If the overexpansion level of a Laval nozzle run by a settling chamber at 5 atm and discharging to sea level atmosphere is 36.1%, determine the design Mach number of the nozzle, treating the flow through the nozzle as adiabatic and reversible.
Question 2.11: If the overexpansion level of a Laval nozzle run by a settli...
Given, p_{0}=5 atm , p_{b}=1 atm and expansion level is 0.361.
The expansion level can be expressed as
\frac{p_{b}-p_{e}}{p_{b}}
Therefore,
\frac{p_{b}-p_{e}}{p_{b}}=0.3611-\frac{p_{e}}{p_{b}}=0.361
\frac{p_{e}}{p_{b}}=1-0.361 = 0.639
p_{e}=0.639 \text { atm }
The pressure ratio at the nozzle exit is
\frac{p_{e}}{p_{0}}=\frac{0.639}{5} = 0.1278
For \frac{p_{e}}{p_{0}}=0.1278, from isentropic table, M_{e}=2.0. Thus, the design Mach number of the nozzle is 2.0.
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