Formula to calculate Hex tank volume?

[JoelR]

I just picked up a quite large Hex tank but I want to replace the frame "rim". I need to calculate the tank volume so I can contact manufactures and try to figure out who makes it & what size to order.

The tank is.... (with plastic rim/frame)

point to point 32"
flat to flat 27 3/4"
height 28"

Thank you.
Joel

 

[flstffxe]

figure the area in 6 triangles and add them together.

Read this
http://www.mathreference.com/geo,hex.html

Then multiply by 28" for height.

divide by 1728(Cubic inches in 1 cubic foot, result is cubic feet of tank space)

multiply by 7.48(1 cubic foot holds 7.48 gallons, results is the tank capacity)

 

[brianp]

Two ways:

1. Calculate the volume of a cylinder using diameter = flat-to-flat and then add 10%. [pi x radius squared x height]

2. Measure height from inside bottom to inside fill level. Add a known volume of water (say, 2-5 gallons) and measure height of water. Multiply by number required to equal fill height. Let's say fill height is 24 inches and 2 gallons = 1 inch. So, every inch of water height within tank contains 2 gallons. Tank volume = 24 x 2 = 48 gallons.

 

[Merbeast]

What is the width of each pane of glass?

 

[CHOMPERS]

I came up with 85 gallons by approximation. The cheater formula is to use the formula of a cylinder with the diameter at the two opposite locations 1/3 the distance from the edge of two panes.

The formula for the tank uses the length of a side (L).

V=(1.3)*h*L^2 this gives the volume in icubic inches.

Divide the answer by 12^3 or 1728 to get cubic feet. Then multiply by 7.5 to get the gallons.

 

[CHOMPERS]

Wait a minute, the sides should be 16 inches because of the geometry of the hexagon, so the volume would be

(1.3)*28*16^2*7.5/1728 = 40.4 gallons.

I don't know how I doubled that in the other calculation.

 

[CHOMPERS]

My math for the approximation is right. What is it that asian parents name retarded kids? Oh yeah, Sum Ting Wong.

 

[CHOMPERS]

V=(1.3)*h*L^2 this gives the volume in icubic inches.

.

I made a mistake in the simplification somehow.

The area of the hexogram is
area = (3/2)r^2*sqrt(3)
which simplifies to
A=(2.598)r^2 ....instead of the (1.3) in the other formula.

Anyway the tank volume with this correction is 80.8 gallons. This is consistant with the approximation.

 

[chesterthehero]

My math for the approximation is right. What is it that asian parents name retarded kids? Oh yeah, Sum Ting Wong.

i just choked on my dr pepper

 

[CHOMPERS]

We're not even going into why Dr. Pepper comes in a bottle.

Actually I was repeating that joke long before I understood it when I was a little kid. No one would explain it to me but adults thought it was hilarious for a little kid to say it.