Water is syphoned from the container to a lower place. The flexible hose has a c
ID: 1855849 • Letter: W
Question
Water is syphoned from the container to a lower place. The flexible hose has a constant diameter, and the location differences are h and d from the water level in the container, respectively, to the highest hose location and the lower hose end. (1) If the distance d =20 cm, find the water flow velocity V through the hose. (2) To avoid cavitation (water changes phases from liquid to vapor bubbles when the absolute pressure decreases to the saturation pressure) in the hose, find the maximum height h we can have if the environmental pressure is 100 kPa and temperature is 25C. Take the saturation pressure of water at this temperature as 3.17 kPa.Explanation / Answer
n fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.[1][2] Bernoulli's principle is named after the Swiss scientist Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.[3] Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers. More advanced forms may in some cases be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation). Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ? g h) is the same everywhere.[4] Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamlinen most flows of liquids, and of gases at low Mach number, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible and these flows are called incompressible flow. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is: (A) where: is the fluid flow speed at a point on a streamline, is the acceleration due to gravity, is the elevation of the point above a reference plane, with the positive z-direction pointing upward
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