering and Gas Dynamics (ME-601) - Unit 5 Short Notes

UNIT 5: Steam Power Engineering and Gas Dynamics

I. Steam Generators (Boilers)

Classification of Steam Generators

Detailed Study of High-Pressure Boilers

Velox Boiler

• Principle: Uses forced circulation of water by a centrifugal pump. Combustion air is also pressurized by a gas turbine-driven fan, achieving high combustion rates.

• Construction: Consists of a cylindrical drum and two headers connected by bent water tubes. A gas turbine (using exhaust from boiler) drives the air fan.

• Significance: Rapid steaming (15-20 min), compact, suitable for peak load plants.

• Diagram:

  DiagramSEARCH: "Velox boiler schematic water tubes gas turbine"

Lamont Boiler

• Principle: Forced circulation of water by a steam-driven reciprocating pump (using steam from boiler drum).

• Construction: Drum, headers, bent water tubes, steam pump for circulation, superheater, economizer.

• Flue Gas Path: Furnace → combustion chamber → horizontal flue tubes → chimney.

• Water Path: Drum → headers → bent tubes (heated) → drum (separation).

• Key Parts: Steam pump, circulation control valve.

• Diagram:

  DiagramSEARCH: "Lamont boiler diagram water flow flue gas"

Boiler Mountings and Accessories

Essential Mountings (Safety Devices)

1. Safety Valve: Releases steam when pressure exceeds safe limit.

2. Pressure Gauge: Indicates steam pressure.

3. Water Level Indicator: Shows water level in drum.

4. Fusible Plug: Melts at high temperature to extinguish fire if water level low.

5. Blow-off Cock: Removes sediments from drum bottom.

6. Steam Stop Valve: Controls steam flow to pipeline.

Three Important Accessories

1. Feed Pump: Supplies water to boiler. Can be injector (for low pressure) or centrifugal/reciprocating.

2. Economizer: Preheats feedwater using flue gases, improving efficiency.

3. Air Preheater: Recovers heat from flue gases to preheat combustion air, increasing boiler efficiency.

Boiler Draught

Definition & Purpose

• Draught: Pressure difference (negative gauge pressure) inside boiler furnace that causes air to flow through fuel bed and flue gases to escape.

• Purpose: Supplies combustion air, removes flue gases, maintains required rate of combustion.

Natural Draught

• Achieved by chimney. Hot flue gases rise due to lower density, creating suction.

• Draught Height:

$$H = 0.353 \times 10^{-3} H \left( \frac{1}{T_a} - \frac{1}{T_f} \right) \ \text{m of water column}$$

Where $H$ = chimney height (m), $$\displaystyle T_a $$ = ambient temp (K), $$\displaystyle T_f $$ = flue gas temp (K).

• Limitation: Limited height, depends on weather.

Artificial Draught

• Forced Draught: Fan pressurizes air before furnace → positive pressure system.

• Induced Draught: Fan sucks flue gases from boiler → negative pressure system.

• Advantages: Independent of weather, higher combustion rates, compact boilers.

• Disadvantages: Power consumption, fan maintenance, risk of furnace explosion if air supply fails.

Chimney Draught Calculation (Air-Fuel Ratio)

Given: Chimney height $H$, draught $d$ (mm water gauge), $$\displaystyle T_f $$, $$\displaystyle T_a $$, $$\displaystyle P_{atm} $$.

1. Draught in Pascals: $$\displaystyle d_{Pa} = d \times 9.81 $$

2. Density of hot gases: $$\displaystyle \rho_g = \frac{P_{atm} \times M}{R T_f} $$ (M = avg molar mass ≈ 29 kg/kmol for air)

3. Density of air: $$\displaystyle \rho_a = \frac{P_{atm} \times M}{R T_a} $$

4. Draught equation: $$\displaystyle d_{Pa} = H g (\rho_a - \rho_g) $$

5. Mass of air per kg fuel: $$\displaystyle m_a = \frac{\text{Volume of air at } T_a}{\text{Volume of flue gases at } T_f} \times \frac{\rho_g}{\rho_a} \times \frac{1}{\text{air-fuel ratio}} $$

   (Solve for air-fuel ratio using ideal gas law and continuity).

Boiler Performance

Boiler Efficiency ($$\displaystyle \eta_b $$)

• Definition: Ratio of heat utilized to produce steam to heat supplied by fuel.

