Hyperloop: Air can be unpleasant
The Hyperloop is a hypothetical new fast transport system between cities, which works by launching pods that carry people through a very low air pressure tunnel. The normal pressure in the tunnel is , which is very low compared to the usual atmospheric pressure of . Since the pressure is so low the Hyperloop tunnel must be well sealed to prevent outside air from rushing in. A sudden increase in air pressure in a section of the tunnel can be rather unpleasant for the passengers in the pod.
Consider for example a hole being created in the Hyperloop tunnel, which leads to a sudden increase in the local air pressure from to while maintaining constant temperature and volume. If the normal drag force on the Hyperloop is , how much acceleration in g 's would the passengers in the Hyperloop experience if the pod hit the region of high pressure?
- The mass of the pod is approximately .
The answer is 2.228.
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1 solution
From here one can see that drag force is directly proportional to the density of the surrounding media (air), and the density is proportional to pressure when the rest is kept constant. Upon a sudden increase in pressure, the pod will have to work against an increased drag force and will decelerate to a lower velocity corresponding to the new drag force. The new drag force will be 101325 Pa / 99 Pa = 1023.5 times higher, so the force balance is:
m × a = 1023.5 × Fd - Fd
where,
Fd - drag force, 320N
m - mass of the pod, 15000kg
a - deceleration of the pod, m/ s 2
The deceleration in terms of "g" is:
a = g × m 1 0 2 3 . 5 × F d − F d
After putting the numbers in, the answer is 2 . 2 3