next up previous
Next: 5 Isothermal Flow Up: Free textbook pdf Fundamentals Previous: 3.2 Isentropic Isothermal Flow


4 Normal Shock

$\displaystyle {T_0}_y = {T_0}_x$ (44)

$\displaystyle {T_y \over T_x} = \left( { P_{y} \over P_{x}} \right)^{2} \left( {M_y \over M_x} \right)^{2}$ (45)

$\displaystyle {P_y \over P_x} = {1 + k{M_{x}}^2 \over 1 + k{M_{y}}^2}$ (46)

$\displaystyle {{P_0}_y \over {P_0}_x} = { P_y \left( 1 + {k-1 \over 2} {M_y}^{2...
...ver k-1} \over P_x \left( 1 + {k-1 \over 2} {M_x}^{2} \right) ^ {k \over k-1} }$ (47)

$\displaystyle {M_y}^2 = { {M_x}^2 + {2 \over k -1} \over {2k \over k -1} {M_x}^2 - 1 }$ (48)

$\displaystyle {P_y \over P_x}$ $\displaystyle = {2k \over k+1 } {M_x}^2 - {k -1 \over k+1}$    
$\displaystyle {P_y \over P_x}$ $\displaystyle = 1 + { 2k \over k+1} \left({M_x}^2 -1 \right )$ (49)

$\displaystyle {\rho_y \over \rho_x} = {U_x \over U_y} = {( k +1) {M_x}^{2} \over 2 + (k -1) {M_x}^{2} }$ (50)

$\displaystyle {T_y \over T_x} = \left( {P_y \over P_x} \right) \left( {k + 1 \over k -1 } + {P_y \over P_x} \over 1+ {k + 1 \over k -1 } {P_y \over P_x} \right)$ (51)

$\displaystyle {\rho_x \over \rho_y} = { 1 + \left( {k +1 \over k -1} \right) \l...
...P_x} \right) \over \left( k+1 \over k-1\right) +\left( {P_y \over P_x} \right)}$ (52)

Moving shocks


next up previous
Next: 5 Isothermal Flow Up: Free textbook pdf Fundamentals Previous: 3.2 Isentropic Isothermal Flow
Genick Bar-Meir ||| www.potto.org
copyright Dec , 2006

The pdf version is also available here