Find the upstream Mach number if there is a entropy increase across the normal shock wave of $$220\,J/\left( {kg.K} \right)$$.

Find the upstream Mach number if there is an entropy increase across the normal shock wave of $$220\,J/\left( {kg.K} \right)$$.

Asked on 11th March 2021 in
$\frac{{{p_{02}}}}{{{p_{01}}}} = {e^{ – \left( {{s_2} – {s_1}} \right)/R}}$
$\Rightarrow \frac{{{p_{02}}}}{{{p_{01}}}} = {e^{ – \left( {220} \right)/287}} = 0.46$
Therefore, from normal shock properties table, for, $$\frac{{{p_{02}}}}{{{p_{01}}}} = 0.46$$, upstream Mach number $$M_1$$, is around $$2.6$$.