• Direct Method:

$$\eta_b = \frac{m_s (h - h_f)}{m_f \times CV}$$

$$\displaystyle m_s $$ = steam generated (kg/h), $h$ = enthalpy of steam (kJ/kg), $$\displaystyle h_f $$ = enthalpy of feedwater, $$\displaystyle m_f $$ = fuel used (kg/h), $CV$ = calorific value (kJ/kg).

• Heat Balance Sheet: Tabular form showing % heat input vs. % heat output (steam, losses).

Equivalent Evaporation ($$\displaystyle m_e $$)

• Definition: Amount of steam (kg) that would be generated from feedwater at 100°C to dry saturated steam at 1 atm (enthalpy = 2257 kJ/kg).

• Formula:

$$m_e = \frac{m_s (h - h_f)}{2257}$$

• Significance: Standardized measure to compare boilers of different pressures/temperatures.

Factors Affecting Performance

• Incomplete combustion, heat loss in flue gases, unburnt fuel, radiation/convection losses, moisture in fuel, blowdown losses.

II. Steam Power Cycles

Carnot Vapor Cycle

• Processes:

  1-2: Isentropic compression (pump)

  2-3: Constant-temperature heat addition (boiler)

  3-4: Isentropic expansion (turbine)

  4-1: Constant-temperature heat rejection (condenser)

• T-s Diagram: Two isotherms, two adiabatics → rectangle.

• Limitations:

  • Pump work input is small but requires isentropic compression of liquid (impractical).

  • Heat addition at constant temperature requires infinite heat transfer surface.

  • Wet vapor in turbine causes erosion.

  • Not feasible for practical steam plants.

Rankine Cycle

Ideal Rankine Cycle

• Processes:

  1-2: Isentropic pumping (saturated liquid to boiler pressure)

  2-3: Constant-pressure heat addition (to superheated steam)

  3-4: Isentropic expansion in turbine

  4-1: Constant-pressure heat rejection in condenser (wet vapor to saturated liquid).

• p-v & T-s Diagrams:

  DiagramCANVAS: "T-s diagram: 1-2 vertical line (pump), 2-3 horizontal right (boiler), 3-4 vertical down (turbine), 4-1 horizontal left (condenser)"

• Thermal Efficiency ($$\displaystyle \eta_{Rankine} $$):

$$\eta = \frac{(h_3 - h_4) - (h_2 - h_1)}{h_3 - h_2} = \frac{w_t - w_p}{q_{in}}$$

For negligible pump work: $$\displaystyle \eta \approx 1 - \frac{h_4 - h_1}{h_3 - h_2} $$.

Effects of Boiler and Condenser Pressures

Regenerative Rankine Cycle

Need for Regeneration

• To increase average T of heat addition by preheating feedwater using steam bled from turbine.

• Reduces fuel consumption, improves efficiency.

Open Feedwater Heater (Direct Contact)

• Steam bled from turbine mixes directly with feedwater. Output is saturated liquid at heater pressure.

• Requires pump to next stage.

• Working: Extraction steam → heater → condenses → mixes with feedwater → saturated liquid → pump.

Closed Feedwater Heater (Shell & Tube)

• Steam bled from turbine condenses on outside of tubes carrying feedwater.

• Drain from heater is throttled to condenser.

• Working: Extraction steam → shell side → condenses → drain out. Feedwater → tubes → heated by steam.

Comparison

Reheat Rankine Cycle

Purpose: To reduce moisture content at turbine exhaust and increase work output.

Cycle: High-pressure turbine → steam reheated in boiler → low-pressure turbine.

T-s Diagram:

DiagramCANVAS: "T-s: 1-2 pump, 2-3 boiler, 3-4 HP turbine, 4-5 reheater, 5-6 LP turbine, 6-1 condenser"

Effects:

• Turbine work increases (area under curve expands).

• Cycle efficiency may increase or decrease slightly (reheat adds heat input). Net work ↑ more than heat input ↑ → often net efficiency ↑.

Binary Vapor Cycle

• Concept: Use two vapor cycles in series (e.g., mercury-steam).

• Working: Mercury cycle (high T) generates heat → used in steam cycle (low T).

• Advantages: Higher average T of heat addition → higher Carnot efficiency → overall efficiency > simple Rankine.

