The Bernoulli equation is an important principle in fluid dynamics that describes the behavior of an ideal fluid. Here are the basic formulas associated with the Bernoulli equation:

  1. General Bernoulli equation:
    [
    P + \frac{1}{2} \rho v^2 + \rho gh = \text{const}
    ]
    where:
  • ( P ) — liquid pressure,
  • ( \rho ) — density of liquid,
  • ( v ) — fluid velocity,
  • ( g ) — acceleration of gravity,
  • ( h ) — height above the selected level.
  1. Special case for horizontal flow (where ( h ) is constant):
    [
    P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2
    ]
    This equation shows that the sum of the pressure and the dynamic pressure remains constant.
  2. Equation for flow in pipes (if the pipe diameter changes):
    [
    A_1 v_1 = A_2 v_2
    ]
    where:
  • (A) — cross-sectional area of ​​the pipe,
  • ( v ) is the velocity of the fluid in the corresponding section.

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