how do i figure the gallons in a cylinder that is laying down?

Question

the cylinder would probably be 12' long and 6' wide

Answer 1

the same way you would standing up!

Answer 2

Well, the total volume of the cylinder isn't effected by the oreintation of the cylinder. So I'm guessing that you want a formula for working out the volume for various levels in the tank.

As a practical matter I would look up the formula in the Standard Math Handbook, it is full of useful formulas such as this.

If I was stranded on a deserted island I'd use calculus to solve the problem. Let the height of the liquid in the tank be "h" and knowing that solving the equation for a circle is x^2 + y^2 = r^2 . I'd correct the formula for moving the center of the cylinder from 0,0 to 0,r. Then working on 1/4 of the cylinder I would calculate what x equaled at y=h. I'd solve the formula for y and subtract the intergal of the formula between the limits of 0 and the x I calcuated above from the area of the rectangle h times x. That would give me 1/2 the area of the liquid and multipling that by the length would give me the volume.

That would take some time for me to complete so I haven't actually attempted it. But it could be done.

Answer 3

The volume of the cylinder is 339 cu ft.( L x pi * (D^2)/4) There are 7.5 gals per cu ft, so the cylinder holds 2542 gallons

Answer 4

h is the depth at the centerline plumb.
r is the cylinder radius.
L is the cylinder length

V(h) = L * A(h) in cubic feet

A(h) = integral(0,h,2*sqrt(2xr - x^2) dx)
A(h) = (r^2)*(pi/2 - arcsin(1-(h/r))) - (r-h)*sqrt(2rh-h^2)


1 cu. ft. = 7.480519481 US Gal (liquid)

and for h = 2r
V(2r) = L*pi*r^2
as expected

As a corollary, the Center of Mass,
C(h) = integral(0,h,2*x*sqrt(2xr - x^2) dx) / A(h)
C(h) = r - [(2/3)*(2rh-h^2)^(3/2)]/A(h)
for h<>0

for h = 2r,
C(2r) = r
as expected

Answer 5

It would contain the same number of gallons laying down or standing up.

Answer 6

pi * 3^2 * 12

= 108 pi

Answer 7

this give the formula and a picture to help id the measurements.
the vol would be the same laying or standing.

http://www.pwcs.edu/i-tech/TLCF/formulas/VCylinder1.htm