A rubber hose is attached to a funnel, and the free end is bent around to point upward. When water is poured into the funnel, it rises in the hose to the same level as in the funnel, even though the funnel has a lot more water in it than the hose does. Why? What supports the extra weight of the water in the funnel?
Solution 2DQ Step 1 of 3 : We have an important relationship called Bernoulli’s equation that relates the pressure, flow speed, and height for flow of an ideal, incompressible fluid. When an incompressible fluid flows along a flow tube with varying cross section, its speed must change, and so an element of fluid must have an acceleration. This means that the pressure must be different in regions of different cross section; if it were the same everywhere, the net force on every fluid element would be zero. When a horizontal flow tube narrows and a fluid element speeds up, it must be moving toward a region of lower pressure in order to have a net forward force to accelerate it. If the elevation also changes, this causes an additional pressure difference. Similar thing happens in the given case, at the bent end. Step 2 of 3: That is, p p = (v1 2 v 2) + g(y y ) 1 2 2 2 1 2 1 This is Bernoulli’s equation. It states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the changes in kinetic and potential energies per unit volume that occur during the flow. We may also interpret in terms of pressures, the first term on the right is the pressure difference associated with the change of speed of the fluid. The second term on the right is the additional pressure difference caused by the weight of the fluid and the difference in elevation of the two ends.