Formula Sheet

)()( 12,1212,12 TTchhTTcuu

T

hc

T

uc

avgPavgv

P

P

v

v

−=−−=−

=

=

∂∂

∂∂

Pv = RT

dS =dQ

T

int rev

dS ≥dQ

T

Incompressible substances:

Ideal gas:

Tds Relations

vdPTdsdh

PdvTdsdu

+=−=

Maxwell Relations:

∂T

∂v

S

= −∂P

∂s

v

∂T

∂P

S

=∂v

∂s

P

∂S

∂v

T

=∂P

∂T

v

∂S

∂P

T

= −∂V

∂T

P

Other useful relations:

P

P

v

v

T

s

T

c

T

s

T

c

=

=

∂∂

∂∂

;

s2 − s1 = c avg lnT2

T1

s2 − s1 = c v ,avg lnT2

T1

+ R lnv 2

v1

= cP ,avg lnT2

T1

− R lnP2

P1

ratio fuel to air tricstoichiome

ratio fuel to air actual=λ

∑∑ −==R

RfRP

PfP0 ,Hn,HnHQ ∆∆∆

constpV n =

−−

=−

−

1n

5

4

2

4454

2

V

V1

1n

VpW

−

−=

−

−

1n2

1

2221

1

1V

V1

1n

VpW

V

Wp,essurePr Effective Mean Indicated

d

ii =

bdb piVj

N2W =&

i

b

i

b

i

bm W

W

p

p

W

W&

&

===η

( )LHVm

W

f

bb

&

&

=η

334443 VpVpW −=−

1

a

s1

a

t1

T

T

P

P −

=γ

γ

, s21

a21t TT

TT

−−

=η , 1a2

1s2c TT

TT

−−=η ,

TcmQ p∆&& =

−

=−=−

1P

PTTTT

1

t1

t2

c

t1t1t212

γγ

η∆

−=−=−γ

γ

η∆1

t4t3t3tt4t334 PP

11TTTT

R1

1cc

cRcc p

v

pvp =

−==−γ

γ

Free-Convection correlation for a vertical plate: