Isentropic flow relations

(Difference between revisions)

Revision as of 21:39, 3 September 2005

$M = \frac{v}{a}$

$a = \sqrt{\gamma R T}$

$\frac{p_0}{p} = (\frac{T_0}{T})^\frac{\gamma}{\gamma - 1}$

$\frac{p_0}{p}=(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma}{\gamma-1}}$

$\frac{T_0}{T}=1+\frac{\gamma-1}{2}M^2$

$\frac{\rho_0}{\rho}=(1+\frac{\gamma-1}{2}M^2)^{\frac{1}{\gamma-1}}$

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

@@ Line 4: / Line 4: @@
 <math>\frac{p_0}{p} = (\frac{T_0}{T})^\frac{\gamma}{\gamma - 1}</math>
-<math>\frac{T_0}{T}=1+\frac{\gamma-1}{2}M^2</math>
 <math>\frac{p_0}{p}=(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma}{\gamma-1}}</math>
+<math>\frac{T_0}{T}=1+\frac{\gamma-1}{2}M^2</math>
 <math>\frac{\rho_0}{\rho}=(1+\frac{\gamma-1}{2}M^2)^{\frac{1}{\gamma-1}}</math>
-<math>\frac{A}{A*}=(\frac{\gamma+1}{2})^{\frac{-\gamma+1}{2(\gamma-1)}}*(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma+1}{2(\gamma-1)}}/M</math>
+<math>\frac{A}{A*}=\frac{1}{M}*(\frac{\gamma+1}{2})^{\frac{-\gamma+1}{2(\gamma-1)}}*(1+\frac{\gamma-1}{2}M^2)^{\frac{\gamma+1}{2(\gamma-1)}}</math>