Volume of water in a cylinder

[Daysleeper]

OK this isn't strictly a computer/internet issue but as this is the cleverest forum here :E

I have a cylindrical water tank (on its side). Its 1210 mm in diameter and 3000mm long. Contains aprox 3000l of water. I need to try to calculate the volume of water in the tank at various depths. Obivously at 605mm its half full so thats an easy 1500 litres.
I've googled a few sites including one that came up with

A = pi*a^2/2 - a^2*arcsin(1-h/a) - (a-h)*sqrt(h(2a-h))

(a = radius, h= height of water)

But my head is starting to hurt and i'm not sure why.

Is there a simpler way?

[jetcollie]

Try this:

http://www.migrant.org/assets/math/scripts/cylinder_volume.html

[Daysleeper]

superb thanks, I knew someone would have an answer but boy that was quick:ok:

[el @]

Wikipedia is your friend.
http://it.wikipedia.org/wiki/Cilindro_(geometria)

the formula is the one at the bottom.

[NutLoose]

want another clever little measurment? Ok say you have 2 odd size round pipes carrying a fluid be it gas or other....... and you want to replace it with one to carry the same amount............ measure the diameter across the pipes internally, draw a right angled triangle using the dimensions of the pipes on both 90 degrees angles of the right angled triangle.............. the long diagonal side of the triangle is the internal diameter of the pipe you need to replace the two :)

[Saab Dastard]

Where's Pythagoras when you need him, eh? :D

[AerBabe]

I think he gave up maths and went to work as a plumber. Certainly pays better!

[airborne_artist]

I think he gave up maths and went to work as a plumber. Certainly pays better!

But not before he helpfully arranged it that one 22mm pipe carries the same amount of fluid, given equal pressure, as two 15mm pipes.

[ORAC]

The Indian mathematician Baudhayana (http://www.answers.com/topic/baudhayana)proved the theorem around 800 BC, 300 years before Pythagoras. Johnnie come lately them Greeks.

You got a maths problem, just call the Indian restaurant and ask them to send the answer round.

Mind you, the Chinese take-away will probably claim to be able to get it to you within 30 minutes.....

[The SSK]

You got a maths problem, just call the Indian restaurant and ask them to send the answer round.

Did that, I asked for a 23 plus a 48 and they delivered a 71.

[n90bar]

Ok maybe I'm barking up the wrong tree but the formulae I would use would be -

Pi X Radius squared X height

[Saab Dastard]

Ok maybe I'm barking up the wrong tree but the formulae I would use would be -

Pi X Radius squared X height

Fine, but the original question was about the cylinder on its side.

[Coconutty]

I asked for No.6 at my chinese and they sent me a pack of cigarettes :rolleyes:

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

... on its side ? - That'll be "pi r squared" times length then :ok:

... Then again you could always replace the tank with a square section one ;)

http://i34.photobucket.com/albums/d129/coconut11/coconut.jpg
Coconutty

[Keygrip]

Don't need the Greeks - there's a way around everything

If the cylinder is not sealed - pour the water into a measuring jug.

If the cylinder is sealed (which I guess it must be if it's lying on its side and still has the same volume of water in it)....what difference does it make how much is in it? Why do we care (we can't do anything about it)?

[Daysleeper]

If the cylinder is sealed (which I guess it must be if it's lying on its side and still has the same volume of water in it)....what difference does it make how much is in it? Why do we care (we can't do anything about it)?

The reason we care is that the cylinder contains the rainwater that is used to flush my loos and wash my clothes. Thus I would like to have a rough idea at what depth of water I should set my system to add mains water so that I dont end up leaving a huge floater in the loo.:\

[Keygrip]

Ahhhhhhhhhh - got you now.

Call the Greeks.

[Loose rivets]

So, is the first calculation in IMP or US? Galls :confused:

Oh, and is there a link for cubes of fluid?

[AerBabe]

How many quarts in a mile?!

[Coconutty]

OK, here we go : I will try and make this sound far more complicated than it really is ;)

The information you need to work out the volume of liquid in your tank is :

1) The Radius of the cylinder ( Half the diameter :rolleyes: )
2) The Width of the cylinder ( or Length if you prefer )
3) The depth of the water in it

Assume the tank is less than half full :

Looking end on the shape formed by the water is a "Segment" as represented by the green area :
http://i34.photobucket.com/albums/d129/coconut11/WaterTank.jpg

The depth of water is the height of the segment represented by Line E-D ( also known as the "Sagitta" ) so you need to make up a dipstick or other method of measuring the depth of water left in the tank.

Go to this web site : Daysleeper's Tank Calculator (http://www.1728.com/circsect.htm)

Check the option for knowing the Radius and Segment Height, fill in the details and click "Calculate" All you need to do then is multiply the answer by the Width ( or Length ) of the tank and you have the volume of water in it.
If the tank is more than half full ( a bit like my Glass :cool: ) then work out the total volume of the tank using "PI x R squared x Width ( or Length )" and halve the answer. ( To get the volume of the bottom half of the tank.

Then perform the segment calculation for the top half of the tank - remembering this time that when you dip the tank, the dry bit will be the segment height ! You need to calculate the dry segment area and subtract it from the volume of a half full tank, then add it it to the bottom half of the tank and multiply it by the Width ( or Length ) to get the total volume.
( Or better still wait until the tank is less than half full :8 )

After a few calculations at various depths you can mark your dipstick ( If you'll excuse the phrase ) and you're done :D

http://i34.photobucket.com/albums/d129/coconut11/coconut.jpg
Coconutty

Edited to sort the typo's and to add :
a huge floater - I think I might know him :p

[curmudgeon]

The reason we care is that the cylinder contains the rainwater that is used to flush my loos and wash my clothes. Thus I would like to have a rough idea at what depth of water I should set my system to add mains water so that I dont end up leaving a huge floater in the loo.

If you're depositing a huge floater (pre flush), shouldn't you be worrying about your own internal plumbing rather than that of your residence?

[Daysleeper]

If you're depositing a huge floater (pre flush), shouldn't you be worrying about your own internal plumbing rather than that of your residence?

Actually I do have some issues with my internal plumbing, comes from having surgery for chronic bowl disease so the reliability of my household plumbing is of moderately high importance. :uhoh:

coconutty

thanks for the reply, it will take me a day or two to figure out what it means!

[Memetic]

...not getting a vertical tank :-)

[Daysleeper]

..not getting a vertical tank :-)

no but I do regret not finding a SQUARE one :sad:

I wonder if theres an ebay market for slightly used cylindrical tanks......

[Brakes on]

Does nobody remember the rule of three?

If 1210 mm give 3000l, then 1mm gives 3000/1210.

500 mm then gives 3000/1210 x 500, etc., etc.

:D

[el @]

Brakes on, outstanding first post, hello, the tank is a CYLINDER laid down HORIZONTALLY.

[jetcollie]

I'm surprised that you haven't sat down in front of the computer with a length of wood or metal rod and calibrated yourself a dipstick from the link in my post #2.

[Brakes on]

el @,
obviously brakes were off :uhoh: . Can somebody help me to get the egg off my face?

[maxter]

Fine, but the original question was about the cylinder on its side.

Stand the B... thing on it's end then:E