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Isentropic Flow

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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 = c v ln(T 2 / T 1 ) + R ln(ρ 1 / ρ 2 )

= c p ln(T 2 / T 1 ) - R ln(p 2 / p 1 )

= 0 (1)


ds = change in specific entropy ( kJ/kgK )

c v = specific heat at constant volume process (kJ/kg K)

c p = 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/m 3 )

p = absolute pressure (Pa, N/m 2 )


κ = c p / c v (2)


κ = specific heat ratio

(1) can be transformed to:

(T 2 / T 1 ) (κ/(κ-1)) = (ρ 2 / ρ 1 ) κ = (p 2 / p 1 ) (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)


v = specific volume (m 3 /kg)

Using (5) in combination with (4) transforms to a common expression:

p v κ = constant (6)

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