Isentropic Flow
The second law of thermodynamics requires that the adiabatic and frictionless flow of any fluid results in no change in entropy. Constant entropy flow is called isentropic flow .
Based on the equation of entropy in a compressible flow :
ds = cv ln(T2/ T1 ) + R ln(ρ1 / ρ2)
= cp ln(T2/ T1 ) - R ln(p2/ p1 )
= 0 (1)
where
ds = change in specific entropy ( kJ/kgK )
cv = specific heat at constant volume process (kJ/kg K)
cp = specific heat at constant pressure process (kJ/kg K)
T = absolute temperature (K)
R = individual gas constant (kJ/kg K)
ρ = density of gas (kg/m3 )
p = absolute pressure (Pa, N/m2)
Using
κ = cp / cv (2)
where
(1) can be transformed to:
(T2/ T1 ) (κ/(κ-1)) = (ρ2/ ρ1 ) κ = (p2/ p1 ) (3)
(3) express the useful relationship between temperature, density and pressure for an isentropic flow of an ideal gas.
From (3) the relationship between pressure and temperature can be concluded:
p / ρ κ = constant (4)
Density can be expressed:
ρ = 1 / v (5)
where
v = specific volume (m3 /kg)
Using (5) in combination with (4) transforms to a common expression:
p v κ = constant (6)
Related Topics
• Fluid Mechanics
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
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