**A-Boiler**

**1-Boiler efficiency direct method**

Boiler efficiency = (Mass of steam flow X Steam enthalpy-Feed water flow at economizer inlet X Enthalpy-Attemperator water flow X Enthalpy) / (GCV of fuel X Fuel consumption)

2-**Boiler efficiency by indirect method**

Boiler efficiency = 100-Various losses

3-**Theoretical air requirement for combustion**

Theoretical air T_{hair} = ((11.6 X C% + (34.8 X (H2-O2/8)) + (4.35 X %S))/100

Where C = % of carbon in fuel

H2 = % of Hydrogen present in fuel

S = % of sulphur present in fuel

4-**Excess air requirement for combustion**

%EA = O2% / (21-O2%)

Where O2 = % of oxygen present in flue gas

5-**Mass of actual air supplied**

AAS = (1 + EA / 100) X Theoretical air

**6-Mass of flue gas**

Mfg = Mass of Air + 1

6-**Mass of dry flue gas**

Mfg = Mass of Co2 in flue gas + Mass of Nitrogen in fuel + Mass of Nitrogen in combustion air + Mass of oxygen in flue gas + Mass of So2 in flue gas

Mfg =(Carbon % in fuel X Molecular weight of CO2 / Mol.weight of Carbon) + N2 in fuel + (Mass of actual air supplied X % of N2 in air i.e 77/100) + ((Mass of actual air – Mass of theoretical air) X 23/100) + S2 in fuel X Mol.weight of SO2 / Mol.weight of sulphur)

7-**% of heat loss in dry flue gas**

**Heat loss = Mfg X Cp X (Tf-Ta) X 100 / GCV of fuel**

Where,

Mfg = Mass of flue gas

Cp = Specific heat of flue gas in kacl/kg

Tf = Temperature of flue gas

Ta = Ambient air temperature

**9-% of heat loss due to moisture in fuel**

Heat loss = M X (584 + Cp X (Tf-Ta)) X 100 / GCV of fuel

Where,

M = Moisture in fuel

Cp = Specific heat of flue gas in kcal/kg

10-**% of heat loss due to moisture in air**

**Heat loss = AAS X humidity X Cp X (Tf-Ta) X 100/ (GCV of fuel)**

Where,

AAS = Actual air supplied for combustion

Cp = Specific heat of flue gas in kcal/kg

Tf = Temperature of flue gas

Ta = Ambient air temperature

11-**% of Boiler water blow down**

**Blow down % = (Feed water TDS X % of makeup water) X 100 / (Maximum permissible TDS in Boiler water –Feed water TDS)**

12-**Steam velocity in line**

**Velocity of steam in pipe line,V = Steam flow in m3/sec / Area of pipe line (A)**

**Steam flow in m3/sec = (Steam flow in kg/hr / Density of steam X 3600)**

Area of pipe, A = Pi X D^{2} / 4

Where D is pipe internal diameter

13-**Condensate flash steam calculation**

**Flash steam % = (H1-H2) X 100 / Hfg)**

Where, H1 = Sensible heat at high pressure condensate in kcal/kg

H2 = Sensible heat of steam at low pressure in kcal/kg

Hfg = Latent heat of flash steam

14-**Calculation of amount of heat required to raise the water temperature**

**Heat required in kcal=Mw X Cp X (T2-T1)**

Where, Mw = Mass of water

Cp = Specific heat of water in kcal/kg (1 kcal/kg)

T1 = Initial temperature of water in deg C

T2 = Final temperature of water in deg C

15-**Calculation of heat required to raise air temperature**

**Heat required in kcal=M****air**** X Cp X (T2-T1)**

Where, Mw = Mass of water

Cp = Specific heat of flue gas in kcal/kg (0.24 kcal/kg)

