Water in a Horizontal TankDate: 8/7/96 at 18:55:50 From: Michael Sheena Subject: Volume of Water in Side-ways Cylinder Hi, I'm trying to find the partial volume (in gallons) of a cylinder-like tank that is 72" long AND 36" diameter. Here's what I used to find the TOTAL volume (I am assuming that 231 cubic inches equal a gallon): ((pi*324)72)/231 = 317.26 gallons But now let's say that the cylinder is only filled up to 4.25" In other words, the diameter of the tank being 36", only 4.25" of that is filled with liquid running the entire 72" length of the tank. Do I halve 4.25" and plug that radius into that equation, which would equal 4.42169 gallons? Do I shorten the tank from 72" to 4.25", which would equal 17.7272 gallons? Or do I divide 4.25" by 36" to get a percentage of the tank and then take that percentage of 317.26 gallons for a total of 37.45430556 gallons? Or am I all wet? Date: 8/7/96 at 20:45:22 From: Doctor Robert Subject: Re: Partial Volume of a Cylinder In other words, you are trying to find the liquid volume of a cylinder whose axis is parallel to the ground. I worked out this problem many years ago and it involves a lot of calculus. Here is the general way to work it. Look at the end face (the circular face) of the cylinder and try to calculate the area which is covered by the liquid. Then multiply this area by the length of the cylinder. I believe that you'll need some calculus to find that area. The volume is definitely not a linear function of the height, because the cross section is circular, not rectangular, so taking a percentage of the diameter would not give the correct answer. If you want a calculus answer, please write back. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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