inzinerski formuli equations

8/12/2019 Inzinerski Formuli Equations

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Engineering F ormulas

Here are some of the basic engineering formulas/equations related to energy conversion systems:

Continui ty Equation

m = vA

Momentum Equation

F = (vm + pA)out - in

Energy Equation

Q - W = ((h + v2/2 + gh)m)out - in

State Equation for I deal Gas

pv= RT/MW

Perfect Gas

cp= constant

= cp/cv


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I sentropic Compression

T2/T1= (p2/p1)(-1)/

T2/T1= (V1/V2)(-1)

p2/p1= (V1/V2)

Combustion -- F lame Temperature

hreactants= hproducts

CombustionHHV

HHV= hreactants-hproducts

I sentr opic Expansion

T1/T2= (p1/p2)(-1)/

T1/T2= (V2/V1)(-1)

p1/p2= (V2/V1)

Sonic Velocity

vs= (RT/MW)1/2

Mach Number

M= v/vs

I sentropic F low

Tt /T= (1 + M2( - 1)/2)

pt/p= (1 + M2( - 1)/2)/(-1)

ht= (h + v2/2)


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Tt= (T + v2/(2cp))

Thrust

Thrust= vm + (p - pa)A

Cycle Ef fi ciency

Cycle Efficiency= Net Work/Heat

Carnot Cycle Ef fi ciency

Carnot Cycle Efficiency = 1 - Theat rejection/Theat addition

Brayton Cycle Ef fi ciency

Brayton Cycle Efficiency = 1 - 1/(p2/p1)(-1)/

Otto Cycle Ef fi ciency

Compression Ratio = V1/V2

Otto Cycle Efficiency= 1 - 1/Compression Ratio(-1)

Diesel Cycle Ef fi ciency

Compression Ratio (CR) = V1/V2

Cut-Off Ratio (COR) = V3/V2

Diesel Cycle Efficiency =1 - (COR- 1)/(*CR(-1)*(COR - 1))

Fuel Cell

Fuel Cell Efficiency= - (Gout- Gin)/HHV

Heat Rate

Heat Rate = (1/Cycle Efficiency)*3,412


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Physical Properties

For each reaction species, the thermodynamic functions specific heat, enthalpy and entropy asfunctions of temperature are given in the form of least squares coefficients as follows:

Cp/R = A1 + A2T + A3T

2

+ A4T

3

+ A5T

4

H/(R*T) = A1 + A2T/2 + A3T2/3 + A4T

3/4 + A5T

4/5 + A6/T

S/R = A1lnT + A2T + A3T2/2 + A4T

3/3 + A5T

4/4 + A7

or

S/R = A1lnT + A2T + A3T2/2 + A4T

3/3 + A5T

4/4 + A7- lnp

For each species, two sets of coefficients are included for two adjacent temperature intervals, 273

to 1,000 [K] and 1,000 to 5,000 [K]. The data have been constrained to be equal at 1,000 [K].

Also,

U = H - p*v*MW or U = H - R*T

G = H - S*T

and

u = h - p*v or u = h - R*T/MW

g = h - s*T

Legend:

m -- Mass Flow Rate [kg/s]

-- Density [kg/m3]

v -- Velocity [m/s]

A -- Cross Sectional Area [m

2

]

F -- Force [N]

p -- Pressure [N/m2]

q -- Heat [kJ/kg]


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w -- Work [kJ/kg]

g -- Gravitational Acceleration [m/s2]

h -- Height [m]

k -- Kappa [/]

hreactants-- Reactants Enthalpy [kJ/kg]

hproducts-- Products Enthalpy [kJ/kg]

HHV -- Higher Heating Value [Btu/lbm]

vs-- Sonic Velocity [m/s]

M -- Mach Number [/]

Cp-- Specific Heat [kJ/kmol*K]

cp-- Specific Heat [kJ/kg*K]

MW -- Molecular Weight [kg/kmol]

R -- Universal Gas Constant [kJ/kmol*K]

Gas Constant = R/MW [kJ/kg*K]

H -- Enthalpy [kJ/kmol]

h -- Enthalpy [kJ/kg]

T -- Temperature [K]

S -- Entropy [kJ/kmol*K]

s -- Entropy [kJ/kg*K]

p -- Pressure [atm]

U -- Internal Energy [kJ/kmol]

u -- Internal Energy [kJ/kg]

v -- Specific Volume [m3/kg]


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G -- Gibbs Free Energy [kJ/kmol]

g -- Gibbs Free Energy [kJ/kg]

inzinerski formuli equations

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