Free Engineering Formulas/Equations



Here are some of the basic engineering formulas/equations related to energy conversion systems which are built into the Engineering Software product line:

Continuity Equation

m = vA

Momentum Equation

F = (vm + pA)out - in

Energy Equation

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

Ideal Gas State Equation 

pv = RT/MW

Perfect Gas

cp = constant

k = cp / cv

Isentropic Compression

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

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

p2 / p1 = (V1 / V2)k

Combustion -- Flame Temperature

hreactants = hproducts

Combustion -- HHV

HHV = hreactants - hproducts

Isentropic Expansion

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

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

p1 / p2 = (V2 / V1)k

Sonic Velocity

vs = (kRT/MW)1/2

Mach Number

M = v/vs

Isentropic Flow

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

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

ht = (h + v2/2)

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

Thrust

Thrust = vm + (p - pa)A

Cycle Efficiency

Cycle Efficiency = Net Work/Heat

Carnot Cycle Efficiency

Carnot Cycle Efficiency = 1 - Theat rejection / Theat addition

Brayton Cycle Efficiency

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

Otto Cycle Efficiency

Compression Ratio = V1 / V2

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

Diesel Cycle Efficiency

Compression Ratio (CR) = V1 / V2

Cut-Off Ratio (COR) = V3 / V2

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

Fuel Cell

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

Heat Rate

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

Physical Properties

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

Cp/R = A1 + A2T + A3T2 + A4T3 + A5T4

H/(R*T) = A1 + A2T/2 + A3T2/3 + A4T3/4 + A5T4/5 + A6/T

S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + A7

or

S/R = A1lnT + A2T + A3T2/2 + A4T3/3 + A5T4/4 + 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].

 

Species

C

H2

S

O2

N2

CO2

H2O

SO2

CH4

Molecular Weight [kg/kmol]

12

2

32

32

28

44

18

64

16


Gas

Gas

Kappa
[/]

Gas Constant
[J/kg*K]

Specific Heat
[J/kg*K]

Air

1.4

286.7

1,004

Ammonia

NH3

1.3

488.2

2,092

Argon

Ar

1.67

208.1

519

Carbon Dioxide

CO2

1.28

188.9

845

Carbon Monoxide

CO

1.4

296.8

1,042

Helium

He

1.66

2,078.5

5,200

Hydrogen

H2

1.4

4,124

14,350

Methane

CH4

1.32

518.2

2,223

Nitrogen

N2

1.4

296.9

1,038

Oxygen

O2

1.4

259.8

916

Water Vapor

H2O

1.33

188.5

1,690

 

Fuel

HHV [Btu/lbm]

Hydrogen

60,000

Natural Gas

20,000 through 24,000

Oil

18,000 through 21,000

Carbon

14,000

Coal

8,000 through 12,000

Wood

6,000

 
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 [m2]

F -- Force [N]

p -- Pressure [N/m2]

Q -- Heat [kW]

W -- Work [kW]]

g -- Gravitational Acceleration [m/s2]

h -- Height [m]

k -- Kappa [/]

hreactants
-- Reactants Enthalpy [kJ/kg]

h
products
-- 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 -- Volume [m3]

v -- Specific Volume [m3/kg]

G -- Gibbs Free Energy [kJ/kmol]

g -- Gibbs Free Energy [kJ/kg]


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