# Bernoulli's Principle

by democritus
Tags: bernoulli, principle
 P: 4 This isn't really a homework problem, but my physics teacher was going over a test review and he made up some numbers on the spot for a problem involving Bernoulli's equation and a building. The specifics were, A water pipeline with the water under a pressure of 5 atm is being pumped into a building through a pipe of radius .2m with a velocity of 5 m/s. The pipe then proceeds to climb the 20m tall building and narrow to a radius of .02m. What is the pressure and velocity of the water at the top of the building? Now it makes sense to me to take the ratio of the areas, which ends up being 100:1 and applying it to the equation of continuity, giving me a velocity of 500 m/s at the top. When I plus this into Bernoulli's equation, 506500 + .5(1000)(5)^2 + 0(9.8)(1000) = P2 + (.5)(1000)(500)^2 + (20)(9.8)(1000) And I end up with the wonderful pressure of around -1.2 x 10^8 Pascals, which obviously can't be the real pressure for the water. I've been racking my brain trying to figure out why exactly this situation is impossible, assuming that water is an ideal nonviscous incompressible fluid. So I can't figure out why in the real world, the pressure should turn out to be some negative number, and it seems like this would happen for any large differences in velocity in Bernoulli's equation. I've been looking around for an explanation of this, as our AP Physics class spent half an hour trying to reason out logically why this would happen, and our Physics teacher couldn't explain it either. Any help would be greatly appreciated. -J Stoncius
 Sci Advisor P: 882 The first thing that came to mind when you found a negative pressure was that the water couldnt get that high under those conditions, and after a few calculations, I might have been onto something. Assuming you filled the entire 20 meter pipe with a radius of .2 meters with water, that comes out to be 2.52E6 mL of water. That water is heavy, it has a mass of 2520 kg! So it weighs 24621.2 Newtons. This weight is distributed on the new water trying to come up the pipe, the water on top is exerting a pressure downward on the water on bottom. To find the downward pressure, P = F/ A, 24721.2 Newtons / .126 meters squared = 196.2 kPa = 19.4 atmospheres of pressure downward. Remember, the water at the bottom is only being pushed up at 5 atmosphers. So using my logic, the water is too heavy to reach all the way up the pipe to squrit out the top if it is only being pumped up at 5 atm.
 Sci Advisor P: 5,095 That is probably correct after a quick run through of your equation. Like Mrjeffy stated, that negative pressure is needed to obtain that flowrate under those conditions. Since the pressures are stated in gauge pressures, the negative sign indicates that you would need a slight vacuum source to help pull the water to those conditions at the other end, i.e. atmospheric pressure minus your answer.
 P: 4 Bernoulli's Principle 101.3kPa = 1 atm...not 10.13. The downward pressure of the water is only about 2 atm. (Water increases 1 atm in pressure about every 10.34m in depth). So it's not that there isn't enough pressure, the pressure actually runs around 3atm gauge... So I guess we're back to the drawing board... -J Stoncius