what is volume of liquid in partially filled cylinder. Asvolume= (Area of liquid)*(length of cylinder). I came across the following formula for volume of liquid incylinder but i can't understand it. the formula which i came across is: V= A*h = [(pi*R^2)/2- (R^3+R^2*h-3*R*h^2+h^3)/sqrt(2*R*h-h^2)] *L

 

 

 

R= radius of cylindrical shell

 

h= height of cylindrical shell

 

L= length of cylindrical shell

 

 

 

please tell me how it is derived and what it mean.

 

 

My first thought was that the equation was for a cylinder on it's side, but before I even went to check the math I find myself confused..... What is this "shell" you're speaking of? Do we get any more context? I'm guessing we have a language barrier here....

Edited December 1, 201213 yr by InigoMontoya

for time being consider cylinder and cylindrical shell the same, then try to understand the equation , what does it mean

Ok, so what is h and how does it differ from L?

Your cylinder is horizontal in this formula. Forget A*h here, it's A*L. h is the liquid's depth (from the bottom or from the center?).

 

The simplest method is to compute the angle resulting from h/R, the area of the disk's sector, the area of the triangle that completes the sector, then add and convert everything into h and R if you feel it simpler than the angle - that's rather a complication.