What is Bernoulli equation: Definition and 133 Discussions

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.
Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation. 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 its kinetic energy (dynamic pressure) – occurs with a simultaneous decrease in (the sum of) its potential energy (including the static pressure) 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 ρ g h) is the same everywhere.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.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.

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  1. A

    B What actually is static pressure?

    I’ve been confused about the term static pressure for quite some time. Different sources use very different definitions. From the problems perspective, it’s usually some external pressure. For example we are having a pool with tiny hole on the bottom which makes water level decrease and it flows...
  2. M

    Bernoulli vs. Reynold Transport Theorem Problem for Raincap

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  3. Juanda

    I Exit velocity through a nozzle: Bernoulli vs. Experience

    There is a classical example when teaching Bernoulli equations to get the exit velocity of a fluid leaving through the bottom of a tank. If we consider no energy is lost due to friction, the exit velocity turns out to be ##v=\sqrt {2gh}##. I'm having trouble processing the fact that exit speed...
  4. gamecult

    Bernoulli equation for calculation of water flow

    Hello everyone; Please need some help to check if my calculation are correct (and if possible some explantation) Bernoulli's equation between point 1 and 3 is given by: P_1+1/2 ρv_1^2 + ρgh_1 = P_3+1/2 ρv_3^2 + ρgh_3 P_1 = P_(atm ) v_1= 0 m/s h_1= 0.875 m P_3 = P_(atm ) v_3= ? m/s h_3= 0...
  5. C

    Can you please explain Bernoulli's equation?

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  6. G

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  7. A

    Bernoulli equation and parallel pipe branch

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  8. P

    Bernoulli equation / fluid flow / finding height

    Hi, everyone! Doing some fluid flow/Bernoulli tasks. Ok, so the task is: «A hose with a radius of 0,035m is connected to a nozzle, which reduces the radius of the hose to 0,018m (2). The hose carries (qv) 0,0075 m3/sec and the totalpressure (3) in the wide section (1) is 211 kPA. The density of...
  9. Franklie001

    Engineering Fluid mechanics question and the Bernoulli Equation

    Good afternoon, I am struggling to find the solution at Q2 and Q3. For Q2 the absolute pressure at point 1 is at the bottom of the tank, so do i need to use the formula P=Patm+qgh ? If using this formula I've got a bigger number than 100Pa. Same issue for Q3, isn't the pressure at point 2...
  10. jdgotts

    I Help Regarding Application of Bernoulli in a Boundary Layer

    Hey all, I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied...
  11. F

    Fluid flow inside a cylindrical tank

    Hi, I´m quite lost and would appreciate guidance I have solved for 2 tubes using Bernoulli´s equation before, but now how does it change? Is it really going to rise water level inside? Why?
  12. Dario56

    I Work - Energy Principle Application to Fluid Flow

    In classical and continuum mechanics if we want to find equation of motion of the body we draw force diagram and apply Newton's 2nd law. In continuum mechanics, equation of motion actually refers to a special point of the body known as center of mass (COM) which can be proven by definition of...
  13. Dario56

    I Work - Energy Principle Application to Fluid Flow

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  14. Dario56

    I Bernoull's Equation Derivation From Work - Energy Principle

    Work - Energy principle states that work of resultant force or sum of work of all forces acting on some system equals change in kinetic energy of the system. For inviscid fluid flowing in a pipe such theorem can be used to derive Bernoulli's equation because as fluid flows it is subjected to...
  15. S

    How pressure increases in centrifugal compressor?

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  16. lahanadar

    Cause-effect relation between pressure & velocity

    For a steady, non-viscous and incompressible flow, one can apply both Bernoulli's principle (no potentials) as $$p+\frac{\rho v^2}{2} = p_t$$ where ##p##, ##\rho,##, ##v##, and ##p_t## are static pressure, density, flow velocity, and total pressure, respectively, and continuitiy principle as...
  17. bjarke

    Hagen-Poiseuille vs Bernoulli

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  18. S

    Bernoulli Equation — Discharging water from a partially-filled sealed tank

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  19. F

    Sorry, another Bernoulli equation paradox

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  20. curiously new

    I Laminar-turbulent transition and Reynolds number

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  21. Tymofei

    Pressure Differential in Fluid Dynamics: Why More on the '+s' Side?

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  22. A

    Bernoulli's equation from an elemental fixed streamtube control volume

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  23. rjomega

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  24. S

    Calculate pump height by using the Bernoulli Equation

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  25. nohappy

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  26. acalcstudent

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  27. I

    Bernoulli equation in a closed loop system

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  28. nuclearfireball_42

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  29. F

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  30. S

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  31. Q

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  32. S

    Help with Bernoulli's equation for a central heating system

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  33. A

    MHB Differential Equations - Bernoulli equation

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  34. Logic hunter

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  35. S

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  36. Zahid Iftikhar

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  37. JTC

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  38. J

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  39. E

    How do we use Bernoulli's Principle in this situation?

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  40. Zahid Iftikhar

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  41. S

    Confusion about Bernoulli's Equation & Airplane Wing

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  42. R

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  43. TheRumpus

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  44. U

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  45. S

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  46. M

    Fan Selection for air cooling of a computer

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  47. T

    Is the Bernoulli Equation enough to determine pump selection?

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  48. X

    Bernoulli Equation and Velocities

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  49. T

    Why is Bernoulli's Equation Isentropic

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  50. RMalt

    Evaluate Problems using fluid dynamics

    I have a diagram similar to the following. Water entering the larger end is at 20degreesC. The larger end has a diameter of 8cm and Area 50.26cm2. The small side has a diameter of 3cm and Area 7.0685cm2. The water jet exerts a force of 87N on a flat plate at an unknown distance. Assuming no...