The grain in a solid propellant rocket is a hollow cylinder bonded to the casing so that it burn only on its inner cylinder surface and on one end. It s density is 1650 kg/m3, and its burning rate is characterized by r = 13.3 Po0.63 mm/s where Po is the chamber pressure in MPa. At a point in the burning period when Po = 0.70 MPa, the grain d/D 0.4 and L/D = 6 where L is the grain length, d is the inner grain diameter, and D is the outer grain diameter = 1 m. Determine the rate of change of the chamber pressure assuming the temperature stays constant at 2750 K and that the gas specific heat ratio, , is 1.24 Hint: assume that this is a series of steps between two steady-state conditions. You are looking for dP/dt at an instant in time rather than over the entire burn cycle. Consider dP/dt = d P/dAb * d Ab/dt where d Ab /dt comes from the geometry specific to this problem. Answer: dP/dt = 0.0862 MPa/s