Question 2176: Dear Mr.Jon,
Thanks for your reply,
I am sorry for the confusion in my previous queation.Actually, I am a Chemical Engineer and I am doing research in Ball Mill. Actually Ball mill is a Cylindrical mill used for grinding powders in Powder processing industries like cement, ceramic and paint.In this cylindrical mill, balls are added for grinding powders. So I have to calculate Volume of mill occupied by balls.
But the company people will give only ball bed height of the mill i.e. they are having a standard ROD and they will insert the rod into the mill and measure the ball bed height inside the mill. So with this given data I have to find out the Volume of mill occupied by balls.
Here I assumed the part of mill occuying the balls as Segment area of Circle. So I wish to calculate the Area of this segment. So by multiplying this area with Length, I will easily get my desired result. i.e. Volume of mill occupied by balls. I HAVE TRIED WITH AREA OF SEGMENT FORMULA WHICH IS (AREA OF SECTOR - AREA OF TRIANGLE) AND IT CONTAINS AN INVERSE OF COSINE TERM. BUT I AM GETTING HIGHER VALUE(WHICH IS LARGER THAN MILL AREA).SO PLEASE HELP IN THE FORMULAE AVAILABLE FOR DETERMINING SEGMENT AREA OF CIRCLE. I NEED DIFFERENT FORMULAE OF THIS. PLEASE REPLY
Thankyou,
Premanand
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! right, i am getting there slowly :-)
You have a cylinder which is hollow? and balls of cement (or whatever) are added to the mill?
Now, is the cyclinder filled with balls, until no more can be fitted in?
Assume each ball is the same but do not know the dimensions of it...then we will have to theorise on the volume of a ball by 4/3pi*r^3 and know how many it takes to fill the mill, then work out their total volume then calculate the mill volume, from its cross-sectional area times its length.
Then just work out the percentage of the total area taken up by the balls.
Hope this helps. If not, explain some more please :-)
Jon
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