If the temperature of the fluid element is held constant, Tn is identified as the thermal compression等温缩 T (7.34) If the process takes place isentropically, then 等熵压缩性 v(op (7.35
If the temperature of the fluid element is held constant, then is identified as the isothermal compressibility (等温压缩性) (7.34) If the process takes place isentropically, then (等熵压缩性) (7.35) T T p v v = − 1 s s p v v = − 1
p=pt ap 7.37 If the fluid is a ous, where comprpsibin T is large then for a given pressure change dp from one point to another in the flow, Eq. 7. 37) states that decan be large.(如果流体为气体则值大对于一个给定压强 变化方程3指出也会大 Thus, p is not constant the flow of a gas is a compressible ow The exception is the -speed flow of a g. Where is the limit? If the mach number mev/a>0.3. the flow should be considered
If the fluid is a gas, where compressibility is large, then for a given pressure change from one point to another in the flow , Eq.(7.37) states that can be large. (如果流体为气体,则 值大,对于一个给定压强 变化 ,方程.(7.37)指出, 也会大.) Thus, is not constant; the flow of a gas is a compressible flow. The exception is the low-speed flow of a gas. Where is the limit? If the Mach number , the flow should be considered compressible. d = dp d M V / a 0.3 (7.37) dp dp d
7.4 GOVERNING EQUATIONS FOR INVISCID COMPRESSIBLE FLOW(无粘、可压缩流控制方程) For inviscid, incompressible flow, the primary dependent variables are the pressure b and the veloci Hence, we need only o bas equator, namely the contin and the omentum e∥ 对于无粘 基本自变量是 E囗 压强力和速度 因此我们只需要 即罗方和量方
7.4 GOVERNING EQUATIONS FOR INVISCID, COMPRESSIBLE FLOW (无粘、可压缩流控制方程) For inviscid, incompressible flow, the primary dependent variables are the pressure p and the velocity . Hence, we need only two basic equations, namely the continuity and the momentum equations. 对于无粘、不可压缩流动，基本自变量是 压强 p和速度 。因此我们只需要两个基 本方程，即连续方程和动量方程
Indeed. the basic equations are combined to obtain Laplace's equation and Bernoullis equation, which are the primarily tools the applications discussed in Chaps. 3 to 6. Note that both p and Tare assumed to be constant through out such inviscid incompressible flows 连续方程与动量方程相结合可以得到 Laplace方 程和 Bernoulli方程,这是我们讨论第三章至第 六章内容用到的基本工具.对于无粘不可压缩 流动,我们假定密度和温度保持不变 Basically, incompressible flows obey purel echanical laws and do not need thermodynamic consideratons
Indeed, the basic equations are combined to obtain Laplace’s equation and Bernoulli’s equation, which are the primarily tools the applications discussed in Chaps. 3 to 6. Note that both and T are assumed to be constant through out such inviscid, incompressible flows. 连续方程与动量方程相结合可以得到Laplace 方 程和Bernoulli 方程，这是我们讨论第三章至第 六章内容用到的基本工具．对于无粘不可压缩 流动，我们假定密度和温度保持不变． Basically, incompressible flows obey purely mechanical laws and do not need thermodynamic considerations
In contrast, for compressible flow, is variable and becomes an unknown. Hence we need an additional equation the energy equation-which in turn introduces internal energy e as an unknown 对于可压缩流,相反的是 是一个变量 并且是一个未知数.因此,我们需要一个附加 方程一能量方程一进而引入未知数肉能 Internal energy e is related to emperature then T also becomes an important variable Therefore, the 5 primary dependent variables are v,p, e, and T To solve for these me vorable s, we need ne governing
In contrast, for compressible flow, is variable and becomes an unknown. Hence we need an additional equation – the energy equation – which in turn introduces internal energy e as an unknown. 对于可压缩流，相反的是 是一个变量， 并且是一个未知数． 因此，我们需要一个附加 方程－能量方程－进而引入未知数内能e。 Internal energy e is related to temperature, then T also becomes an important variable. Therefore, the 5 primary dependent variables are: To solve for these five variables, we need five governing equations p,V, , e, and T