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 40F.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?

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We are given following data for control rocket :

P=3000 psiaP=3000\text{ psia}

n=100n=100

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

Δt=5 s\Delta t=5\text{ s}

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

From properties table we can find air gas constant:

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

Calculating mass:

m=nm˙Δt=1000.55=250 lbmm=n\cdot \dot m\cdot \Delta t=100\cdot 0.5\cdot 5=250\text{ lbm}

Calculating volume by using ideal gas EOS:

V=mRTP=2500.0685003000778144=15.3 ft3V=\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 psiaP=3000\text{ psia} and T=40 FT=40\text{ F} we can find specific volume :

ν=0.028 ft3 lbm\nu=0.028\frac{\text{ ft}^3}{\text{ lbm}}

Calculating volume:

V=mν=2500.028=7 ft3V=m\cdot \nu=250\cdot 0.028=7\text{ ft}^3

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

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