Sunday, August 12, 2012
I made a minor but significant mistake in my calculations. I realized this on my way home as I was driving. It occurred to me that there was something wrong with how I was understanding the flow of water pressure through the cross sectional diameter of the pipe. According to my calculations, the larger the pipe, the stronger the water pressure. This I realized was impossible since the smaller the pipe, the greater the water pressure. Consider putting your finger over a hose when the water is pouring out of the hose. When this is done, the water pressure increases significantly. Therefore, the diameter being smaller should create greater pressure. However, if I plug in a number greater than 12 feet and I square this number, the water pressure will be greater, according to my calculations. This result is of course impossible. Realizing this as I was speeding down the high way, I remembered that I forgot to implement a very important formula. I actually mentioned this formula to find out the water pressure variance at a different part of the pipe were that area of the pipe to be smaller. The formula is as follows: V2=AiVi/A2 In order to find the velocity, we have to divide the cross sectional shape of the pipe by the initial velocity which is 3000 lbs of pressure. This means we have to divide 3k by twelve. The answer is V2=250 lbs of pressure. Now that we know the pounds of pressure that will be squeezed through the cross sectional of this pipe, we can use P=1/2P(Vi-V2) to find the total amount of pressure at this diameter. Since we know that the initial velocity is 3K, and we know that the velocity is 250 pounds per pressure at the pipe that is 4 meters wide, we can plug in the numbers. P=1/2P(Vi-V2)=585 billion lbs of pressure! were you to use a smaller number than twelve to divide by 3K the number would have been smaller and the pressure would be greater!