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# Isentropic Flow

## Fluid flow with constant entropy is also called 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.

## Related Documents

• ### Compression and Expansion of Gases

Isothermal and isentropic gas compression and expansion processes.
• ### Speed of Sound - Equations

Calculate the speed of sound (the sonic velocity) in gases, fluids or solids.
• ### Turbo Machines - Specific Work done by Pumps, Compressors or Fans

Calculate specific work done by pumps, fans, compressors or turbines.

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## Citation

• The Engineering ToolBox (2004). Isentropic Flow. [online] Available at: https://www.engineeringtoolbox.com/isentropic-flow-d_630.html [Accessed Day Month Year].

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6.3.17

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