• Disadvantages: Mercury toxicity, complexity, cost.

Modified Rankine Cycle for Steam Engines

• Assumptions:

  1. Admission at constant pressure $$\displaystyle P_1 $$.

  2. Cut-off at volume ratio $$\displaystyle r_c $$ (cut-off ratio).

  3. Expansion adiabatic to pressure $$\displaystyle P_2 $$ (release pressure).

  4. Pressure drops to back pressure $$\displaystyle P_b $$ at constant volume (release).

  5. Exhaust at constant pressure $$\displaystyle P_b $$.

• Work per cycle (without clearance):

$$W = (P_1 V_1 - P_2 V_2) + P_2 V_2 \ln\left(\frac{V_2}{V_3}\right) - P_b (V_4 - V_1)$$

Where $$\displaystyle V_3 = V_2 \times \left(\frac{P_2}{P_b}\right)^{1/n} $$ (if expansion polytropic with index $n$), $$\displaystyle V_4 = V_1 $$ (constant volume release).

• Modified Rankine Efficiency: $$\displaystyle \eta = \frac{W}{P_1 V_1} $$.

Overall Plant Efficiency & Steam Rate

Overall Efficiency ($$\displaystyle \eta_{overall} $$):

$$\eta_{overall} = \eta_{boiler} \times \eta_{cycle} \times \eta_{turbine} \times \eta_{generator}$$

Steam Rate (SR):

$$SR = \frac{3600}{w_t \times \eta_{generator}} \ \text{kg/kWh}$$

Where $$\displaystyle w_t $$ = turbine work output (kJ/kg). Lower SR = better performance.

Mollier Chart Use: Read $$\displaystyle h_3 $$, $$\displaystyle h_4 $$ (quality at exhaust), efficiency directly.

III. Gas Turbine Cycles

Brayton Cycle with Regeneration & Reheat

Ideal Brayton Cycle:
1-2: Isentropic compression
2-3: Constant-pressure heat addition
3-4: Isentropic expansion
4-1: Constant-pressure heat rejection.

Thermal Efficiency: $$\displaystyle \eta = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}} $$ ($$\displaystyle r_p $$ = pressure ratio).

Regenerator:

• Uses turbine exhaust to preheat compressed air before combustion.

• Effect: Reduces fuel input → efficiency ↑ (approaches Carnot between $$\displaystyle T_{max} $$ and $$\displaystyle T_{min} $$).

Reheat:

• Expansion in two stages with reheating in between.

• Effect: Net work output ↑ (more area in T-s), efficiency may ↑ slightly.

Conditions for Maximum Output (with Reheat & Regenerator)

• With Regenerator: Max net work when pressure ratio $$\displaystyle r_p = \sqrt{\frac{T_{max}}{T_{min}}} $$ (for ideal Brayton with regeneration).

• With Reheat & Regenerator: Optimal pressure ratio for max net work is lower than without reheat.

  Derivation: For given $$\displaystyle T_{max} $$, $$\displaystyle T_{min} $$, and fixed $$\displaystyle T_{reheat} $$, maximize $$\displaystyle w_{net} = w_t - w_c $$ with respect to $$\displaystyle r_{p1} $$ and $$\displaystyle r_{p2} $$. Condition: $$\displaystyle r_{p1} = r_{p2} $$ for perfect intercooling (if used).

IV. Steam Turbines and Nozzles

Steam Turbines

Impulse vs. Reaction

Compounding

• Need: Reduce blade speed (from high velocity) to practical limits, improve efficiency.

• Velocity Compounding: Multiple velocity stages (nozzles + moving blades) in series. Pressure drop in one nozzle set.

• Pressure Compounding: Multiple pressure drops (nozzle + moving blade sets). Each stage has small pressure drop.

• Diagram:

  DiagramSEARCH: "velocity compounding steam turbine diagram"

Flow Through Nozzles

Isentropic Flow (Steam)

• Convergent Nozzle: For subsonic flow only. Throat at exit.

• Convergent-Divergent (C-D) Nozzle: For supersonic flow. Throat at minimum area, divergent section accelerates to supersonic.

• Critical Pressure Ratio ($$\displaystyle r_c $$): Pressure ratio at throat where $$\displaystyle M=1 $$.

  For steam: $$\displaystyle r_c = \left( \frac{2}{\gamma+1} \right)^{\gamma/(\gamma-1)} \approx 0.546 $$ for $$\displaystyle \gamma=1.3 $$.

