Volume of Water Passing through a Pipe
Date: 08/12/97 at 16:35:15 From: veronica Subject: Volume My husband asked me if I remembered the math formula for "volume". I searched with Infoseek and found you. Can you help? Thank you, Veronica from Tennessee
Date: 08/12/97 at 17:48:33 From: Doctor Mike Subject: Re: Volume Hi Veronica, This is sort of a tough one because there are so MANY answers. The volume of a rectangular box is Width times Length times Height. Make sure you use the same units consistently. For instance, if the box is 1 foot by 2 feet by 3 inches, then you have to do some conversion. If you use feet, the answer will be 1*2*(1/4) cubic feet. If you use inches, the answer will be 12*24*3 cubic inches. The volume of a "tin can" cylinder is pi*R*R*H where R is the radius of the circle at the end, H is the height, and pi is that famous number 3.1415926535898............ So, maybe I accidentally picked the ones you were interested in, but if not, write back and say what shape you want to find the volume of. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 08/12/97 at 18:14:56 From: veronica Subject: Re: Volume Thanks Dr. Math, I bet you are still laughing at this Tennessee farm girl. I mis-spoke the question. Perhaps I can re-state: The situation: I have a 12" cylinder pipe under a bridge in my meadow that flood water sometimes passes through. My husband wants to know how many gallons of water per minute this pipe can handle. Somehow I thought there was a formula for this. I know length of the pipe....resistence.....water pressure all factor into this. I just don't know how to answer him. Thanks again for your help. Veronica
Date: 08/12/97 at 19:23:01 From: Doctor Mike Subject: Re: Volume >I bet you are still laughing at this Tennessee farm girl. Never ! Let's start with the easy part. Assuming the 12" is the inside diameter of the pipe, the radius is 6, and the radius squared is 36. The area of the circular pipe opening is then 36*pi square inches. Pi is about 3.1415926535898 - or just use the "pi key" on your calculator. This comes out to about 113 square inches. One square foot is 144 square inches, so the cross-sectional area of this pipe is less than one square foot. Multiply that cross-sectional area by the length of the pipe to get the volume in cubic inches of the pipe. This just tells how much the pipe will hold. This says nothing about through-put. In fact, the diameter is the important thing, not the length. >I know length of the pipe....resistence.....water pressure all factor >into this. You bet, there are a lot of variables. The most important is how fast the water is moving. If it is a real gully-washer you might be able to assume that the pipe stays completely full. Reasonable? If you assume that the water flows through this circular opening at the rate of, say, 3 feet per second, then the volume of water flowing through the opening is the same as the volume of water that would fit into a 3-foot-long cylinder with radius 6. That volume would be pi*6*6*36 = 4071.5 cu. in. or 2.356 cu. ft. This would give it a flow capacity of 2.356 cu. ft. per second, or about 141 cu. ft. per minute. Keep in mind that I have made a lot of assumptions for my sample calculations. Also I used the fact that there are 12*12*12 = 1728 cubic in. per cubic foot. If you want to get wet you could go out there during some storm and try to roughly measure the speed of the water. Put a leaf into the water and count "one thousand and one, one thousand and two" etc., to roughly measure how long it takes to flow a certain measured distance. Then observe whether our assumption of a 100 percent full pipe is correct. If it looks as if it never gets much above 2/3 full then you would decrease the through-put correspondingly. >I just don't know how to answer him. Say, "it depends", and you need some empirical data that it would be real nice of him to help you gather. Let us know if you need to ask anything more as you get closer to the answer. The effects of resistance or swirling water within the pipe are much beyond this straightforward type of analysis. Good luck. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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