工程流体力学基础作业答案(6)

c1??RT1?518.851m/s Ma1?v1?1.76351 c1?2?Ma12???1???238611p2?p1?Pa ????1???2?Ma12??1??2??1???T2?T1??????1008.02K 2???1????1????1????1?Ma1?v2?v1

2????1?Ma12???1?Ma12?397.6794m/s

9-2 气体在管道中作绝热流动并产生一个正激波。已知在激波上游截面处，

T1?278K，v1?668m/s，p1?65kPa；激波下游截面处，T2?469K。试求激波下游截面处的v2、?2、p2，并与上游截面处的值进行比较。

解：设??1.4

2?T2?2?Ma1??1?2??1???由??解得Ma1?1.999446 ???????1?Ma2??1?T1???1??1?1????c1?v1?334.0925Ma1m/s

2cR?1?286.7878J/(kg·K)

?T1v2?v12????1?Ma12???1?Ma12?250.577m/s

?2?Ma12???1???292.332kPa p2?p1?????1???2?

p2?2.1734kg/m3 RT29-7 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