Consider the possibility of constructing a vehicle that operates on compressed air. A practical vehicle requires about $0.6 \mathrm { MJ } / \mathrm { km }$, and a practical highpressure storage tank might store gas at a pressure of $7.5 \mathrm { MPa }$. Derive a relationship between range (in kilometers) and storage tank volume (in cubic meters). If a maximum practical tank volume is $1 \mathrm {~m} ^ { 3 }$, what is the range of the vehicle?

Question

Quizplus · Accepted Answer

The Answer is From equation (18.4),

E / V = P _ { \max } \cdot \ln \left( P _ { \max } / P _ { \min } ight)

Using

P _ { \max } = 7.5 \mathrm { MPa }

and

P _ { \min } = 0.101 \mathrm { MPa }

then the operating range in

\mathrm { km }

is

R = [ E ( \mathrm { MJ } ) / ( 0.6 \mathrm { MJ } / \mathrm { km } ) ] = [ ( 7.5 \mathrm { MPa } ) imes V imes \ln ( 7.5 \mathrm { MPa } / 0.101 \mathrm { MPa } ) ] / ( 0.6 \mathrm { MJ } / \mathrm { km } )

where

V

is in

\mathrm { m } ^ { 3 }

. So

R = \left[ 53.8 \left( \mathrm {~km} / \mathrm { m } ^ { 3 } ight) ight] imes V

So for

V = 1 \mathrm {~m} ^ { 3 }

then the range is

53.8 \mathrm {~km}

.

Consider the Possibility of Constructing a Vehicle That Operates on Compressed