3The pressure is onWhich is the best design for a dam? Explain your answer.Which dam is more likely to break? Explain your answer.
4Pressure Differential Whiteboard A large cylindrical water tank is sealed with a vacuum on top, and develops a small hole at a depth h below the surface of the water, as shown above. Assuming that atmospheric pressure is 101,000 Pa and the density of water is 1,000 kg/m3, what is the maximum possible depth of the hole that will result in no water leaking out?(A) 10 m (B) 100 m (C) 1,000 m(D) Water will leak out, no matter what.(E) Water will not leak out, no matter what.
5but there is also an inward force caused by the atmospheric pressure! At the hole,there is an outward force caused by the water above the hole creating a large gauge pressure…but there is also an inward force caused by the atmospheric pressure!When the outward gauge pressure (ρgh) from the weight of the fluid matches the inward force from atmospheric pressure, the fluid will be in equilibrium.
6Pressure depends only on depth and density of the fluid! This means that if you have an irregularly shaped container of fluid, any two points with the same depth will have the same pressure
7This is the principle used in hydraulics. P1 = P2A hydraulic lift is a container of fluid with a large cross-sectional area on one end, and a small cross-sectional area on the other.
8Because the pressure is the same at both ends (since they are at the same height), a hydraulic lift acts as a force multiplier!F1/A1 = F2/A2P1 = P2
9(Equal amounts of fluid must be displaced on either side) The only tradeoff is that you will also have to push further in order to lift the larger end.(Equal amounts of fluid must be displaced on either side)
10Why does the liquid stay in the straw when you plug the end? Before lifting it out of the glass, you need to press your finger tightly against the top of the straw.This seals a finite amount of air in the top part of the straw, which is initially at atmospheric pressure.
11However, when you lift the straw… the water level drops!!!Now the same amount of air is occupying a larger space inside the straw, and the pressure inside will be lower than atmospheric pressure!Less than atmospheric pressureAtmospheric pressureIn order for the liquid to stay in the straw, it must be true thatPinside + ρgh = PoutsideThe water level will continue to drop until this equation is satisfiedGauge pressure from the weight of the fluid
16Why does buoyancy exist? As you go deeper into a fluid, the pressure increases.Pressure is isotropic!It pushes inward on all sides of a submerged object.
17Differential Pressure The bottom of the object is at a greater depth than the top of the object.The downward force exerted on the top of the object is less than the upward force exerted on the bottom of the object.
18Buoyant pressure Pbuoyant = Pbottom – Ptop A partially submerged block floating in a liquid.PatmhsubmergedρfluidPtop = PatmPbottom = Patm + ρfluidghsubmergedPbuoyant = Pbottom – PtopPbuoyant = ρfluidghsubmerged
20Determining Buoyant Force VsubmergedhsubmergedρfluidFbuoyant = ρfluidghsubmergedAFbuoyant = ρfluidgVsubmerged
21Fbuoyant = ρfluidgVsubmerged 1) The buoyant force is directly proportional to the density of the fluid.- More dense fluids exert a greater buoyant force!2) The buoyant force is also directly proportional to the amount of volume that is submerged.- The buoyant force depends on the amount of liquid that is displaced by the object.
22Rubber ducky, you’re the one. A 10-g rubber ducky floats in a tub of water at bath time.Draw and label a force diagram for the ducky.How much of the volume of the ducky must be submerged in order for it to float?