工程流体力学基础作业答案(7)

9-7 一拉瓦尔喷管出口面积与喉部面积之比A1/Acr=4。空气通过喷管并在A/Acr=2处产生一正激波。已知波前的滞止压强p0?100kPa，试求出口处的压强。

解：求激波前的马赫数

A1?2???12???1?Ma?1??AcrMa1???12??????12(??1)由

解得Ma1?2.197198

???12?Ma1?激波前压强 p1?p0?1?2??2????1?9.393266kPa

2?Ma1???1激波后压强 p2?p1?51.340075kPa

??12Ma1????1??2激波后马赫数 Ma2?Ma12?Ma1????1?2?0.5474317

激波后的总压 p02???12???1?p2?1?Ma2??62.941294kPa

2???激波后的相当临界截面积

Acr2?2???12???Ma2?Ma2???1?A2?????1????12(??1) ?0.79439114由

Ae1?2???12???1?Ma?e??Acr2Mae???12????????12(??1)得出口马赫数Mae?0.23774214

出口压强pe?p02?1???12?Mae?2?????1?60.5131kPa