Formula Sheet: Applied Thermodynamics Notes | Study Formula Sheets of Mechanical Engineering - Mechanical Engineering

Mechanical Engineering: Formula Sheet: Applied Thermodynamics Notes | Study Formula Sheets of Mechanical Engineering - Mechanical Engineering

The document Formula Sheet: Applied Thermodynamics Notes | Study Formula Sheets of Mechanical Engineering - Mechanical Engineering is a part of the Mechanical Engineering Course Formula Sheets of Mechanical Engineering.
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 Page 1


Mechanical Engineering - GATE Exam 
 
I.C Engine 
• Mean Effective Pressure MEP:- Wnet=PMEP?V 
                                                              =MEP?? Piston area?? Stroke 
                                                            = MEP?? Displacement 
                                                            MEP= Wnet/Displacement= Wnet/Vmax-Vmin 
• Otto Cycle Efficiency:-   ?th,Otto = 1 - (1/r
k-1
) 
where r = compression ratio k = cp/cv for air at room T 
• Diesel Efficiency:-  ?th,Diesel = 1 -(1/r
k
-1)[(rc)
k
 - 1/k(rc-1)] 
r = compression ratio, rc = cutoff ratio (rc = V3/V2 = v3/v2) k = cp/cv for air at 
room T. 
• Indicated Thermal Efficiency:- 
?
???????? =
?????????????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Here, Ip = Indicated power, Cv = Calorific value of fuel, and Mf = Mass of 
fuel/second 
• Brake Thermal Efficiency:- ?
?????????? =
?????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Psychrometry 
•  Partial Pressure of Water Vapour:-  
 
 pv = partial pressure of water vapour 
ps = partial pressure of dry air 
where, (pvs)wb = saturation pressure of water vapour corresponding to wet bulb 
temperature 
p = atmospheric pressure of moist air 
Twb = wet bulb temperature 
Tdb = dry bulb temperature 
• Absolute Humidity:- 
                                =
???????????? ???? ?????????? ???????????? ???????????? ???? ?????? ( ?????????????? )
 
 
• Specific Humidity(w):- 
                                 = 
???????? ???? ?????????? ???????????? ???? ?????? ???????? ???? ?????? ?????? 
Page 2


Mechanical Engineering - GATE Exam 
 
I.C Engine 
• Mean Effective Pressure MEP:- Wnet=PMEP?V 
                                                              =MEP?? Piston area?? Stroke 
                                                            = MEP?? Displacement 
                                                            MEP= Wnet/Displacement= Wnet/Vmax-Vmin 
• Otto Cycle Efficiency:-   ?th,Otto = 1 - (1/r
k-1
) 
where r = compression ratio k = cp/cv for air at room T 
• Diesel Efficiency:-  ?th,Diesel = 1 -(1/r
k
-1)[(rc)
k
 - 1/k(rc-1)] 
r = compression ratio, rc = cutoff ratio (rc = V3/V2 = v3/v2) k = cp/cv for air at 
room T. 
• Indicated Thermal Efficiency:- 
?
???????? =
?????????????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Here, Ip = Indicated power, Cv = Calorific value of fuel, and Mf = Mass of 
fuel/second 
• Brake Thermal Efficiency:- ?
?????????? =
?????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Psychrometry 
•  Partial Pressure of Water Vapour:-  
 
 pv = partial pressure of water vapour 
ps = partial pressure of dry air 
where, (pvs)wb = saturation pressure of water vapour corresponding to wet bulb 
temperature 
p = atmospheric pressure of moist air 
Twb = wet bulb temperature 
Tdb = dry bulb temperature 
• Absolute Humidity:- 
                                =
???????????? ???? ?????????? ???????????? ???????????? ???? ?????? ( ?????????????? )
 
 
• Specific Humidity(w):- 
                                 = 
???????? ???? ?????????? ???????????? ???? ?????? ???????? ???? ?????? ?????? 
Mechanical Engineering - GATE Exam 
 
                                              ?? = ?? . ??????
?? ?? ?? -?? ?? Kg water vapour/kg of dry air 
• Relative Humidity :-   
Ø =
?? ?? ?? ?? =
?? ?? ?? ????
 