T1 = Initial temperature of air in deg C

T2 = Final temperature of air in deg C

16-**Surface heat loss calculation **

**S = (10 + (Ts-Ta) / 20) X (Ts-Ta) X A**

S = Surface heat loss in kcal/hr m2

Ts= Hot surface temperature in deg C

Ta = Ambient air temperature in deg C

**17-Dryness fraction of steam **

**X = Mass of dry steam / (Mass of dry steam + Mass of water suspension in mixture)**

**18-Heat content in wet steam **

**h = hf + xhfg**

h= Heat content in saturated steam

x = Dryness factor of steam

Hfg =Enthalpy of evaporation

19-**Heat content in dry saturated steam **

**h = hf + hfg**

h= Heat content in saturated steam

Hfg =Enthalpy of evaporation

**20-Heat content in superheated steam**

**h = hf + hfg + Cps (Tsup - Ts)**

h= Heat content in super heated steam

hfg =Enthalpy of evaporation

Cps = Specific heat of super heated steam

Tsup= Superheated steam temperature in deg C

Ts = Saturated temperature of steam in deg C

**21-Calculation of Equivalent evaporation**

**Me = Ms X (h-hf) / hfg**

Ms = Mass of steam

h = Steam enthalpy

hf= Feed water enthalpy

**22-Factor of evaporation**

**Fe = (h-hf) / 539**

**23-Ash (Total) generation calculation**

**Ash generation in TPH = Fuel consumption per hour X % of ash in fuel / 100**

**24-Fly ash generation calculation**

Fly ash generation in TPH = Fuel consumption per hour X % of ash in fuel X 80% / 100

**25-Bottom ash generation calculation**

**Bottom ash generation in TPH = Fuel consumption per hour X % of ash in fuel X 20% / 100**

**26-Calculation of ash generation in ESP**

**Ash generation in ESP in TPH = Fuel consumption per hour X % of ash in fuel X 80% X 80% / 100**

**27-Boiler safety valve blow down calculation**

**Blow down % = (Set pressure - Re seat pressure) X 100 / Set pressure**

**28-Calculation of attemperator water flow**

**Attemperator water flow in TPH= Steam flow in TPH X (h1-h2) / (h2-h3)**

**h1 = Enthalpy of steam before desuper heating in kcal/kg**

**29-Economiser efficiency calculation**

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

30-**APH efficiency calculation**

__APH air side efficiency__

**ηAPHa = (Air outlet temp-Air inlet temp)) X 100 / (Flue gas inlet temperature -Air inlet temperature)**

__APH gas side efficiency__

**ηAPHg = (Flue gas inlet temp.-Flue gas outlet temp) X 100 / (Flue gas inlet temperature -Air inlet temperature )**

31-**Calculation of steam cost**

**Steam cost per ton = Steam enthalpy in kcal/kg X Fuel price per ton/ (Boiler efficiency % X GCV of fuel used in kcal/kg)**

32-**Travelling grate Boiler heating surface calculation**

**Boiler heating surface (Appx) = Boiler capacity in kg/hr / 18**

33-**AFBC Boiler heating surface calculation**

**Boiler heating surface (Appx) = Boiler capacity in kg/hr / 22**

34-**Travelling grate slop fired Boiler heating surface calculation**

**Boiler heating surface (Appx) = Boiler capacity in kg/hr / 12**

35-**AFBC slop fired Boiler (Low pressure up to 10 kg/cm2 WP) heating surface calculation**

**Boiler heating surface (Appx) = Boiler capacity in kg/hr / 8.2**

36-**Calculation of draught produced in Chimney**

**Hw = 353 X H (1/Ta – 1/Tg (Ma+ 1)/Ma)**

**H = Chimney height in meters**

**Ta = Atmospheric temperature in K**

**Tg = Flue gas temperature in K**

**Ma = Mass of air & Mass of flue gas = Ma+1**

** **

**Also given as;**

** P = 176.5 X H / Ta**

**Hw = Chimney height in meters**

**Ta = Absolute atmospheric temperature in Kelvin**

**Hw = Draught in mmwc**

37-**Calculation of mass of flue gas flowing through chimney**

**Mg (kg/sec)= Density of gas (kg/m3) X Area of Chimney (m2) X Velocity of flue gas in Chimney (m/sec)**

B-**Turbine and Auxiliaries**

1-**Turbine heat rate calculation**

**a-Heat rate of Thermal power plant Turbine in kcal/kg = **

**Steam flow X (Steam enthalpy in kcal/kg-Feed water enthalpy in kcal/kg) / Power generation**

**b-Heat rate of Co-ge**n plant T**urbine in kcal/kg = **

**Inlet steam flow X Enthalpy-(Sum of extraction steam flow X Their enthalpy + Exhaust steam X Enthalpy) / Power generation **

**i.e THR = ((Steam Flow x Steam Enthalpy)-(1St EXT Flow x Its Enthalpy + 2nd Ext flow x its Enthalpy + 3rd Ext flow x Its Enthalpy+ Exhaust Steam flow x its Enthalpy)) /Power Generation**

**Or**

**THR=((Steam Flow x Steam Enthalpy +Makeup Water flow x Its Enthalpy+ RC Flow x RC Enthalpy)-(Process-1 steam flow x its Enthalpy + Process-2 steam flow x Its Enthalpy+ FW Flow x FW Enthalpy)) /Power Generation**

