**Efficiency is the ratio of useful energy output to the total energy input to the system or equipment**

**So, efficiency = Useful energy output X 100 / Total energy input.**

**1-Furnace efficiency:**

**Furnace efficiency = Heat released in furnace X 100 / Fuel energy supplied**

**Solved example:**

**Calculate the furnace efficiency of a Boiler which releases 18 Mcal/hr heat & consumes coal fuel 10 TPH, take fuel GCV as 2250 kcal/kg**

**ηfurnace**= 18 X 1000000 X 100 / (10 X 1000 X 2250) = 80%

**2-Boiler efficiency:**

**1-Direct method:**

**A-Boiler feed water & attemperator water is at same temperature**

**Boiler efficiency in %=Steam flow X (Steam enthalpy –Feed water Enthalpy) X 100 / (Fuel GCV X Fuel consumption)**

**B- Boiler feed water & attemperator water is at different temperature**

**Boiler efficiency in %=( Steam flow X Steam enthalpy –Feed water flow X Feed water Enthalpy) X 100 / (Fuel GCV X Fuel consumption)**

**Note:**

- Blow down water loss is not considered

- Steam used for soot blowers is not considered

- L1-Heat loss due to dry flue gas.

- L2-Heat loss due to moisture content in burning fuel.

- L3-Heat loss due to moisture content in combustion and spreading air.

- L4-Heat loss due to formation of water from hydrogen present in fuel.

- L5-Heat loss due to conversion of carbon into carbon monoxide.

- L6-Heat loss due to unburnt in bottom and fly ash.

- L7-Heat loss due to radiation

- L8-Heat loss due to convection & other un measurable

- L9-Heat loss due to soot blowing

- L10-Heat loss due to blow down.

- Losses in bearings

- Losses in oil seals

- Losses in Gears

- Losses in lubrication due to churning effect.

**Examples:**

**Calculate the efficiency of 100 TPH Boiler operating at 88 kg/cm2G pressure & temperature 515 deg C, consumes 17 TPH coal whose GCV is 5000 kcal /kg & is supplied with feed water at temperature 165 deg C. Assume no blow down loss.**

**Calculate the efficiency of 100 TPH Boiler operating at 88 kg/cm2G pressure & temperature 515 deg C, consumes 17 TPH coal whose GCV is 5000 kcal /kg & is supplied with feed water 92 TPH at temperature 165 deg C & 10 TPH water for attemperating at temperature 105 Deg C.**

**2-Indirect method**

**Boiler efficiency = 100-Losses**

**Example**

**A boiler generates steam 80 TPH at 66 kg/cm2 and 485 °C. Mesured O2, CO and CO2 in flue gas are 8%, 850 ppm and 12% respectively. Ash analysis shows unburnt in fly ash and bottom ash are 10.5% and 3% respectively, GCV of fly ash and bottom ash are 695 kcal/kg and 1010 kcal/kg respectively. Coal analysis shows carbon 50%, Hydrogen 3.2%, Oxygen 8.2%, Sulphur 0.4%, Nitrogen 1.1%, Ash 19% and moisture 18.1 and its GCV is 4100 kcal/kg. Then calculate the Boiler efficiency. Consider ambient air, flue gas out let temperature are 30 and 150 °C respectively, humidity in ambient air is 0.02 kg/kg of dry air.**

**3-Economiser Effectiveness/Efficiency Economiser effectiveness is calculated as**

**ηEco. = (Economiser outlet feed water temperature Two-Economiser inlet feed water temperature Twi) X 100 / (Economiser inlet flue gas temperature Tfi- Economiser inlet feed water temperature Twi)**

**Example:**

**Calculate the economiser effectiveness, whose feed water inlet & outlet temperatures are 200 Deg C & 290 Deg C respectively & flue gas inlet & outlet temperatures 400 deg C & 230 deg c respectively.**

**4-Air Preheater (APH) Effectiveness/Efficiency**

**APH gas side efficiency**

**APH air side efficiency**

**Example:**

**A tubular APH has air inlet & outlet temperatures are 25 deg c & 185 deg C & flue gas inlet & outlet temperatures are 230 deg C & 145 deg C. Calculate the APH effectiveness on Gas side & Air side**

**5-ESP efficiency:**

**Efficiency of ESP ηESP = 1-eˆ(-AV/Q) X 100**

**Example:**

**An ESP handles total flue gas at the rate of 80 m3 /sec., it has total collecting surface area 5890 m2, calculate the efficiency of ESP if ash particles migration velocity is 0.077 m/sec.**

