Problem $6$: $(25$ points$)$

In the movie Rocketeer $(1991),$ a rocket propulsion system is used to propel a person through the air. In real life, these systems use hydrogen peroxide $(H_2{O}_2)$ as a propellant and use a catalyst to decompose it to gaseous water $(H_{2}O(g))$ and oxygen $(O_2).$ Suppose the following information about the propulsion system.

$I_{sp}=135sec$

$c^{**}=1100\frac{m}{s}$

${}_{H_2{O}_2}=1395\mathrm{.}8k\frac{g}{m^3}$

${}_{\text{i}\text{n}\text{e}\text{r}\text{t}}=0\mathrm{.}5$

$P_c=2$MPa

Person mass $=70kg$

Two cylindrical propellant tanks of $0\mathrm{.}7$ m long and $0\mathrm{.}4$ m diameter.

Assume that $5\%$ of propellant is consumed during take$-$off, and $5\%$ is consumed during landing. Assume ideal nozzle expansion such that nozzle exit pressure equals atmospheric pressure.

Part $($a$)(20$ points$)$

Part $($b$)(5$ points$)$

Determine the amount of time the person can hover at sea level.

Calculate the nozzle throat diameter.

$2$Problem $6$: $(25$ points$)$

In the movie Rocketeer $(1991),$ a rocket propulsion system is used to propel a person through the air. In real life, these systems use hydrogen peroxide $(H_2{O}_2)$ as a propellant and use a catalyst to decompose it to gaseous water $(H_{2}O(g))$ and oxygen $(O_2).$ Suppose the following information about the propulsion system.

$I_{sp}=135sec$

$c^{**}=1100\frac{m}{s}$

${}_{H_2{O}_2}=1395\mathrm{.}8k\frac{g}{m^3}$

${}_{\text{i}\text{n}\text{e}\text{r}\text{t}}=0\mathrm{.}5$

$P_c=2$MPa

Person mass $=70kg$

Two cylindrical propellant tanks of $0\mathrm{.}7$ m long and $0\mathrm{.}4$ m diameter.

Assume that $5\%$ of propellant is consumed during take$-$off, and $5\%$ is consumed during landing. Assume ideal nozzle expansion such that nozzle exit pressure equals atmospheric pressure.

Part $($a$)(20$ points$)$

Part $($b$)(5$ points$)$

Determine the amount of time the person can hover at sea level.

Calculate the nozzle throat diameter.

$2$