Derive the detonation velocity $\backslash (\backslash$left$(\backslash$mathrm$\{$u$\}\_\{1\}\backslash$right$)\backslash )$ by considering the following assumptions:

a$.1-$Dimensional, steady flow

b$.$ Constant area

c$.$ Ideal gas behavior

d$.$ Constant and equal specific heat

e$.$ Negligible body force

f$.$ Adiabatic conditions $($no heat losses to surroundings$)$

g$.\backslash (\backslash$mathrm$\{$P$\}\_\{2\}\backslash$gg $\backslash$mathrm$\{$P$\}\_\{1\}\backslash )($Pressure of burned gas is much higher than unburned mixture$)$ Represent with $1-$D detonation wave diagram for the derivation