Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Isentropic Flow

Fluid flow with constant entropy is also called isentropic flow.

Sponsored Links

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)


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)


κ = cp / cv                                                   (2)


κ = specific heat ratio

(1) can be transformed to:

(T2 / T1)(κ/(κ-1)) = 2 / 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 / ρκ = constant                                       (4)

Density can be expressed:

ρ = 1 / v                                              (5)


v = specific volume (m3/kg)

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

p vκ = constant                                      (6)

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

About the Engineering ToolBox!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.


This page can be cited as

  • Engineering ToolBox, (2004). Isentropic Flow. [online] Available at: [Accessed Day Mo. Year].

Modify access date.

. .


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

1 27

Sponsored Links