2-**Turbine efficiency calculation**

**Efficiency = 860 X 100 / Turbine heat rate**

3-**Steam condenser efficiency calculation**

**Condenser efficiency =Difference in cooling water inlet & outlet temperatures X 100/(Vacuum temperature-condenser Inlet temperature of cooling water)**

**Condenser efficiency = (T2 - T1) X 100/(T3 - T1)**

**T2: Condenser outlet cooling water temperature,**

**T1: Condenser inlet cooling water temperature,**

**T3: Temperature corresponding to the vacuum or absolute pressure in the condenser.**

4-**Vacuum efficiency calculation**

**Vacuum efficiency = (Actual vacuum in condenser X 100)/Max. Obtainable vacuum.**

**I.e**

**Vacuum efficiency in % =Actual vacuum X 100 / (Atmospheric pressure or barometric pressure-Absolute pressure)**

5-**Cooling tower range**

**Range = Cooling tower outlet water temperature-Cooling tower inlet water temperature**

6-**Cooling tower approach**

**Approach = Cooling tower outlet cold water temperature - Wet bulb temperature**

7-**Cooling efficiency calculation**

**Efficiency = Range X 100 / (Range + Approach)**

8-**Heat rejected or heat load of cooling towers**

**Heat load =Mass of circulating water X Specific heat of water Cp X Range**

9-**Cooling tower evaporation loss calculation**

**Evaporation loss in m3/hr = 0.00085 X 1.8 X Water circulation rate m3/hr X Range **

**Evaporation loss in % = Evaporation loss X 100 / Water circulation rate m3/hr**

10-**Cooling tower blow down loss calculation**

**Blow down loss in % = Evaporation loss X 100 / (COC-1)**

**Where COC: Cycles of concentration**

**Its generally calculated as;**

**COC = Conductivity in circulation water / Conductivity in makeup water**

**OR**

**COC = Chloride in circulation water / Chloride in makeup water**

11-**Calculation of mass of cooling water required to condenser steam in surface condensers**

**Mw = (Ms X (hfg X dryness fraction(x) + Cpw (T3 - Tc)))/(Cpw X (T2 - T1))**

**Mw = Mass of cooling water required in TPH**

**Ms = Mass of exhaust steam to condenser in TPH**

**Hfg = Enthalpy of evaporation at exhaust pressure in kcal/kg**

**Cpw = Specific heat of cooling water in kcal/kg**

**T3= Temperature at exhaust pressure in deg C**

**Tc= Temperature of condensate in deg C**

**T1=Cooling water temperature entering condenser in deg C**

**T2 = Cooling water temperature leaving condenser in deg C**

**12-Steam turbine wheel chamber pressure calculation (Appx)**

**Turbine wheel chamber pressure (kg/cm2 ) = (Turbine inlet pressure (kg/cm2 ) X Turbine operating load (MW) X 0.6) / Turbine rated capacity (MW).**

**13-Calculation of power generation in steam Turbine**

**Power generation in MW= Turbine inlet steam flow in TPH X (Inlet steam enthalpy in kcal/kg- Exhaust steam enthalpy in kcal/kg) / 860**

**14-Power generation calculation in multi stage Turbines**

**Power generation in MW= Steam flow from 1st stage X (Inlet steam enthalpy in kcal/kg- 1st stage extraction steam enthalpy in kcal/kg) + Steam flow from 2nd stage X (Inlet steam enthalpy in kcal/kg- 2nd stage extraction steam enthalpy in kcal/kg) + Exhaust steam flow to condenser X (Inlet steam enthalpy in kcal/kg- Exhaust steam enthalpy in kcal/kg) / 860**

**15-Calculation of work done per kg of steam in Turbine**

**Work done/kg of steam = Inlet steam enthalpy in kcal/kg-Exhaust steam enthalpy in kcal/kg**

**16-Calculation of steam required per per KWH**

**Steam required per KWH = 860 / (Work done per kg of steam)**

**Or**

**Steam required per KWH =860/(Inlet steam enthalpy in kcal/kg-Exhaust steam enthalpy in kcal/kg)**

**17-Thermal power plant efficiency calculation**

**Efficiency = 860 X Power generation / Heat input**

**Efficiency = 860 X PG X 100 / (Fuel consumption X Fuel GCV)**

**18-Co gen-plant efficiency calculation**

**Efficiency = 860 X Power generation X 100 / (Fuel consumption X GCV + Make up water X Make up water enthalpy + Return condensate water X Enthalpy-Process steam flow X Enthalpy)**

**19-HP heater steam consumption calculation**

**Steam flow in TPH = FW flow in TPH X (HP heater outlet FW temperature-HP heater inlet FW temperature) /(Steam enthalpy in kcal/kg-HP heater outlet condensate water enthalpy in kcal/kg)**

