Simple problem but for some reason I get double the answer in the book and I can't understand why. Two hemispherical shells of diameter D are placed together and the air is pumped out so that the pressure inside is p. The pressure outside the shells is q. How much force would you have to exert on each shell to pull them apart?
Force = pressure*area
Surface area of a sphere = 4*pi*r^2
The Attempt at a Solution
If I just concentrate on one shell, then the force from the outside is 2*pi*(D/2)^2*q = 0.5*pi*D^2*q . The force on the inside is then 0.5*pi*D^2*p, so the difference between these would be the force required I would have thought? This gives
F = 0.5*pi*D^2*(q-p).
However the answer in the book gives it as F = 0.25*pi*D^2*(q-p) and I don't understand why.