• Degree of Saturation (µ):-  
µ =
Specific humidity of air
Specific humidity of Saturated air
=
?
?
s
 
• Dew Point Depression:- 
                                           DPD = DBT – DPT 
• Enthalpy of Air (h):-  
                                          h = Cpm tab + w(hg – Cpv tdb) 
• Sensible Heat Factor- 
=
?? ?? ?? ?? + ?? ?? 
• By Pass Factor:-  
?? =
?? ?? - ?? ???????? ?? ?? - ?? ???????? 
Air temperature at entry and exit is t1 and t2 respectively 
 
• Volumetric Efficiency :-  
?
?? = ?? + ?? - ?? ( ?? ?? )
?? ?? /
 
C = Compression ratio, r
p
=
p
2
p
1
/ 
• Vapour Absorption System C.O.P 
?? . ?? . ?? = (
?? ?? ?? ?? - ?? ?? ) × (
?? ?? - ?? ?? ?? ?? ) 
Te=Evaporator Temperature 
Tg=Generator Temperature 
TC= Condenser Temperature 
• Designation of Refrigerant:- 
For a hydrocarbon Chemical formula is Cr Hs F1 CIy 
If S+t+y=2r+2, designation of refrigerant is R(r-1)(S+1)t 
It S+t+y=2r, designation of refrigerant is R1(r-1)(S+1)t 
For an Inorganic Refrigerant 
Designation is R(700 + molecular weight) 
Power Plant Engineering 
• Ranking Cycle efficiency- 
Page 3


Mechanical Engineering - GATE Exam 
 
I.C Engine 
• Mean Effective Pressure MEP:- Wnet=PMEP?V 
                                                              =MEP?? Piston area?? Stroke 
                                                            = MEP?? Displacement 
                                                            MEP= Wnet/Displacement= Wnet/Vmax-Vmin 
• Otto Cycle Efficiency:-   ?th,Otto = 1 - (1/r
k-1
) 
where r = compression ratio k = cp/cv for air at room T 
• Diesel Efficiency:-  ?th,Diesel = 1 -(1/r
k
-1)[(rc)
k
 - 1/k(rc-1)] 
r = compression ratio, rc = cutoff ratio (rc = V3/V2 = v3/v2) k = cp/cv for air at 
room T. 
• Indicated Thermal Efficiency:- 
?
???????? =
?????????????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Here, Ip = Indicated power, Cv = Calorific value of fuel, and Mf = Mass of 
fuel/second 
• Brake Thermal Efficiency:- ?
?????????? =
?????????? ?????????? ???????????? ???? ???????? ?????? ???????????? =
?? ?? ?? ?? ×?? ?? 
Psychrometry 
•  Partial Pressure of Water Vapour:-  
 
 pv = partial pressure of water vapour 
ps = partial pressure of dry air 
where, (pvs)wb = saturation pressure of water vapour corresponding to wet bulb 
temperature 
p = atmospheric pressure of moist air 
Twb = wet bulb temperature 
Tdb = dry bulb temperature 
• Absolute Humidity:- 
                                =
???????????? ???? ?????????? ???????????? ???????????? ???? ?????? ( ?????????????? )
 
 
• Specific Humidity(w):- 
                                 = 
???????? ???? ?????????? ???????????? ???? ?????? ???????? ???? ?????? ?????? 
Mechanical Engineering - GATE Exam 
 
                                              ?? = ?? . ??????
?? ?? ?? -?? ?? Kg water vapour/kg of dry air 
• Relative Humidity :-   
Ø =
?? ?? ?? ?? =
?? ?? ?? ????
 
• Degree of Saturation (µ):-  
µ =
Specific humidity of air
Specific humidity of Saturated air
=
?
?
s
 
• Dew Point Depression:- 
                                           DPD = DBT – DPT 
• Enthalpy of Air (h):-  
                                          h = Cpm tab + w(hg – Cpv tdb) 
• Sensible Heat Factor- 
=
?? ?? ?? ?? + ?? ?? 
• By Pass Factor:-  
?? =
?? ?? - ?? ???????? ?? ?? - ?? ???????? 
Air temperature at entry and exit is t1 and t2 respectively 
 
• Volumetric Efficiency :-  
?
?? = ?? + ?? - ?? ( ?? ?? )
?? ?? /
 
C = Compression ratio, r
p
=
p
2
p
1
/ 
• Vapour Absorption System C.O.P 
?? . ?? . ?? = (
?? ?? ?? ?? - ?? ?? ) × (
?? ?? - ?? ?? ?? ?? ) 
Te=Evaporator Temperature 
Tg=Generator Temperature 
TC= Condenser Temperature 
• Designation of Refrigerant:- 
For a hydrocarbon Chemical formula is Cr Hs F1 CIy 
If S+t+y=2r+2, designation of refrigerant is R(r-1)(S+1)t 
It S+t+y=2r, designation of refrigerant is R1(r-1)(S+1)t 
For an Inorganic Refrigerant 
Designation is R(700 + molecular weight) 
Power Plant Engineering 
• Ranking Cycle efficiency- 
Mechanical Engineering - GATE Exam 
 
 
 
• Overall efficiency:-  
  =Eff. Boiler ?? Eff. of Cycle ?? Eff. of turbine ?? Eff. of generator ?? Eff. of auxiliary 
• Efficiency of Brayton Cycle:-  
 
 
 
 
 
Where rp is pressure ratio 
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