We have a pond and want to prove that it is not divided in two because of a pipe that helps water flow?

Question

We want to prove mathimatically,statistically,ecologically or in any way,that a half acor pond remains one and is not devided in two because of an 8 foot diameter pipe.The pipe is 4 foot underwater and 4 foot above and is covered with a bridge.The purpose of this pipe is to equalize the water flow.This project is not made yet and if need to, the pipe could be bigger.How do we prove this pond is still considered one???

Answer 1

WELL, NOT JUST BECAUSE YOU HAVE A PIPE BETWEEN THE TO SUPERFICIAL HALVES THAT YOU CAN SAY YOU HAVE ONE POND. AT ANY TIME YOUR PIPE CAN GET CLOGGED WITH SEDEMENT AND VOILA...YOU'RE BLOWN OUT OF THE WATER...

Answer 2

Well first of all, you should realize that the pond is infact divided in 2 in a few ways. Tree's shedding leaves into one half of the pond will no longer float to the other side. Similarly, animals travelling on the surface of the water (such as ducks) will not be able to cross the pipe. And visually, the pond is definitely cut in 2!

That being said, you can prove that the body of water itself will remain equal in composition on both sides of the pipe, given that water can slip UNDER the pipe. Sampling of water from different regions around each half of the pond can be used to statistically prove the water is with a finite probability "the same."

Been a while since I did this type of statistics problem, but I believe you are looking for something like this to prove your point:

1. take samples of water on one side of the pipe as follows:
sample right next to the pipe
sample 10 feet from the pipe
sample 20 feet from pipe
sample 30 feet from pipe
..... until you reach the edge.

2. take same samples on OTHER side of the pipe.

3. TO PROVE that the pipe ISNT making the two sides' water different, you must show:

variation in opposite-side samples is on-average less than or equal to variation on same-side samples. increased sample size will help bring up the strength of "on average"

Answer 3

well, the simple answer is to put somehting traceable (i.e. food coloring) on the one side and then test the other side for that varible. if you have a lot of food coloring then you could dump some in.