Need help 4. (20 poiAoverging diverging de with an area ralio of AfA2. exhair fo

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Need help

4. (20 poiAoverging diverging de with an area ralio of AfA2. exhair form a highi prsureserwoiro K) to a lk plane where the pressaure is 1 alm. The lest section area is 0.01 m2 T, (a) Antxk to erlropic: throughout, find the mini stagnalion pressure, Po,under which the Lunnel will start. prsuruner L conditis? (b) What is the leet secli (c) If the reseroir is a a presure of 550 peia and a volue f 1805 3, how long can the Lunnel run if a presesure rngulator maintains a fixed slagnation presesure al the vale caculated in part A? Assum hal Lhe revoir empalur does nol change. (d) In a real wind Lunnel with leses, one must rare Ilie slagnaLion preseare unsughly 5/% higher than the minimum presdictesd by part A in order to start the lunnel. How dos thies allect the run Lime?

Explanation / Answer

(a)For steam, =1.30 (e.g. from cp=2050 J/(kg·K),

cp/cv=cp/(cpR)=2050/(2050-462)=1.29).

For isentropic nozzles, pt=const and Tt=constant.

Choking must occur if pe/pt<(2/(+1)/(1)=0.55 and in our case is pe/pt=100/300=0.33;

hence, it is a CD-nozzle. Exit temperature is Te=Tt(pe/pt) (1)/=445 K (172 ºC). Solving in (13) one finds p* =164 kPa and Me=1.39.

b) Exit area can be found fince p, T and M are known, obtaining Ae=2.87 cm2 .

Throat area can be obtained with Ae=2.87 cm2 and Me=1.39, with a result A* =2.57 cm2 .

Exit speed is ee e v M RT = =717 m/s.

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