**Where, FW = Feed water **

**20-Deaerator steam consumption**

**Mass of steam in TPH = (Deaeraor outlet Feed water flow in TPH X Enthalpy –CEP flow X Enthalpy-Makeup water X Enthalpy) / (Enthalpy of steam-Enthalpy of deaerator outlet water)**

**Note: Enthalpy in kcal/kg**

**Feed water, CEP water & Make up water flow in TPH**

**C-Pumps fans and air compressors**

**1-Centrifugal pumps hydraulic power consumption**

**Hydraulic power in Kwh = Flow (M3/sec) X Total head (m) X Fluid density (kg/m3) X g (m/s2) / 1000**

**2-Pump shaft power calculation**

**Pumps shaft power Ps = Hydraulic power / Pump efficiency**

3-**Pump electrical power calculation**

**Electrical power = Pump shaft power / Motor efficiency**

4-**Pump affinity laws**

**a-Q1/Q2 = N1/N**^{2}

**Q1 & Q2 are pump flow at different RPM**

**N1 & N2 are pump speed**

**b-H1 / H2 = (N1)**^{2}** / (N2)**^{2}

**Where H1 & H2 are pump head at different RPM**

**N1 & N2 are pump speed**

**c-P1 / P2 = (N1)**^{3}** / (N2)**^{3}

**P1 & P2 are pump flow at different RPM**

**N1 & N2 are pump speed**

5-**Relation between head,flow ,power and impeller diameter**

**Q = D (Flow is directly proportional to impeller diameter)**

**H = D2 (Head is directly proportional to square root of impeller diameter)**

**P =D3 (Power is directly proportional to impeller diameter)**

6-**Relation between NPSHR, flow and speed**

**NPSHR = N2 (NPSHR is directly proportional to square root of speed)**

**That is as the flow and speed increase, pump need more NPSH**

7-**Fans volumetric flow calculation**

**Flow (m3/sec) = Velocity of fluid (m/sec) X Area of duct (m2)**

8-**Fans Mechanical efficiency calculation**

**Mechanical efficiency % = Flow (m3/sec) X Total pressure (mmwc) X 100 / (102 X power input to fan shift in KW)**

9-**Fans Technical efficiency calculation**

**Static efficiency % = Flow (m3/sec) X Static pressure (mmwc) X 100 / (102 X power input to fan shift in KW)**

**11-Fans affinity laws**

**a-Q1/Q2 = N1/N2**

**Q1 & Q2 are fans flow in m3/sec at different RPM**

**N1 & N2 are fans speed**

**b-SP1 / SP2 = (N1)**^{2}** / (N2)**^{2}

**Where SP1 & SP2 are static pressure in mmwc of fan at different RPM**

**N1 & N2 are pump speed**

**c-P1 / P2 = (N1)**^{3}** / (N2)**^{3}

**P1 & P2 are flow flow at different RPM**

**N1 & N2 are pump speed**

**11-Isothermal power of reciprocating compressors**

**P = P1 X Q X log**_{e}** r/36.7**

**Where, P = Isothermal power**

**Q = Free air delivered by compressor in m3/hr**

**R = P2/P1**

**P1 & P2 are absolute inlet & deliver pressure respectively**

10-**Isothermal efficiency of reciprocating compressors**

**Isothermal efficiency = Isothermal power X 100 / Actual measured input power**

11-**Isothermal efficiency of reciprocating compressors**

**Isothermal efficiency = Free air delivered (m3/min) X 1007 / Compressor displacement (m3/min)**

12-**Compressor displacement = 3.142 X D2 X L X S X n X N**

**Where, D = Cylinder bore in meter**

**L = Cylinder stroke in meter**

**S = Compressor speed in rpm**

**n= 1 for single acting & 2 for double acting cylinders**

**N=No.of cylinders**

13-**Compressed air leakage calculation**

**% of leakage = T X 100 / (T+t) **

**Or air leakage in m3/min = T X Compressor capacity (m3/min) / (T+t)**

**T = Loading time in minutes, t = Unloading time in minutes**

14-**Calculation of intermediate pressure of reciprocating air compressors**

**P2 =SQRT ( P1 X P3)**

**Where P1,P2 & P3 are suction pressure, intermediate pressure and discharge absolute pressure respectively**

**D-Fuel handling**

**1-Minimum length of belt conveyor take up**

**Total belt length X 1.5%**

**2-Conveyor belt speed calculation**

**Belt speed (m/sec) = 3.142 X D X N / 60**

**Where, D= Head pulley diameter in meter**

**N = Head pulley speed in RPM**

**Head pulley speed = Moto RPM / Gear box reduction ratio**

**3-Conveyor start up tension calculation**

**T (N/mm)= P X 3.2 / (V X W)**

**Where,P = Power consumption of conveyor**

**V = Belt speed in m/sec**

**W = Belt width in mm**

**4-Tensile strength of belt**

**Initial tension of the belt X 5.4 / Belt splicing efficiency**

E-**Mechanical Maintenance**

