# Isentropic Flow

## Constant entropy flow is called 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)

where

ds= entropy change

c_{v}= specific heat capacity at a constant volume process

c_{p}= specific heat capacity at a constant pressure process

ρ= density of gas

Using

κ = c_{p}/ c_{v}(2)

where

(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)

where

v= specific volume

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

p v^{κ}= constant(6)

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