volume of tank

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kpx001

Junior Member
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Mar 6, 2006
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r=20 H=15 L=60
and here is the diagram


It is basically a fuel tank made of a rectangular prism center and half circular cylinders at the the top and bottom.
it should be a function of h and i have no idea how to come up with the formula. my guess would be to find total volume - liquid volume.
2*pi*r^2*L*2*r*H*L - ???
 
Stand it upright. The volume is equal to the area of the base times the highth. The area of the base is the area of the circle + the area of the rectangle.
V=(?r[sup:1ky30tky]2[/sup:1ky30tky]+2rH)L where r is the radius of the half circle, H is the width of the rectangle, 2r is the length of the rectangle and L is length of the tank.
 
sorry for the bad drawing but yeah. basiclly i need to make a function where i plug in h to find the volume of the liquid... so there are two heights, one is the height of the prisim and the other is the height of the liquid. (ignore the water that looks distorted.)


 
Ahhh...OK: you have a rectangular prism and a regular cylinder; the cylinder has been cut in half
along its length, a half placed on top of the prism, other half at the bottom.
I remember them gas tanks: we had a large one on the farm where I was brought up;
many other farmers also did; a gas truck would come and fill them; I remember 10 cents per gallon !

(P = pi)
cylinder: r = radius, L = length; so volume = P L r^2
prism: 2r = width, L = length, H = height; so volume = H L 2r

So if full, liquid volume is P L r^2 + H L 2r

If liquid's height = h, then maximum h = H + 2r

So a simple formula is not possible; something like this required:

[1] if h =< r then h = ? , else
[2] if h =< H + r then h = ? , else
[3] h = ?

[1]: partial cylinder volume
[2]: half cylinder plus partial prism
[3]: half cylinder + prism + partial cylinder

I'll let someone else confirm all that...or tell me to stay out of the gas tank business :shock:

To calculate partial cylinder volume, go learn here:
http://www.lmnoeng.com/Volume/CylConeSphere.htm
 
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