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### Ideal Energy Conversion Engineering Equations

This section provides free Ideal Energy Conversion Engineering 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 = ρvA

Momentum Equation
F = (vm + pA)
out - in

Energy Equation
Q - W = ((h + v^2/2 + gh)m)
out - in

Ideal Gas State Equation
pv = RT/MW

Perfect Gas
c
p = constant
ϰ = c
p/cv

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

Combustion -- Flame Temperature
h
reactants = hproducts

Isentropic Expansion
T
1/T2 = (p1/p2)^(ϰ-1)/ϰ
T
1/T2 = (V2/V1)^(ϰ-1)
p
1/p2 = (V2/V1)^ϰ

Sonic Velocity
v
s = (ϰRT/MW)^1/2

Mach Number
M = v/v
s

Isentropic Flow
T
t/T = (1 + M^2(ϰ-1)/2)
p
t/p = (1 + M^2(ϰ-1)/2)ϰ/(ϰ-1)
h
t = (h + v^2/2)
T
t = (T + v^2/(2cp))

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

Cycle Efficiency
Cycle Efficiency = Net Work/Heat

Carnot Cycle Efficiency
Carnot Cycle Efficiency = 1 - T

Brayton Cycle Efficiency

Compression Ratio = p2/p1
Brayton Cycle Efficiency = 1 - 1/Compression Ratio^(ϰ-1)/ϰ

Otto Cycle Efficiency
Compression Ratio = V
1/V2
Otto Cycle Efficiency = 1 - 1/Compression Ratio^(ϰ-1)

Diesel Cycle Efficiency
Compression Ratio (CR) = V
1/V2
Cut-Off Ratio (COR) = V
3/V2
Diesel Cycle Efficiency = 1 - (COR^ϰ - 1)/(ϰ*CR^(ϰ-1) *(COR - 1))

Fuel Cell
Fuel Cell Efficiency = - (G
out - Gin)/HHV

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

Heat Exchanger (Heat Transfer)
m
hot(Thot inlet - Thot outlet)cp-hot = mcold(Tcold outlet - Tcold inlet)cp-cold

Air Conditioner (AC) Operation
AC Coefficient of Performance (COP) = 1/(T
high temperature/Tlow temperature -1)

Heat Pump Operation
HP Coefficient of Performance (COP) = 1/(1 - T
low temperature/Thigh temperature)
or

HP Coefficient of Performance (COP) = 1 + AC Coefficient of Performance (COP)

Physical Properties
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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