公式展示区

(5-3)声速计算公式

$$a=\sqrt{\kappa RT}$$

(5-4)马赫数计算公式

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

(5-5)一元定常可压缩流动质量流量

$$q_m=\rho uA$$

(5-17)温度比

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

(5-18)压力比

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

(5-19)密度比

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

(5-26)速度系数

$$\lambda=\sqrt{\frac{\kappa+1}{2}M^{2}/\left(1+\frac{\kappa-1}{2}M^{2}\right)}$$

(5-27)马赫数与速度系数关系

$$M=\sqrt{\frac{2}{\kappa+1}\frac{\lambda^2}{1-\frac{\kappa-1}{\kappa+1}\lambda^2}}$$

(5-29)温度比与速度系数关系

$$\tau(\lambda)=\frac{T}{T_0}=1-\frac{\kappa-1}{\kappa+1}\lambda^2$$

(5-30)压力比与速度系数关系

$$\Pi(\lambda)=\frac{p}{p_0}=\left(1-\frac{\kappa-1}{\kappa+1}\lambda^2\right)^{\frac{\kappa}{\kappa-1}}$$

(5-31)密度比与速度系数关系

$$\varepsilon(\lambda)=\frac{\rho}{\rho_0}=\left(1-\frac{\kappa-1}{\kappa+1}\lambda^2\right)^{\frac{1}{\kappa-1}}$$

(5-33)速度计算公式

$$(5\text{-}33) \quad u_2=\sqrt{\frac{2\kappa}{\kappa-1}RT_0\left[1-\left(\frac{p_2}{p_0}\right)^{\frac{\kappa-1}{\kappa}}\right]}$$

(5-34)质量流量计算公式

$$q_m=p_0A_2\sqrt{\frac{2\kappa}{\kappa-1}\frac{1}{RT_0}\left[\left(\frac{p_2}{p_0}\right)^{\frac{2}{\kappa}}-\left(\frac{p_2}{p_0}\right)^{\frac{\kappa+1}{\kappa}}\right]}$$

(5-35)临界质量流量计算公式

$$q_m^*=\left(\frac{2}{\kappa+1}\right)^{\frac{\kappa+1}{2(\kappa-1)}}\sqrt{\frac{\kappa}{R}}\frac{p_0}{\sqrt{T_0}}A_2$$

(5-39)截面积比与马赫数关系

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

(5-45)流量函数

$$q(\lambda)=A_* / A=\left(\frac{\kappa+1}{2}\right)^{\frac{1}{\kappa-1}}\lambda\left(1-\frac{\kappa-1}{\kappa+1} \lambda^2\right)^{\frac{1}{\kappa-1}}$$

(5-46)质量流量计算公式

$$q_m=\sqrt{\frac{\kappa}{R T_0}\left(\frac{2}{\kappa+1}\right)^{\frac{\kappa+1}{\kappa-1}} }p_0 A q(\lambda)$$

(5-47)y(λ)函数

$$y(\lambda)=\left(\frac{\kappa+1}{2}\right)^{\frac{1}{\kappa-1}} \frac{\lambda}{1-\frac{\kappa-1}{\kappa+1} \lambda^2}$$

(5-49)Z(λ)函数

$$Z(\lambda)=\lambda+\frac{1}{\lambda}$$

(5-51)f(λ)函数

$$f(\lambda)=(\lambda^2+1)\left(1-\frac{\kappa-1}{\kappa+1} \lambda^2\right)^{\frac{1}{\kappa-1}}$$

(5-52)r(λ)函数

$$r(\lambda)=\frac{1-\frac{(\kappa-1)\lambda^2}{\kappa+1}}{1+\lambda^2}$$

(5-59)正激波前后马赫数关系

$$M_2^2=\frac{1+\frac{\kappa-1}{2}M_1^2}{\kappa M_1^2-\frac{\kappa-1}{2}}$$

(5-61)正激波前后压力比关系

$$\frac{p_{2}}{p_{1}}=\frac{2\kappa}{\kappa+1}M_{1}^{2}-\frac{\kappa-1}{\kappa+1}=\frac{1-\frac{\kappa+1}{\kappa-1}\lambda_{1}^{2}}{\lambda_{1}^{2}-\frac{\kappa+1}{\kappa-1}}$$

(5-62)正激波前后温度比关系

$$\frac{T_{2}}{T_{1}}=\frac{2+(\kappa-1)M_{1}^{2}}{(\kappa+1)M_{1}^{2}}\left(\frac{2\kappa}{\kappa+1}M_{1}^{2}-\frac{\kappa-1}{\kappa+1}\right)=\frac{1}{\lambda_{1}^{2}}\frac{1-\frac{\kappa+1}{\kappa-1}\lambda_{1}^{2}}{\lambda_{1}^{2}-\frac{\kappa+1}{\kappa-1}}$$

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