Bernoulli's Principle
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A Bernoulli's Principle is a Fluid Dynamics principle that ...
- See: Newton's Laws of Motion#Newton.27s Second Law, Ordinary Differential Equation, Fluid Dynamics, Pressure, Fluid, Potential Energy, Daniel Bernoulli, Hydrodynamica, Incompressible Flow, Lift Flow.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Bernoulli's_principle Retrieved:2017-10-24.
- In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. [1] [2] The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation ; there are different forms of Bernoulli's equation for different types of flow. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may 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 energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid – implying an increase in both its dynamic pressure and kinetic energy – occurs with a simultaneous decrease in (the sum of) its static pressure, potential energy and internal 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) is the same everywhere. [3] Bernoulli's principle can also be derived directly from Isaac Newton's Second Law of Motion. 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 streamline.[4] [5] [6] Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest. [7]
- ↑ Clancy, L.J., Aerodynamics, Chapter 3.
- ↑ Batchelor, G.K. (1967), Section 3.5, pp. 156–64.
- ↑ Streeter, V.L., Fluid Mechanics, Example 3.5, McGraw–Hill Inc. (1966), New York.
- ↑ "If the particle is in a region of varying pressure (a non-vanishing pressure gradient in the -direction) and if the particle has a finite size, then the front of the particle will be ‘seeing’ a different pressure from the rear. More precisely, if the pressure drops in the -direction (< 0) the pressure at the rear is higher than at the front and the particle experiences a (positive) net force. According to Newton’s second law, this force causes an acceleration and the particle’s velocity increases as it moves along the streamline... Bernoulli's equation describes this mathematically (see the complete derivation in the appendix)."
- ↑ "Acceleration of air is caused by pressure gradients. Air is accelerated in direction of the velocity if the pressure goes down. Thus the decrease of pressure is the cause of a higher velocity."
- ↑ " The idea is that as the parcel moves along, following a streamline, as it moves into an area of higher pressure there will be higher pressure ahead (higher than the pressure behind) and this will exert a force on the parcel, slowing it down. Conversely if the parcel is moving into a region of lower pressure, there will be an higher pressure behind it (higher than the pressure ahead), speeding it up. As always, any unbalanced force will cause a change in momentum (and velocity), as required by Newton’s laws of motion." See How It Flies John S. Denker http://www.av8n.com/how/htm/airfoils.html
- ↑ Resnick, R. and Halliday, D. (1960), section 18-4, Physics, John Wiley & Sons, Inc.