Question

You are to design a small, directional control rocket to operate in space by providing as many as 100 bursts of 5 seconds each with a mass flow rate of 0.5 lbm/s at a velocity of 400 ft/s. Storage tanks that will contain up to 3000 psia are available, and the tanks will be located in an environment whose temperature is $40^\circ F.$ Your design criterion is to minimize the volume of the storage tank. Should you use a compressed-air or an R-134a system?

Solution

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We are given following data for control rocket :

$P=3000\text{ psia}$

$n=100$

$T=40\text{ F}=500\text{ R}$

$\Delta t=5\text{ s}$

$\dot m=0.5\frac{\text{ lbm}}{\text{ s}}$

From properties table we can find air gas constant:

$R=0.068\frac{\text{ Btu}}{\text{ lbm R}}$

Calculating mass:

$m=n\cdot \dot m\cdot \Delta t=100\cdot 0.5\cdot 5=250\text{ lbm}$

Calculating volume by using ideal gas EOS:

$V=\dfrac{m\cdot R\cdot T}{P}=\dfrac{250\cdot 0.068\cdot 500}{3000}\cdot \dfrac{778}{144}=15.3\text{ ft}^3$

Now let's concider R-134a. From Superheated R-134a table corresponding to $P=3000\text{ psia}$ and $T=40\text{ F}$ we can find specific volume :

$\nu=0.028\frac{\text{ ft}^3}{\text{ lbm}}$

Calculating volume:

$V=m\cdot \nu=250\cdot 0.028=7\text{ ft}^3$

To minimize volume we will use R-134a system.

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