• Critical Conditions (Throat): $$\displaystyle P^* $$, $$\displaystyle T^* $$, $$\displaystyle \rho^* $$ given by isentropic relations.

• Maximum Discharge (Choked Flow): When $$\displaystyle P_{exit} \leq P^* $$, mass flow limited by throat conditions.

$$\dot{m}_{max} = C_d A^* \sqrt{\frac{\gamma P_0}{R T_0} \left( \frac{2}{\gamma+1} \right)^{(\gamma+1)/(\gamma-1)}}$$

Where $$\displaystyle C_d $$ = discharge coefficient, $$\displaystyle A^* $$ = throat area, $$\displaystyle P_0 $$, $$\displaystyle T_0 $$ = inlet stagnation.

Nozzle Efficiency & Friction

Nozzle Efficiency ($$\displaystyle \eta_n $$):

$$\eta_n = \frac{\text{Actual kinetic energy at exit}}{\text{Isentropic enthalpy drop}} = \frac{V_a^2/2}{h_0 - h_e (s)}$$

Friction Losses: Reduce exit velocity, increase entropy (irreversibility).

$$\displaystyle V_a = \sqrt{2 \eta_n (h_0 - h_e)} $$ where $$\displaystyle h_e $$ = actual exit enthalpy (from steam tables at $$\displaystyle P_e $$ and $$\displaystyle s_a = s_0 $$).

Supersaturated Flow in Steam Nozzles

• Conditions: High expansion rate, negligible nucleation sites → steam remains superheated metastable beyond saturation line.

• Effects:

  • Discharge mass flow rate nearly same as isentropic (since depends on throat conditions).

  • Heat drop less than isentropic (since actual $T$ > saturation $T$ at $$\displaystyle P_e $$).

  • Entropy increase (irreversible).

• Comparison: Isentropic flow reaches saturation at some point, may have two-phase flow. Supersaturated remains single-phase vapor longer.

V. Gas Dynamics

Mach Number ($M$)

$$M = \frac{c}{a} = \frac{\text{Flow velocity}}{\text{Local speed of sound}}$$

• Regimes:

  $$\displaystyle M < 1 $$: Subsonic

  $$\displaystyle M = 1 $$: Sonic (critical)

  $$\displaystyle M > 1 $$: Supersonic

  $M \gg 1$: Hypersonic (typically $$\displaystyle M>5 $$).

• Significance: Determines flow behavior, compressibility effects, shock formation.

Isentropic Flow in Variable Area Ducts

One-Dimensional Assumptions: Properties uniform across section, no friction, adiabatic, steady.

Area-Velocity Relation:

$$\frac{dA}{A} = (M^2 - 1) \frac{dV}{c}$$

• Converging Duct ($$\displaystyle dA < 0 $$):

  $$\displaystyle M < 1 $$ → $$\displaystyle dV > 0 $$ (accelerates subsonic)

  $$\displaystyle M > 1 $$ → $$\displaystyle dV < 0 $$ (decelerates supersonic).

• Diverging Duct ($$\displaystyle dA > 0 $$):

  $$\displaystyle M < 1 $$ → $$\displaystyle dV < 0 $$ (decelerates subsonic)

  $$\displaystyle M > 1 $$ → $$\displaystyle dV > 0 $$ (accelerates supersonic).

• To accelerate subsonic to supersonic: Convergent → throat ($$\displaystyle M=1 $$) → divergent (C-D nozzle).

• Normal Shocks: Occur only in supersonic flow ($$\displaystyle M>1 $$) in diverging section. Sudden increase in $P$, $\rho$, $T$; decrease in $M$ (to subsonic); entropy ↑; stagnation pressure loss.

Diffusers

Function: Decelerate flow, convert kinetic energy to pressure rise (increase static pressure).

Types:

• Subsonic Diffuser: Gradual divergence, no shocks, pressure recovery good.

• Supersonic Diffuser: Must first decelerate supersonic to subsonic via normal shock in diverging section, then subsonic diffusion. Shock location adjustable.

Effect: $V \downarrow$, $$\displaystyle P_{static} \uparrow $$, $$\displaystyle P_{stagnation} $$ may ↓ across shock.

