A solid-propellant rocket has chamber pressure of 6.35 atm with propellant density of 3.8 g/cm3 and burn area of 975 cm2. Find the total burn time (in seconds) if the propellant mass is 320 kg.

Given:

P = 6.35 atm

= 1.01 * 10^5 * 6.35

= 6.434 * 10^5 N/m^2

As = 975 cm^2

D = 3.8 g/cm^2

M = 320 kg

Since the propellant volume is equal to the cross sectional area, As times the fuel length, the volumetric propellant consumption rate is the cross section area times the linear burn rate, bs, and the instantaneous mass flow rate of combustion, ms gases generated is equal to the volumetric rate times the fuel density, D

ms = D * As * bs

ms : bs = M/L

M/L = 3.8 * 975

= 3705 g/cm

= 3.705 * 10^6 kg/m^3

Pressure = mass * g/area

= mass/length * time^2

t = sqrt (3.705 * 10^6/6.43 * 10^5)

= 2.4 s