{"id":2590,"date":"2024-03-05T15:29:17","date_gmt":"2024-03-05T14:29:17","guid":{"rendered":"https:\/\/www.bf-hydraulik.com\/encyclopedia\/bernoullis-equation\/"},"modified":"2026-04-15T10:52:05","modified_gmt":"2026-04-15T08:52:05","slug":"bernoullis-equation","status":"publish","type":"encyclopedia","link":"https:\/\/www.bf-hydraulik.com\/en\/bernoullis-equation\/","title":{"rendered":"Bernoulli’s Equation"},"content":{"rendered":"\t\t
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Bernoulli’s Equation<\/strong><\/h1>

Bernoulli’s equation is an adaptation of the general law of conservation of energy<\/a> to hydraulic systems<\/a>.<\/p>

The law of conservation of energy<\/a> states that the amount of energy in a closed system remains constant. The form of the energy is irrelevant. Consequently, energy is not “generated” or “consumed,” but is always only converted from one form into another. <\/p>

Bernoulli’s Equation: The Law of Conservation of Energy<\/h2>

A fundamental distinction is made between “potential” or “static” energy and “kinetic” or “dynamic” energy.<\/p>

An example:<\/strong>
A boulder resting on the top of a mountain has a mass (m) and is located at a height (h). Furthermore, acceleration (a) acts upon it—in this case, the force of gravity (g).
Therefore, the description of potential energy is also written as “m ·<\/strong> g ·<\/strong> h.” <\/p>

If the boulder now rolls down from the mountain peak, it converts the previously “stored” potential energy into kinetic energy. This is described as “1\/2 m ·<\/strong> v².” Thus, if the velocity and the height of the peak are known, the mass of the rock can be inferred, and vice versa. <\/p>

The formula for the law of conservation of energy<\/a> generally states:<\/p>

m · h · g = 1\/2 m · v²<\/strong><\/p>

The law of conservation of energy<\/a> can be applied to practically all other energy systems. It is only in particle physics that it is no longer sufficient to explain the phenomena prevailing there. <\/p>

Applied Law of Conservation of Energy for Hydraulic Systems<\/h3>

Bernoulli’s equation transfers the law of conservation of energy<\/a> to hydraulic system<\/a>s. For it to be applicable, two conditions must be met: <\/p>

  1. The system is completely filled with an incompressible fluid.<\/li>
  2. The flow in the system is friction-free.<\/li><\/ol>

    These conditions exclude interfering factors. <\/strong><\/p>

    For the example of a downpipe, Bernoulli’s equation is:<\/h3>

    E = m\/2 · v² + p · V + ϱ(rho) · h · g = Constant<\/strong><\/p>

    E = Specific total energy in the closed system (J=Nm)
    v = Flow velocity (m\/s)
    p = Pressure (N\/m²)
    V = Volume (m³)
    ϱ (rho) = Density of the hydraulic fluid (kg\/m³)
    g = Gravitational acceleration (m\/s²)
    h = Height of the fall (m)<\/p>

    For technical reasons, the values g, h, and v can be replaced by other factors, such as the delivery rate of a drive pump.<\/p>

    Application of Bernoulli’s Equation<\/h3>

    Essentially, this equation explains a curious effect that occurs when the cross-sections of pipelines change.<\/p>

    Along the streamline—the centerline of a fluid flow—pressure and velocity change along a line depending on the cross-sections of the tubes.<\/p>

    In a closed system (Condition 1) with incompressible fluid (Condition 2), the same volume per unit of time must always pass every point in the system. It follows that in a constriction, the velocity of the fluid increases, and it decreases when the cross-section widens. <\/p>

    Additionally, a remarkable effect occurs: although the velocity increases as the cross-section narrows, the pressure at this point drops. Likewise, it rises again when the cross-section widens in the next pipe section. This effect is explained by Bernoulli’s equation and can be derived from it. <\/p>

    In practice, the velocity and pressure behavior of fluids in closed hydraulic system<\/a>s can be calculated exactly in this way.<\/p>

    This is very important for the design of wall thicknesses, seals, tightening torques, and many other factors. Hydraulic system<\/a>s can thus be designed for optimized purposes and reinforced accordingly at critical points. In summary, Bernoulli’s equation is part of the basic knowledge of every hydraulics specialist. <\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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