ecuaciones

Las ecuaciones se muestran en el mismo orden en que aparecen en el libro.

\rho=\frac{p}{g_sRT}

\frac{p}{\gamma}\approx\frac{p_0}{\gamma_0}\

dp=-\gamma dz

\frac{dp}{p}\approx-\frac{dz}{\frac{\rho_0}{\gamma_0}}

p\approx p_0 e^-\frac{z}{\frac{p_0}{\gamma_0}}

\frac{p}{\rho}=\frac{p_1}{\rho_1}

{\rho}=\frac{p}{\rho_1} \rho_1

{\rho} V= \rho_1 V_1

V=\frac{\rho_1}{\rho} V_1=\frac{p_1}{p} V_1

{\rho} V^2= \rho_1 V_1 \frac{p_1}{p}

-dp=\frac{f}{D}\frac{\rho V^2}{2} dx+\rho VdV

-\frac{p}{p_1}dp\approx\frac{f}{D}\frac{\rho_1 V_1}{2}dx

L=x_2-x_1

\frac{p_1^2-p_2^2}{2p_1}\approx f \frac{L}{D}\frac{\rho_1 V_1^2}{2}

\frac{p_1^2-p_2^2}{2p_1}=\frac{(p_1-p_2)(p_1+p_2)}{2p_1}=\frac{1}{2} (p_1-p_2) (1+\frac{p_2}{p_1})

(p_1+p_2)=\frac{2}{1+\frac{p_2}{p_1}} f \frac{L}{D}\frac{\rho_1V_1^2}{2}

\frac{\rho}{\rho_1}=(\frac{p}{p_1})^\frac{1}{k}

-dp=\rho V dV

-p_1^\frac{1}{k}\frac{dp}{p^\frac{1}{k}}=\rho_1 V dV

\frac{p_1^\frac{1}{k}}{1-\frac{1}{k}}(p_1^{1-\frac{1}{k}}-p_2^{1-\frac{1}{k}})=\frac{\rho_1}{2}(V_2^2-V_1^2)

p_2-p_1=\frac{\rho}{2}(V_1^2-V_2^2)(1+\frac{\rho_1 (V_1^2-V_2^2)}{4kp_1}+...)

-\frac{\rho_1 (V_1^2-V_2^2)}{4kp_1}

c=\sqrt{\frac{E}{\rho}}

log p - k log \rho=constant'

\frac{dp}{p}-k\frac{d\rho}{\rho}= 0

E=\frac{dp}{\frac{d\rho}{\rho}}=kp

c=\sqrt{\frac{kp}{\rho}}=\sqrt{kg_sRT}

M=\frac{V}{\sqrt{\frac{E}{\rho}}}= \frac{V}{c}