**1-V pulley speed calculation**

**N1/N2 = D2/D1**

**N1 & N2 are speed in RPM of drive and non drive end pulleys**

**D1 & D2 are diameter (inch or mm) of drive and non drive end pulleys**

**2-Gear box output speed calculation**

**Gear box out put shaft speed = Motor RPM / Reduction ratio**

3-**Speed of pulley calculation**

**Pulley speed (m/sec) = 3.142 X D X N / 60**

**Where, D = Diameter of pulley in meter**

**N = Pulley rotary speed in RPM**

4-**V belt length calculation**

** L =∏ (R1+R2) + 2C + (R2+R1)2/C**

**Where, R1 & R2 are radius of DE & NDE pulleys**

5-**C is centre distance between two pulleys**

6-**Torque developed on a shaft**

**T = P X 60 / (2 X ∏ X N)**

**Where, P = Power consumption, N is speed of the shaft**

7-**Calculation of hub diameter of a shaft**

**Hub diameter = 2 X Shaft diameter**

**8-Bearing lubrication quantity calculation**

**Bearing lubrication quantity in grams = Bearing OD (D) X Width (B) X 0.05**

**9-Safe working load of steel wire rope of size D (inches)**

**SWL = 8D**^{2}^{}

**10-Safe working load of Chain block having Load link diameter ****D in**** mm**

**Safe working load of chain block = 80 X 0.4 X D**^{2}

**Where 80 is the grade of chain block steel material**

**D is the link diameter in mm**

12-**Safe working load of ****Nylon lifting rope of **** diameter ****D in**** mm**

**Safe working load of chain block = D**^{2}

13-**Calculation of weight of steel plate**

**Weight in kg = Plate length (m) X width (M) X Thickness (m) X density of steel (kg/m3)**

14-**Calculation of weight of round steel plate**

**Weight in kg = (∏D**^{2}**/4) X plate thickness in meter**

**D is diameter of plate in meter**

15-**Calculation of weight of hollow cylinder**

**Weight in kg = (∏R**^{2}_{2}**X h-**** ∏R**^{2}_{1}**X h) X steel density in kg/m3**

**Where, R1 & R2 are outer radius & inner radius of tank in meter**

**H is height of tank in meter**

**F-Electrical and Instrumentation**

**1-Single phase power consumption calculation**

**P = VI Cos θ**

**Where,Cos θ P is power consumption in Watts, V&I are Voltage in volts and current in Amps receptively**

**Cos θ is power factor**

2-**Three phase power consumption calculation**

**P = ****√****3****VI Cos θ**

3-**Apparent power = V X I (Voltage X Current)**

4-**Real power = ****√****3****VI Cos θ**

5-**Reactive power of 3-phase power =****√****3****VI Sin θ**

**Reactive power of single-phase power =VI Sin θ**

** **

** **

6-**Resistance of a conductor**

**R = ****ƍ**** X L/A**

**R = Resistance in Ohm-meter or Ohm-cm**

**L & A are Length and area of conductor measured in meter & m2**

7-**Voltage, current and resistance relation**

**Voltage = Current X Resistance, i.e. V = IR**

**8-****Resistance of a conductor at temperature t °C is given by**

**Rt = R0 (1 + α t) Where α is temperature coefficient at t °C.**

8-**Electrical ****Power**** calculation**

** **** ****Power=**** Work done watt-sec./Time in second**

** P = VI X t/t i.e. VI Watts**

** P = I**^{2}**R… Watts**

9-**Power factor calculation**

**Power factor (cosՓ) = Active power (KW) / Apparent power (KVA)**

**10-Synchronous speed calculation**

**Synchronous speed/RPM = (120 X frequency)/No. of poles.**

**11-****Absolute Pressure ****=**** Gauge Pressure ****+**** Atmospheric Pressur****e**

**12-R****elation between flow and differential pressure (DP). Flow (Q) ****=**** √(DP**

**Q1/Q2 ****=**** (√∆P1/∆P2****)**

13-**Compensated flow calculation**

**Compensated flow****=**** Raw value from flow meter ****X**** Sqrt ((Absolute Design temperature/Absolute Operating temperature) ****X**** (Absolute operating pressure/Absolute design pressure))**

**For more read>>> ****Power plant and calculations**