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### Real Energy Conversion Engineering Equations

This section provides free Real Energy Conversion Engineering Equations.

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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 = ρvA

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
c
p = constant
Ï° = c
p / cv

Isentropic Compression
T
2s/T1 = (p2/p1)^(Ï°-1)/Ï°
T
2s/T1 = (V1/V2)^(Ï°-1)
p
2/p1 = (V1/V2)^Ï°

Compression Efficiency = (T2s - T1) / (T2 - T1

Combustion -- Flame Temperature
h
products = hreactants - heat loss
heat loss = ((1 - combustion efficiency)HHV)/(1 + oxidant to fuel ratio)

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Isentropic Expansion
T
1/T2s = (p1/p2)^(Ï°-1)/Ï°
T
1/T2s = (V2/V1)^(Ï°-1)
p
1/p2 = (V2/V1)^Ï°
Expansion Efficiency = (T
1 - T2)/(T1 - T2s)

Sonic Velocity
v
s = (Ï°RT/MW)^1/2
Mach Number
M = v/v
s

Isentropic Flow
T
t/Ts = (1 + M^2(Ï°-1)/2)
p
t/p = (1 + M^2(Ï°-1)/2)^Ï°/(Ï°-1)
ht = (h
s + v^2/2)
T
t = (Ts + v^2/(2cp))
Nozzle Efficiency = (T
1 - T2)/(T1 - T2s
Diffuser Efficiency = (T
2s - T1)/(T2 - T1

Thrust
Thrust = vm + (p - p
a)A

Cycle Efficiency
Cycle Efficiency = Net Work/Heat

Brayton Cycle Efficiency
Brayton Cycle Efficiency = (c
p(T3 - T2) - cp(T4 - T1))/(cp(T3 - T2))

Otto Cycle Efficiency
Otto Cycle Efficiency = (c
v(T3 - T2) - cv(T4 - T1))/(cv(T3 - T2))

Diesel Cycle Efficiency
Compression Ratio (CR) = V
1/V2
Cut-Off Ratio (COR) = V
3/V2
Diesel Cycle Efficiency = (c
p(T3 - T2) - cv(T4 - T1))/(cp(T3 - T2))

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

For each reaction species, the thermodynamic functions specific heat, specific enthalpy and specific entropy as
functions 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 + A3T^2/3 + A4T^3/4 + A5T^4/5 + A6/T

S/R = A1lnT + A2T + A3T^2/2 + A4T^3/3 + A5T^4/4 + A7

or

S/R = A1lnT + A2T + A3T^2/2 + 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].

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