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Next: 4 Normal Shock Up: 3 Isentropic Flow Previous: 3.1 Relationships for Small

3.2 Isentropic Isothermal Flow Nozzle

$\displaystyle T_1 = T_2$

(26)

$\displaystyle {{T_0}_1 \over {T_0}_2} = {\left(1+{k -1\over2} {M_1}^2\right)\ov... ... {\left(1+{k -1\over2} {M_1}^2\right)\over \left(1+{k -1\over2}{M_2}^2\right) }$

(27)

$\displaystyle {P_2 \over P_1} = {\Huge e}^{k({M_1}^2 - {M_2}^2) \over 2} = \left( {\Huge e}^{{M_1}^2} \over {\Huge e}^{{M_2}^2}\right) ^{k\over 2}$

(28)

$\displaystyle {A_2 \over A_1} = { M_1 \over M_2} \left( \mbox{\large e}^{{M_2}^{2}} \over \mbox{\large e}^{{M_1}^{2}} \right)^{k \over 2}$

(29)

$\displaystyle {{P_0}_2 \over {P_0}_1} = { P_2 \over P_1} \left( 1 + {k -1 \over... ...ox{\large e}^{{M_1}^{2}} \over \mbox{\large e} ^{{M_1}^{2}} \right]^{k \over 2}$

(30)

The star values

$\displaystyle T = T^{*}$

(31)

$\displaystyle { P \over P^{*}} = { \rho \over \rho^{*}} =$ e $\displaystyle ^{(1-M^2) k \over 2}$

(32)

$\displaystyle { A \over A^{*}} = {1 \over M}$ e $\displaystyle ^{(1-M^2) k \over 2}$

(33)

$\displaystyle { T_0 \over {T_0}^{*}} = {2 \left( 1 + {k -1 \over 2}{M_1}^2 \right) \over k +1 } ^ {k \over k-1}$

(34)

$\displaystyle { P_0 \over {P_0}^{*}} = {\Huge e}^{(1-M)k \over 2} {2 \left( 1 + {k -1 \over 2}{M_1}^2 \right) \over k +1 } ^ {k \over k-1}$

(35)

The initial stagnation temperature is denoted as ${T_{0}}_{int}$ .

$\displaystyle {T \over{T_{0}}_{int}} = { 1 \over 1 + {k-1 \over 2} M^2}$

(36)

$\displaystyle {P \over{P_{0}}_{int}} = { 1 \over \left( 1 + {k-1 \over 2} M^2 \right) ^{k-1 \over k} }$

(37)

$\displaystyle {F_{net} \over P_0 A^{*}} = \overbrace{P_2A_2 \over P_0 A^{*}}^{f... ...1A_1 \over P_0 A^{*}}^{f(M_1)} \overbrace{\left( 1 + k{M_1}^2 \right)}^{f(M_1)}$

(38)

$\displaystyle {F \over F^{*}} = {P_1A_1 \over P^{*}A^{*}} {\left( 1 + k{M_1}^2 ... ...e function \eqref{variableArea:eq:beforeDefa}}} {1 \over \left( 1 + k \right) }$

(39)

$\displaystyle F_{net} = P_0 A^{*} (1+k) {\left( k+1 \over 2 \right)^{k \over k-1}} \left( {F_2 \over F^{*} } - { F_1 \over F^{*}}\right)$

(40)

for isothermal

$\displaystyle {F_2 \over F_1} = {P_2 A_2 \over P_1 A_1} { 1 + {{U_2}^2 \over RT} \over 1 + {{U_1}^2 \over RT }}$

(41)

$\displaystyle {F_2 \over F_1} = {M_1 \over M_2} { 1 + k {M_2}^2 \over 1 + k {M_1}^2}$

(42)

$\displaystyle {F_2 \over F^{*}} = {1 \over M_2} { 1 + k {M_2}^2 \over 1 + k }$

(43)

Next: 4 Normal Shock Up: 3 Isentropic Flow Previous: 3.1 Relationships for Small Contents

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