Knowing the formulas found inside the special boxes within this chapter is beneficial as it helps solve problems found in the exercises, and other mathematical skills are strengthened by properly applying these formulas. What we are actually concerned with is the ability to solve certain problems by first approximating the solution, then refining the approximation, then recognizing if/when this refining process results in a definite integral through a limit. Work done by a variable force is important, though measuring the work done in pulling a rope up a cliff is probably not. We are not truly concerned with an ability to find fluid forces or the volumes of solids of revolution. We end this chapter with a reminder of the true skills meant to be developed here. Let us calculate the pressure exerted on the bottom by the weight of the fluid.\(\require\) Its bottom supports the weight of the fluid in it. The difference is that water is much denser than air, about 775 times as dense.Ĭonsider the container in Figure 1. You may notice an air pressure change on an elevator ride that transports you many stories, but you need only dive a meter or so below the surface of a pool to feel a pressure increase. In this case, the pressure being exerted upon you is a result of both the weight of water above you and that of the atmosphere above you. Under water, the pressure exerted on you increases with increasing depth. This pressure is reduced as you climb up in altitude and the weight of air above you decreases. At the Earth’s surface, the air pressure exerted on you is a result of the weight of air above you. If your ears have ever popped on a plane flight or ached during a deep dive in a swimming pool, you have experienced the effect of depth on pressure in a fluid. Calculate density given pressure and altitude.Explain the variation of pressure with depth in a fluid.
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