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
heat rejection/Theat addition
 

Brayton Cycle Efficiency
Brayton Cycle Efficiency = 1 - 1/(p
2/p1)^(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)
 

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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Last Update: November, 2019