Exercise $5$:

Given enthalpy $h=c_{p}T,$ stagnation enthalpy $h_0=h+\frac{1}{2}{c}^2$ and $c_p=\frac{R}{-1}.$ The stagnation temperature $T_0$ is related to velocity temperature $(T_c=\frac{c^2}{2}{c}_p)$ by $T_0=T+T_c.$

$1-$ Give expression of Mach number $M$ function of $T,R,C$ and $$

$2-$ In the case of isentropic flow, the variation of Mach number with area $A$ is $\frac{dA}{A}=\frac{dp}{c^2}(1-M^2),$ where $$ is a fluid density.

Give the characteristic of gases and vapors in the case of

a$)$ Purpose of Nozzle; b$)$ Purpose of diffuser

$3-$ For diffuser Subsonic gas, give the variation of area and draw the shape of the pipe that can transport the gas.

$4-$ For Nozzle Subsonic gas, give the variation of area and draw the shape of the pipe that can transport the gas.

$5-$ In which case is a shock wave generated during the propagation of the gas?