## Saturday, December 10, 2016

### Bernoulli Equation and Trains

After learning about Bernoulli Equation I recalled a situation that occurred early in my life. While waiting for the subway in NYC as mischievous 10 year old I always would stand near the edge of the platform before the train would come in. My mother, much to her credit, would always pull me back and berate me saying that the train could suck me in if I stood that close while the subway came by. As I know it all 10 year old I would laugh at this suggestion. Using Bernoulli's Equation however, it is possible to see if my mom was right.

p1+(1/2)p(v1^2)+pgy1=p2+(1/2)p(v2^2)+pgy2

Since we have no change in height and we are looking at the change in air pressure the equation we use becomes:

Δp=(1/2)p(v1^2)-(1/2)p(v2^2)            p(air)= 1.225kg/m^3    v(air)= 500m/s                                                                                                      v(average subway)= 24m/s

Δp= ((.5)( 1.225kg/m^3)(500m/s)^2) - ((.5)( 1.225kg/m^3)(524m/s)^2)=-15,052 N

Rearranging P=F/A to F=PA and assuming the average area of person is 1.7m^2 we get:

F=(15,052N)(.85m^2)= 12,794N                *since the air pushes only on half a person's body the                                                                                  area used is multiplied by a factor of 0.5.

12,974 newtons would certainly be enough to move a small child though bear in mind that to fully experience this force an individual would need to be a the entrance to the tunnel and extremely close to the train. The force would dramatically decrease as the distance between an individual and a train increased. Even so it is not advisable to stand near a moving train, and I guess one should sometimes listen to their parents.