Bernoulli equation

Bernoulli equation . Bernoulli’s principle, also called the Bernoulli equation or Bernoulli’s Trinomial, describes the behavior of a fluid moving along a streamline. It was exposed by Daniel Bernoulli in his work Hydrodynamics ( 1738 ) and expresses that in an ideal fluid (without viscosity or friction ) in circulation through a closed conduit, the energy that the fluid possesses remains constant throughout its path. The energy of a fluid at any time consists of three components:

  • Kinetic : is the energy due to the velocity of the fluid.
  • Gravitational potential : it is the energy due to the altitude that a fluid has.
  • Power Flow: energy is a fluid containing pressure because it possesses.


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  • 1 Brief history of the equation
  • 2 Formulation of the equation
  • 3 Parameters
  • 4 Applicability
  • 5 Bernoulli effect
  • 6 Sources

Brief history of the equation

The effects derived from Bernoulli’s equation were known to the experimentalists before Daniel Bernoulli formulated his equation; in fact, the challenge was to find the law that would account for all of these events. In his work Hydrodynamica he found the law that explained phenomena from conservation of energy (note the similarity between the form of Bernoulli’s law and the conservation of energy). Later, Euler deduced the equation for a liquid without viscosity in all generality (with the only assumption that the viscosity was negligible), from which Bernoulli’s equation naturally arises when considering the stationary case subjected to the gravitational field.

Formulation of the equation

The following equation known as the “Bernoulli Equation” (Bernoulli Trinomial) consists of these same terms.

1/2 V2 ρ + P + ρgz = constant


  • V = fluid velocity in the section under consideration.
  • g = gravitational acceleration
  • z = height in the direction of gravity from a reference dimension.
  • P = pressure along the stream line.
  • ρ = density of the fluid.



This equation applies to fluid dynamics. A fluid is characterized by lack of elasticity of shape, that is, it takes the shape of the container that contains it, this is because the molecules of the fluids are not rigidly joined, as in the case of solids . Fluids are both gases and liquids . To arrive at the Bernoulli equation, certain assumptions must be made that limit the level of applicability:

  • The fluid moves in a stationary regime, that is, the flow velocity at a point does not vary with time.
  • Fluid viscosity (which is an internal friction force) is neglected.
  • The liquid is considered to be under the action of the gravitational field only.

Bernoulli effect

The Bernoulli effect is a direct consequence that arises from the Bernoulli equation: in the event that the fluid flows horizontally, an increase in the flow velocity implies that the static pressure will decrease.

  • In the case of airplane wings , which are designed so that the air passing over the wing flows faster than the air passing under the wing, so the static pressure is higher at the bottom and the airplane becomes Raise.
  • Airsoft , the replicas used in this game usually include a system called HopUp that causes the ball to be projected by making a circular effect, which increases the effective range of the replica. This effect is known as the Magnus effect , the rotation of the ball causes the flow velocity above it to be greater than below, and with it the appearance of a pressure difference that creates the supporting force, which causes the ball to it takes longer to fall.
  • Chimney , they are high to take advantage of the fact that the wind speed is more constant and higher at higher altitudes. The faster the wind blows over the chimney mouth, the lower the pressure and the greater the pressure difference between the base and the chimney mouth, consequently the better the combustion gases are extracted.
  • Pipe, Bernoulli’s equation, and continuity equation also tell us that if we reduce the cross-sectional area of ​​a pipe so that the velocity of the fluid passing through it increases, the pressure will decrease.
  • Swimming , the application within this sport is directly reflected when the swimmer’s hands cut the water generating less pressure and greater propulsion.
  • Movement of a ball or ball with effect, that is, rotating on itself, deviates to one side. Also due to the well-known Magnus effect, typical is the chopped ball, when the player inserts the instep under the ball causing a rotational effect so that it traces a parabolic path. It is what we know as petroleum jelly.
  • Carburetor of automobile , the pressure of the air passing through the carburetor body, decreases when passing through a constriction. By lowering the pressure, gasoline flows, vaporizes, and mixes with the air stream.
  • Fluid flow from a tank, the flow rate is given by the Bernoulli equation.
  • Venturi devices , in oxygen therapy, most high debit supply systems use Venturi type devices, which is based on the Bernoulli principle


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