Water displacement inside container

I would say a 6" x 64 would hold the same as 8" x 36

sqrt (36/64) x 8" = 0.75 x 8 = 6"

And 4²/3² is the same ratio as 64/36.

A bladder may not be limited to a uniform 6".

Formula here: http://wiki.answers.com/Q/How_do_you_calculate_volume_of_a_pipe

Thanks guys.

I calculated the volume of the 8" x 36" container, and arrived at 7.83 cubic inches. The question now is how do I convert this to weight capacity?

Weight equals volume times density. Density of water is normally taken to be 1 gram per cubic centimeter or 0.036 lb per cubic inch.

BTW, does 7.83 cubic inches seem like a reasonable volume for your container?

First of all, you cannot have a cylindrical container 8" diameter and 36" tall holding 75lbs of water. The volume of the cylinder is A_b*h where A_b = area of base and h = height.

A_b = pi*d²/4

So Volume = pi*h*d²/4

Volume of 8" dia. x 36" tall container = 1809 in³ = 1.047 ft³. If filled with water, this would weight about 65 pounds.

If you want a 64" tall cylinder to hold 75 pounds of water, its volume = 75/62.4 = 1.20 ft³ or 2077 in³.

So, pi*64*d²/4 = 2077 and d = √[2077*4/(64*pi)] = 6.43 in.

Check it! pi*64*6.43²/4 = 2078 in³. okay.

Weight at case 1 = Weight at case 2

(Π/4) d² x l x Ρ = (Π/4) D² x L x Ρ

where Ρ = water density

(Π/4) (8)² x 36 x Ρ = (Π/4) D² x 64 x Ρ

D² = (8)² x 36 / 64

D = 6"

Note. This simple solution is based on a consideration that the water container is cylindrical with flat heads. If the container is furnished with other type of heads, e.g. elliptical, the diameter D shall have another figure than 6".

OK. Let's see:

Water weighs 62.4# per cubic feet. (here in the U.S.) So, the 75 pounds of water would be 1.202 pounds. Save that.

Next, the cylinder in which you are holding the water is 8" diameter x 36" tall. Therefore, first of all it won't hold the 75# of water. The volume of that cylinder is only 1.o47 cubic feet.

V= (pi)(D/2)sq(H) with H=3', D=.66667' and pi = 3.141592 so:

V = 1.047 cubic feet. This is less than 75 pounds of water. This would be 65.33#.

The bladder that you describe is 5.333 feet tall and holds (let's take the 75 pounds of water) 1.202 cubic feet. Therefore, the volume would be 1.202 cubic feet, the height would be 5.333 feet and the radius would be D/2. Therefore, the diamter of this bladder would be .13496 feet or 1.6295 inches. This is all in US terms and figures. You can do the easy part and convert it to metric. What I can't figure out is what are you using a bladder that is about 1-5/8" diameter x 5' - 4" long for?

Actually, I made a mistake as I am sure someone has already noticed. I forgot to convert to inches in my computation. The actual diameter would be 6.15 inches. I am embarrassed! Accept my appologies.

Thanks to all for their imput!!

My question is now as follows:

How do I calculate the cylindrical container's diameter and height if I know it must contain 1,937.63 cubic inches of volume?

There is more than one answer. In fact, there are an infinite number of answers. You would solve the equation V = πd²h/4 = 1937.63 or d²h = 2467.07.

If d = 6, h = 68.53

If d = 8, h = 38.55

if d = 10, h = 24.67

BA/AEL - where does the 4 come from?

The volume of a cylinder is A*h where A = area of circle and h = height.

The area of a circle is πd ²/4 where d is the diameter.

So the volume of a cylinder is πd²h/4.