|MadSci Network: Physics|
Dear Ravi: Thank you very much for your question. Bernoulli's principle is a very interesting topic. Let us consider first what the following site says: http://www.britannica. com/eb/article?eu=80998 Bernoulli's theorem: in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli's theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow. Bernoulli's theorem implies, therefore, that if the fluid flows horizontally so that no change in gravitational potential energy occurs, then a decrease in fluid pressure is associated with an increase in fluid velocity. If the fluid is flowing through a horizontal pipe of varying cross-sectional area, for example, the fluid speeds up in constricted areas so that the pressure the fluid exerts is least where the cross section is smallest. This phenomenon is sometimes called the Venturi effect, after the Italian scientist G.B. Venturi (1746-1822), who first noted the effects of constricted channels on fluid flow. Bernoulli's theorem is the basis for many engineering applications, such as aircraft-wing design. The air flowing over the upper curved surface of an aircraft wing moves faster than the air beneath the wing, so that the pressure underneath is greater than that on the top of the wing, causing lift. Please note that Bernoulli's theorem asks for frictionless motion. Of course this is not the case in the ocean floor, fore example. In this case the fluid is flowing in a turbulent fashion and this causes the apparition of vortices and some other complex motions, because the liquid in contact with the floor will travel at a smaller velocity than the liquid which is just above this first layer. Now, in the following link: http://ldaps.ivv.na sa.gov/Physics/bernoulli.html we find: Bernoulli's Theorem How pressure and velocity interact static pressure + dynamic pressure = total pressure = constant static pressure + 1/2 x density x velocity2 = total pressure = constant General Concept: The Bernoulli effect is simply a result of the conservation of energy. The work done on a fluid (a fluid is a liquid or a gas), the pressure times the volume, is equal to the change in kinetic energy of the fluid. General Facts: Where there is slow flow in a fluid, you will find increased pressure. Where there is increased flow in a fluid, you will find decreased pressure. In a real flow, friction plays a large role - a lot of times you must have a large pressure drop (decrease in pressure) just to overcome friction. This is the case in your house. Most water pipes have small diameters (large friction), hence the need for "water pressure" - it is the energy from that pressure drop that goes to friction. Example: the showerhead A showerhead (if you have a fancy one) has a number of different operation modes. If you go for the "massage" mode, you are moving a little water fast. For the "lite shower," you are moving a lot of water slowly. It takes the same amount of energy to move a little water fast as it does to move a lot of water slowly. This is the amount of energy you have due to your "water pressure". http://ldaps.ivv.nasa.gov/Physics/Images/Engineering_Manual4.gif Some practical problems are considered in the very interesting link: http://www.saj.fi/saj- bernoulli.htm A section I want to highlight says: In a real flow i.e. around an immersed body, friction plays a large role - most of the time when the ship is in service you have a large pressure drop (decrease in pressure) just to overcome friction. For example, if you have a water pipe with a small diameter (large friction), hence the need for "water pressure" - it is the energy from that pressure drop that goes to friction. Example When a liquid runs freely through a pipe of a constant area (B), to which three ascension pipes (D,E,F) are connected, the static pressure will decrease along the dashed line towards the outlet (Fig.1), The pressure decreases as result of friction loss in the horizontal pipe. http://www.saj.fi/images/Pipeflow1.gif Fig. 1 In (Fig.2) the area has been changed in two places, with a thinner pipe at section (G) and a thicker pipe at section (H). The following occurs: Section (G) The resultant constriction causes the liquid to move at a higher speed, increasing the dynamic pressure, with the result that the static pressure in pipe (D) falls below the dashed line. Section (H) In section (H), which has a much larger area, the static pressure rises above the dashed line, the speed of the liquid having decreased due to the larger area, with the result that the dynamic pressure will be decreased. http://www.saj.fi/images/Pipeflow2.gif Fig. 2 A more somewhat more technical discussion could be found in: http://physics.bu.e du/py105/notes/Bernoulli.html I hope this helps Regards Jaime Valencia
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