Answer to Question #97583 in Classical Mechanics for Theo

Question

I am preparing an In-Service for nurses about portable oxygen cylinders. This is (part of) what I tell them:

Dimensions of 2.8 L Cylinders are: H. 40cm, D11 cm

Pressure when full = 200 Bar ( = 200kg / cm2)

Every cm2 inside this cylinder has a force of 200kg pushing against the wall!

How much is that in total?

Well, that is 40cm X ( π X 11) = 1381cm2 + bottom 5.52cm X π = 95cm2 + top 5.52cm X π x4 = 380cm2 = 1856 cm2 X 200 bar = 371.200kg.

I must be making an error somewhere. Please correct me.

Answer 1

$$p=200\ bar=200(0.980665)=196.133\frac{kg}{cm^2}$$

$$A=2\pi r^2+2\pi r h=2\pi r (r+h)$$

$$A=2\pi (5.5)(5.5+40)=1572.37\ cm^2$$

$$F=pA=(196.133)(1572.37)=308394\ kg$$