Real Energy Conversion Engineering Equations

This section provides free Real 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 + v2/2 + gh)m)
out - in 

 

Ideal Gas State Equation  
pv = RT/MW 

 

Perfect Gas 
c
p = constant 
ϰ = c
p / cv 

 

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

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)

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

 

Sonic Velocity 
v
s = (ϰRT/MW)^1/2 
Mach Number 
M = v/v
s 

 

Isentropic Flow 
T
t/Ts = (1 + M^2(ϰ-1)/2) 
p
t/p = (1 + M^2(ϰ-1)/2)^ϰ/(ϰ-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]. 

Engineering Software

P.O. Box 2134

Kensington, MD 20891

Phone:  (301) 919-9670

E-Mail:  info@engineering-4e.com

http://www.engineering-4e.com

Copyright © 1996

Last Update: November, 2019