Solid Propellant Rockets

A radially $($outward and inward$)$ burning solid composite propellant grain is designed as shown

below. The linear burn rate law of propellant in $m\frac{m}{s}$ is given by $r=a{P}^{}$ where $a=0\mathrm{.}0123m\frac{m}{P}{a}^{0\mathrm{.}3}-$

$s$ and $n=0\mathrm{.}3.$ Assume the density of propellant to be $1700k\frac{g}{m^3},$ the characteristic velocity to be

$1600\frac{m}{s}$ and diameter of the throat to be $60$ mm $.$

Determine the following, ignoring the effect of the density of hot gases in the combustion

chamber:

i$)$ Initial and maximum equilibrium chamber pressure

ii$)$ Initial burn rate $r$ of the propellant in $m\frac{m}{s}$

iii$)$ Burning time of the a$)$ outer grain and b$)$ the entire propellant grain

iv$)$ Maximum Thrust if the thrust coefficient is $1\mathrm{.}2$

Ot

I

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Radially inward and outward burning propellant grain