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:
- 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.
- 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. - 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.