_{ESP }= 99.98%

**6-HP heater effectiveness**

**It is calculated as temperature range of steam / Temperature range of feed water**

**Example:**

**A HP heater is been used to raise the feed water temperature from 125 deg C to 145 deg C by using Turbine bleed steam at inlet temperature 325 deg C, calculate the HP heater effectiveness. Consider the HP heater condensate out let temperature is 165 deg C**

**7-Deaerator (D/A) efficiency:**

**η**

_{D/A}= (Concentration of Oxygen in inlet water(Ci)-Concentration of oxygen in outlet water (Co)) X 100 /(Concentration of Oxygen in inlet water(Ci))**Example:**

**Calculate the efficiency of Deaerator if inlet & outlet oxygen concentrations of D/A are 20 ppm & 0.005 ppm respectively.**

**8-Turbine efficiency:**

**Overall efficiency**

**η**

_{Turbine}

**= Power generation in kcal X 100/ Heat input in Kcal**

**Example: Calculate the overall efficiency of a 5 MW back pressure turbines, operating at 67 kg/cm2 pressure & 495 deg C temperature. Consider specific steam consumption (SSC) of the Turbine is 7.5 & steam is exhausted at pressure 1.8 kg/cm2 & temperature 180 deg C**

**Example-2: Calculate the cycle efficiency of 55 MW Turbine operating at 110 Kg/cm2 pressure & 540 degree C temperature. Consider feed water temperature 210 deg C & SSC 3.8**

**Turbine heat rate = Steam flow Qs X (Steam enthalpy Hs-Feed water enthalpy Hw) / Power generation**

**9-Power plant efficiency:**

**Power plant efficiency = 860 X 100 / Heat rate**

**Example:**

**Calculate the efficiency of 100 MW power plant which consumes 65 TPH of coal having GCV 5200 kcal/kg.**

**Note:**Heat rate of cogeneration power plants is calculated as

**Cogen heat rate (CHR)=((Fuel consumption X GCV + Heat content in return condensate + Heat content in makeup water - Sum of heat content in process steam))/Power generation.**

**10-Condenser efficiency:**

**η**

_{condenser}**= Actual cooling water temperature rise X 100 / Maximum possible cooling water temperature rise**

**Example**

**A down flow type surface condenser has vacuum -0.85 kg/cm2 condenses 85 TPH steam at cooling water inlet and outlet temperatures 25 °C and 36 °C respectively, calculate the condenser efficiency.**

**11-Vacuum efficiency:**

**η**

_{vacuum}= Actual vacuum in condenser X 100/Maximum Obtainable vacuum in the condenser

**Example:**

**Exhaust steam from condenser enters at 47 °C, if the vacuum gauge of condenser reads -0.86 kg/cm2, find the vacuum efficiency.**

**η**= 0.86 X 100/0.93 = 92.5%

_{vacuum}**12-Gear box efficiency:**

**η**

_{Gearbox}**= Output power X 100 / Input power**

**Example:**

**A helical gear box is used to drive a fuel feeding system, the input power of the gear box is 9.5 KW & output power is 8.7 KW, calculate GB efficiency**

**η**

_{Gearbox}**= Output power X 100 / Input power =8.7 X 100 / 9.5 =91.5%**

**13-Pump efficiency:**

**Example:**

**A pump is consuming 20 KW to deliver 72 M3/hr of water at height 55 meter, calculate its efficiency.**

**14-Cooling tower (CT) efficiency:**

**η**

_{CT = (CT inlet water temperature Ti-CT outet water temperature }_{To) X 100 /(}

_{CT outet water temperature }_{To-WBT)}

**η**

_{CT =(Ti-T0) X 100 / (To-WBT)}**CT efficiency can also be written as**

**η**

_{CT = Range X 100 /(Range +Approach)}

_{Where Range is temperature difference between CT inlet & outlet water}

_{Approach is the temperature difference between CT outlet water & wet bulb temperature (WBT)}Fans efficiency can be Mechanical efficiency or Static efficeincy.These are calculated based on static pressure & total pressure.

**Static efficiency of the fan ηsfan= (Air flow in M3/sec X Static pressure in mmwc X 100) / (102 X Input power to fan shaft in KW)**

**Similarly mechanical efficiency can be calculated as**

**Mechanical efficiency of the fan ηfan= (Air flow in M3/sec X Total pressure in mmwc X 100) / (102 X Input power to fan shaft in KW)**

**Example:**

**A boiler ID fan consumes 220 KW power to sucky 60 m3/sec flue gas at static pressure 280 mmwc, calculate its static efficiency.**

**ηsfan= Q X Hs X 100 / 102 X Ps**

**ηsfan = 60 X 280 X 100 / (102 X 220) =74.8%**

**Also read efficiency & Heat rate calculation of power plants**

**Heat rate & Efficiency of power plants**

Very informative thank you

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