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Formulas

Bernoulli's Equation

Conservation of energy for steady, incompressible, inviscid flow.

Physics
Subject
Fluid Mechanics
Sub Subject
Fluid Dynamics
Chapter
Bernoulli's Principle
Topic

Bernoulli's Equation

📊 intermediate
$$P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$$
Conservation of energy for steady, incompressible, inviscid flow.
Variables & Units
$P$
Pressure
Unit: $\text{Pa}$
$\rho$
Fluid density
Unit: $\text{kg/m}^3$
$v$
Flow speed
Unit: $\text{m/s}$
$g$
Gravitational acceleration
Unit: $\text{m/s}^2$
$h$
Height above reference
Unit: $\text{m}$
Key Information
📐 Derived From
Euler's equation and streamline integration
💡 Example
Water ($\rho=1000\,\text{kg/m}^3$) flowing at $v_1=2\,\text{m/s}$, $P_1=200\,\text{kPa}$, $h_1=0$. At $h_2=5\,\text{m}$, $v_2=4\,\text{m/s}$: $P_2 = P_1 + \frac{1}{2}\rho(v_1^2 - v_2^2) - \rho gh_2$.
🔧 Applications
Aircraft wings, Venturi meters, blood flow
⚠️ Constraints
Steady, inviscid, incompressible, along streamline

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