Bernoulli

# Bernoulli - previous index next The Bernoulli Effect...

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previous index next The Bernoulli Effect Michael Fowler 6/12/06 Suppose air is being pumped down a smooth round tube, which has a constant diameter except for a section in the middle where the tube narrows down to half the diameter, then widens out again. Assume all the changes in diameter take place smoothly, and the air flows steadily down the tube, with no eddies or turbulence. Question : where in the tube do you expect the pressure to be greatest? Most people asked this for the first time predict that the pressure will be greatest in the narrow portion of the tube. But in fact, if we actually do the experiment, by putting pressure gauges at various points along the tube, we find, counter intuitively, that the air pressure is lowest where the air is moving fastest ! The difference in heights of the dark liquid in the two arms of the U-tubes measures the pressure difference between that point in the flow tube and the outside atmospheric pressure. To see how this could be, we will apply the techniques we developed to find how pressure varied in a stationary fluid. The way we did that, remember, was by drawing a free body diagram for a small cylinder of fluid. Since this small cylinder was at rest, the total force on it was zero, so the net pressure balanced the weight. Now consider a steadily moving fluid. It’s helpful to visualize the flow by drawing in streamlines, lines such that their direction is the direction the fluid is moving in at each point.

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2 Actually, these streamlines not only tell you the direction
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## This note was uploaded on 12/07/2011 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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