thermodynamics (eggn 371) equation sheet · thermo equation sheet (cycles) author: steven c....

Thermodynamics (EGGN 371) Equation Sheet Air Standard

(variable specific heats)

Cold Air Standard (const. specific heats)

Process

DIESEL 1-2 ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

1

212 vvvv rr

)1(

2

112

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

k

vvTT

isentropic compression

2-3 23 hhqin −= )( 23 TTCq pin −= const. P heat addition

3-4

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

434 vvvv rr

)1(

4

334

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

k

vvTT

isentropic expansion

4-1 14 uuqout −= )( 14 TTCq vout −= const. V heat rejection

in

outdiesel q

q−=1η ⎥

⎦

⎤⎢⎣

⎡

−

−−= −

)1(11 )1(

c

kck

diesel rkrrη

2

1

vvr =

BRAYTON 1-2

⎟⎟⎠

⎞⎜⎜⎝

⎛=

1

212 PPPP rr k

k

PPTT

)1(

1

212

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

isentropic compression

2-3 23 hhqin −= )( 23 TTCq pin −= const. P heat addition

3-4

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

434 PPPP rr k

k

PPTT

)1(

3

434

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

isentropic expansion

4-1 14 hhqout −= )( 14 TTCpqout −= const. P heat rejection

in

outbrayton q

q−=1η k

k

pbrayton r)1(

1−

−=η 1

2

PPrP =

4

3

PP

rp =

12

1221 hh

hh

a

s

−

−=−η

s

a

hhhh

43

4343 −

−=−η

12

1221 TT

TT

a

s

−

−=−η

s

a

TTTT

43

4343 −

−=−η

OTTO 1-2

⎟⎟⎠

⎞⎜⎜⎝

⎛=

1

212 vvvv rr

)1(

2

112

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

k

vvTT

isentropic compression

2-3 23 uuqin −= )( 23 TTCq vin −= const. v heat addition

3-4

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

434 vvvv rr

)1(

4

334

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

k

vvTT

isentropic expansion

4-1 14 uuqout −= )( 14 TTCq vout −= const. v heat rejection

in

outotto q

q−=1η

)1(1 kotto r −−=η

2

1

vvr =

3

4

vvr =

JET PROPULSION

1-2 DIFUSER: ;

2

21

22

121212 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+−=−

VVhhwq ;2

)(021

12 ⎟⎟⎠

⎞⎜⎜⎝

⎛−−=VTTCp

;1

2

1

2

PP

PP

r

r = kk

PP

TT

)1(

1

2

1

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2-3 COMPRESSOR:

;23 PrP p= ;2

3

2

3

PP

PP

r

r = kk

PP

TT

)1(

4

3

2

3

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3-4 COMBUSTION: )( 3434 TTChhq pin −=−= 4-5 TURBINE: ;,, outturbincomp ww = ;5423 hhhh −=− );()( 5423 TTTT −=−

;4

5

4

5

PP

PP

r

r = kk

PP

TT

)1(

4

5

4

5

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

5-6 NOZZLE: ;

2

25

26

565656 ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+−=−

VVhhWq ;2

)(026

56 ⎟⎟⎠

⎞⎜⎜⎝

⎛+−=VTTCp

kk

PP

TT

)1(

5

6

5

6

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Propulsion Efficiency in

aircraftinletexit

in

p

qVVV

qw )( −

==

RANKINE

1-2 PUMP: ;1 fhh = ;12 inwhh += 12121 )( hhPPvwin −=−= isentropic compression

2-3 BOILER: ;23 hhqin −= svhh =3 at T & P for S.V. const. P heat addition

3-4 TURBINE: ;43 hhwout −= ;4

4fg

f

sss

x−

= fgf hxhh 44 += isentropic expansion

4-1 CONDENSER: 14 hhqout −= const. P heat rejection

in

outin

in

netrankine q

qqqw −

==η

REFRIGERATION

1-2 COMPRESSOR: );( 12 hhmwin −= ;1ssg = 1hhg = isentropic compression

2-3 CONDENSOR: ;12 ss = ;3 fhh = )( 32 hhmQH −= const. P heat rejection

3-4 THROTTLING: 34 hh ≅ throttling in an expansion device

4-1 EVAPORATOR: )( 41 hhmQL −= const. P heat absorption

12

12

hhhh s

comp −

−=η

in

LR wQPOC

=...