Wave Propagation & Zones

Mach Cone:

$$\mu = \sin^{-1}(1/M)$$

Half-angle of disturbance cone behind supersonic object.

Zone of Action: Region inside Mach cone where disturbances from source are felt (influenced by source).

Zone of Silence: Region outside Mach cone where disturbances not yet reached (uninfluenced).

Application: Shock wave analysis, supersonic flight, nozzle design.

VI. Compressors

Classification of Air Compressors

Reciprocating Compressors

Single-stage, Single-acting:

• Suction → compression → discharge in one cylinder, one end of piston active.

• p-V Diagram:

  DiagramSEARCH: "reciprocating compressor p-V diagram clearance"

Work Input (without clearance):

For polytropic $$\displaystyle PV^n = C $$:

$$W = \frac{n}{n-1} P_1 V_1 \left[ \left( \frac{P_2}{P_1} \right)^{(n-1)/n} - 1 \right]$$

For isentropic ($\gamma$): replace $n$ with $\gamma$.

Double-acting: Both sides of piston used → double capacity per revolution.

Volumetric Efficiency ($$\displaystyle \eta_v $$)

Definition: Ratio of actual volume of air drawn (at inlet conditions) to piston displacement volume.

With Clearance Volume $C$ (fraction of $$\displaystyle V_s $$):

$$\eta_v = 1 + C - C \left( \frac{P_2}{P_1} \right)^{1/n}$$

Where $$\displaystyle P_2/P_1 $$ = discharge/suction pressure ratio, $n$ = polytropic index.

Factors: Clearance ↑ → $$\displaystyle \eta_v $$ ↓; Pressure ratio ↑ → $$\displaystyle \eta_v $$ ↓; $n$ ↑ → $$\displaystyle \eta_v $$ ↓.

Diagram: Shows clearance volume, expansion line from $$\displaystyle P_2 $$ to $$\displaystyle P_1 $$.

Multistage Compression

Advantages over Single-stage:

• Lower work input (for same $$\displaystyle P_2/P_1 $$) due to reduced temperature rise.

• Lower discharge temperature → less lubrication issues.

• Higher volumetric efficiency.

• Better mechanical balance.

Perfect Intercooling: Intercooler cools air to inlet temp $$\displaystyle T_1 $$ before next stage.

Work per kg (n stages, equal pressure ratios):

$$W_{total} = \frac{n}{\gamma-1} R T_1 \left[ \left( \frac{P_2}{P_1} \right)^{(\gamma-1)/(n\gamma)} - 1 \right]$$

Heat Rejected to Intercooler:

$$Q_{intercooler} = n \times C_p (T_{after\ compression} - T_1)$$

per kg air.

Condition for Minimum Work: Equal pressure ratios in all stages.

$$r_{p1} = r_{p2} = ... = \left( \frac{P_{final}}{P_{initial}} \right)^{1/n}$$

Compressor Efficiencies

Isentropic Efficiency ($$\displaystyle \eta_{isen} $$):

$$\eta_{isen} = \frac{\text{Isentropic work input}}{\text{Actual work input}} = \frac{w_s}{w_a}$$

Isothermal Efficiency ($$\displaystyle \eta_{iso} $$):

$$\eta_{iso} = \frac{\text{Isothermal work input}}{\text{Actual work input}} = \frac{w_{iso}}{w_a}$$

Isothermal work minimum → $$\displaystyle \eta_{iso} $$ measures closeness to isothermal.

Mechanical Efficiency ($$\displaystyle \eta_m $$):

$$\eta_m = \frac{\text{Indicated work}}{\text{Shaft power input}}$$

(accounts for friction, bearing losses).

Centrifugal Compressors

Working Principle: Air enters axially → impeller rotates → centrifugal force increases velocity → diffuser converts kinetic to pressure.

Components: Inlet guide vanes, impeller (rotor), diffuser (vaned or vaneless), volute.

Performance: Higher flow rates, lower pressure rise per stage than reciprocating. Surge/stall limits.

VII. Condensers and Feedwater Systems

Condensers

Jet Condensers: Steam mixed directly with cooling water.

• Low-level: Condensate collected below jet level → requires extraction pump.

• High-level: Condensate collected above → gravity discharge.

• Counter-flow: Steam & water opposite flow → better cooling.

• Parallel-flow: Same direction → less effective.

Surface Condensers: Steam separated from cooling water by tube walls (shell & tube).

