![]() In order to answer this question, we'll need to make use of Bernoulli's equation. We're then told that the same fluid begins to move through the pipe at a new speed of, and we're asked to determine what the new pressure will be. In the question stem, we're told that a fluid with a density of moves through a pipe at a speed of and has a pressure of. Put in numbers and solve for the height difference: Since the water is no longer moving, the terms containing are equal to zero. Our points will be on the surface outside the vertical tube (point A) where the pressure is one atmosphere, and inside the vertical tube at the surface of the risen column (point B). This is saying that the pressure inside the tube is below the pressure outside. Finally, as mentioned, we care only about the difference in pressure: The air is still at point A, so the velocity term is zero for the left side. ![]() The heights are the same, so they cancel out of the equation. For the air, choose our two "Bernoulli points": point A is just outside the horizontal tube and point B is just inside. ![]() In this problem we will ignore the atmospheric pressure since it is applied at the tube ends and at the surface of the water outside the vertical tube. The central principle here is that the moving stream of air has a lower pressure than still air. We must do this twice: once for the air and once for the water. We will use Bernoulli's equation to solve this. ![]()
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