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Bernoulli's Principle explanation help

  1. Nov 4, 2007 #1


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    There's a simple explanation that wasn't covered in the last thread about this.

    Start off with an ideal incompressable fluid with no viscosity in a pipe. The flow rate in the pipe is fixed. The amount of mass per unit time moving past any cross section in the pipe is constant, otherwise mass would be accumulating in the pipe.

    The fact that the flow rate is fixed is one of the key factors in this explanation of Bernoulli's principle. The pipe transitions through various diameters. Since the flow rate in terms of mass per unit time is fixed, the mass is traveling faster when the diameter of the pipe is smaller, changing speed in proportion to the cross sectional area.This faster speed means that the kinetic energy of the fluid has increased. The pipe doesn't perform any work on the fluid, leaving pressure differential as the only explanation for the changes in speed that are inversely proportional to cross sectional area. Therefore the pressure in the smaller diameter sections must be less than the larger diameter sections, because it's the pressure differential that peforms work and causes the acceleration and deceleration of the fluid as it transitions between sections of the pipe with various diameters (cross sectional area changes).

    I'll leave to others here to show the math, but if pressure is treated as a form of energy, then the total energy (the sum of pressure and kinetic energy), per unit mass, at any point in the pipe, is constant. So an increase in kinetic energy corresponds to a decrease in pressure energy, and vice versa, keeping the total energy constant.

    For all of this to work requires a closed system. There are no holes in the walls of the pipe that would allow the fluid to escape and/or re-enter the pipe.

    What's missing from this explanation is what is causing the initial and constant flow rate (maybe a pump), and what is going on at the ends of the pipe, but the cause doesn't have to be known, the important thing is that the flow rate is constant.
  2. jcsd
  3. Nov 4, 2007 #2
    Bernoulli's Principle

    For a fluid at rest, the pressure is the same at all points on the same level. However, this is not true when the fluid is moving.

    The pressure in a moving fluid depends on its flow velocity.

    Thus Bernoulli's principle states that In a steady flow of a fluid, the pressure of the fluid increases - and the converse is also true.

    Air, being fluid, has the same characteristics as water and other liquids, and obeys Bernoulli's principle.

    Bernoulli's Principle Applied to Fluid Flow in Tubes

    1. Water flowing in a tube from A to C. The water level is highest at A with decreasing heights at B and C. This is because water flows from a region of high pressure to a region of low pressure.

    2. When a fluid passes through a tube which narrows or widens along its length, the velocity
    of the fluid varies. As the tube narrows, the fluid flows more quickly and, correspondingly,
    pressure in the narrow section decreases.

    E. g. Insecticide Sprayer

    when the plunger is pushed in, the air flows at a high velocity through a nozzle.

    the flow of air at high velocity creates a region of low pressure just above the metal tube. The higher atmospheric pressure acts on the surface of the liquid insecticide causing it to rise up the metal tube.

    the insecticide leaves the top of the metal tube through the nozzle as a fine spray.

    [For all of this to work requires a closed system. There are no holes in the walls of the pipe that would allow the fluid to escape and/or re-enter the pipe.]

    actually there are small narrow tubes connected vertically on the horizontal tube which determine or show the level of water at different regions of the horizontal tube as the water or fluid flows.


    http://home.earthlink.net/~dmocarski/chapters/chapter7/graphics/bnli1.gif [Broken]

    go to both URL above to see diagrams and get a better understanding what I am talking about.

    Not forgetting the flight of an airplane is based on the principle regarding the effect of the flow of air around its wings, which are in the form of an aerofoil.

    When a wing in the form of an aerofoil moves through air, the flow of air over the top has to travel faster to cover a longer distance and creates a region of low pressure. the flow of air below the wing is slower resulting in a region of higher pressure.

    the difference between the pressure at the top and the underside of the wing causes a net upward force, called lift, which helps the plane to take-off.

    In addition to its use in airplanes, aerofoil is also used in racing cars. In this case, the downward force helps to stabilize the car at high speeds. Thus this shows that Bernoulli's principle does not require a closed system as even the motion of air on an aerofoil is not in a closed system.


    http://www.hiflykites.co.za/kite-online-shop/x-zylo-flying-principles-3.gif [Broken]


    Go to the each of the URL above to see the motion of air on an Aerofoil.

    If I may say so my self, I think you have confused yourself between Pascal's and Bernoulli's principle.

    Hope all this Information helps.
    Last edited by a moderator: May 3, 2017
  4. Nov 4, 2007 #3


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    This isn't true. On some civilian aircraft, such as a Cessna, there is a hole in the side of fuselage, called a static port, which leads to an internal chamber, and the chamber's pressure is basically the same as the static (non-moving) pressure of the external air, and it's not affected by air speed of stream flowing across the opening (within the range of air speeds a Cessna experiences, 0 to about 160mph). Pressure within the chamber is used to determine the altitude of the aircraft. There is a maximum airspeed that this hole in the side method works, but it's well above the maximum speed of a Cessna.

    However, put a similarly placed hole in the sidewall of a "closed system" narrowed pipe, and you get venturi effect, and there will be reduced pressure as air flows across the hole. Carburetors and water driven syphons (commonly used for aquarium drainage) use Venturi effect.

    The point here is that a wing operatates in an open environment, in which case the classic Bernoulli example doesn't hold.

    A link to an article that includes info about the static port:

    http://home.comcast.net/~clipper-108/lift.htm [Broken]

    This article also mentions the Coanda effect. Friction of the air with the surface of the wing, combined with viscosity of the air, causes the nearby air to follow the upper surface of a cambered airfoil. However, the article leaves out the "void" effect. When a solid object travels through the air, most of the affected air at the front will seperate and flow around the object, but as the back of the object passes by, a low pressure void is created, and air accelerates towards this moving void. A wing is designed so that with an effective angle of attack, this void is introduced with a mostly downwards component (for lift), while minimizing the forwards component (drag). In addition to the surface effects near the wing, there is also significant acceleration of air away from high pressure areas and towards low pressure areas from much further away. The article mentions this and includes diagrams, and explanations of the actual volume of air (per unit time) that is involved.

    Which brings me to post this link to a picture of a M2-F2, flat top. curved bottom, flying body glider (pre shuttle prototype) and it flies just fine. Alongside is a F104, basically a jet powered missle with small wings. Note that in this picture, the flat top is bascially horizontal.


    The powered version, m2-f3, went Mach 1.6, so it's not as draggy as it looks.

    Last edited by a moderator: May 3, 2017
  5. Nov 6, 2007 #4
    Hello Jeff,

    What is your take on a problem I described in "Bernoulli's spinning-top-cylinder problem" thread ?

    On one hand it looks like a little modified Magnus effect. On the other, there is something disconcerning about getting lift for free.

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