Air Leakage Sources: Joints, seals, pump glands, non-condensables in steam.

Effect on Performance:

• Air in condenser reduces partial pressure of steam → condenser vacuum decreases (pressure rises).

• Increases pumping work, reduces turbine output, increases fuel consumption.

Feedwater Heaters

Open-type (Deaerator): Direct contact between steam and feedwater. Removes dissolved gases ($$\displaystyle O_2 $$, $$\displaystyle CO_2 $$). Output is saturated liquid at heater pressure. Requires pump.

Closed-type: Shell & tube. Steam on shell side, feedwater in tubes. Drain cooler often included. Drain throttled to condenser.

Comparison:

VIII. Performance Calculations and Properties

Velocity of Sound

Ideal Gas:

$$a = \sqrt{\gamma R T}$$

Superheated Steam (given $v$, $P$, $T$):

$$a = \sqrt{\gamma \frac{P}{\rho}} = \sqrt{\gamma \frac{P}{1/v}} = \sqrt{\gamma P v}$$

(Since $$\displaystyle \rho = 1/v $$). Use consistent units.

Wet Steam Properties (Closed Vessel)

Given: Volume $V$, mass of liquid $$\displaystyle m_f $$, temperature $T$ (saturated).

1. Pressure: From steam tables at $T$ → $$\displaystyle P_{sat} $$.

2. Quality ($x$):

$$x = \frac{m_g}{m_{total}} = \frac{V - m_f v_f}{m_f (v_g - v_f)}$$

where $$\displaystyle v_f $$, $$\displaystyle v_g $$ at $$\displaystyle P_{sat} $$.

3. Specific volume: $$\displaystyle v = v_f + x (v_g - v_f) $$.

4. Enthalpy: $$\displaystyle h = h_f + x h_{fg} $$.

5. Entropy: $$\displaystyle s = s_f + x s_{fg} $$.

6. Internal energy: $$\displaystyle u = u_f + x u_{fg} $$ (or $$\displaystyle u = h - Pv $$).

Problem-Solving Techniques (Key Formulas)

Draught (Air-Fuel Ratio):

$$\frac{m_a}{m_f} = \frac{\text{Mass of flue gases}}{\text{Mass of fuel}} \times \frac{\text{Volume of air at } T_a}{\text{Volume of flue gases at } T_f}$$

Compressor MEP (Mean Effective Pressure):

$$MEP = \frac{W}{V_s} = \frac{\text{Work per cycle}}{\text{Swept volume}}$$

Nozzle with Friction:

$$V_a = \sqrt{2 \eta_n (h_0 - h_e)}$$

, where $$\displaystyle h_e $$ from steam tables at $$\displaystyle P_e $$ and $$\displaystyle s_a = s_0 $$.

Cycle Efficiency (Rankine): Use steam tables/Mollier to get $$\displaystyle h_1, h_2, h_3, h_4 $$.

Steam Rate:

$$SR = \frac{3600}{w_t \times \eta_{gen}} \ \text{kg/kWh}$$

Exam Tips & Common Pitfalls

[!TIP]

• Boiler Draught: Always convert all units consistently (mm water → Pa, °C → K). Use $$\displaystyle R = 287 $$ J/kgK for air.

• Rankine Cycle: Remember pump work is small but not zero for precise calculations. Use $$\displaystyle h_2 = h_1 + v_1 (P_2 - P_1) $$.

• Nozzles: Critical pressure ratio is for ideal gas. For steam, use steam tables to find $$\displaystyle P^* $$ where $$\displaystyle s_0 = s^* $$.

• Compressors: Volumetric efficiency formula with clearance is crucial. For multistage, equal pressure ratios give minimum work only with perfect intercooling.

• Gas Dynamics: Area-velocity relation is key. Remember $$\displaystyle M=1 $$ at throat for C-D nozzle in isentropic flow.

• Mollier Chart: Read carefully – enthalpy lines are diagonal, constant pressure lines curved.

• Modified Rankine: Don’t forget constant volume release step (pressure drop at constant volume).

• Supersaturated Flow: Discharge mass flow ≈ isentropic because throat conditions unchanged; only exit velocity/heat drop affected.

• Overall Efficiency: Product of component efficiencies – often asked in numericals.

• Centrifugal Compressor: Surge is low-flow instability; choke is high-flow limit.