The diameter of the hollow core of a solid propellant grain remains axially uniform during burning. Its length is 5 m, and initially its inner diameter is 0.37m; the outer diameter of the grain is 0.82m. The burning rate r is 1.2cm/s, which as a first approximation may be assumed uniform over the entire inner surface of the grain. The grain density is 1875 kg/m^3. The combustion chamber pressure and gas temperature downstream of the grain are 2.17 MPa and 2580K, respectively. Neglecting the effects of friction, estimate, at the beginning and end of combustion:
a) The static pressure ratio p2/p1 along the length of the grain
b) The Mach number M2 at the downstream end of the grain
The gas specific heat ratio and molecular weight are 1.2 and 20.