Equations for Steady 1D Isentropic Flow

The equations used to describe steady 1D isentropic flow are derived from conservation of mass, momentum, and energy, as well as an equation of state (typically the ideal gas law).

These equations are typically described as ratios between the local static properties (p, T, \rho) and their stagnation property as a function of Mach number and the ratio of specific heats, \gamma. Recall that Mach number is the ratio between the velocity and the speed of sound, a.

These ratios are given here:

Temperature: T_o/T = \left(1+\frac{\gamma -1}{2} M^2\right)

Pressure: P_o/P = \left(1+\frac{\gamma -1}{2} M^2\right)^{\frac{\gamma}{\gamma-1}}

Density: \rho_o/\rho = \left(1+\frac{\gamma -1}{2} M^2\right)^{\frac{1}{\gamma-1}}

In addition to the relationships between static and stagnation properties, 1D nozzle flow offers an equation regarding the choked cross-sectional flow area (recall that the flow is choked when M=1.)

A/A^* = \frac{1}{M}\left(\left(\frac{2}{\gamma+1}\right)\left(1+\frac{\gamma -1}{2} M^2\right)\right)^{\frac{\gamma+1}{2\left(\gamma-1\right)}}

Some excellent references for these equations are:

  • Gas Dynamics Vol. I – Zucrow and Hoffman – 1976
  • Gas Dynamics – John and Keith – 2nd Ed. – 2006


One thought on “Equations for Steady 1D Isentropic Flow”

  1. Hi admin, i must say you have hi quality articles here.
    Your page should go viral. You need initial traffic boost only.

    How to get it? Search for: Mertiso’s tips go viral


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s