Bernoulli's Theorem

Bernoulli's Theorem

For an ideal fluid, total mechanical energy per unit volume remains constant along a streamline.

### Formula

$$P+\frac{1}{2}\rho v^2+\rho gh=constant$$

### Between Two Points

$$P_1+\frac{1}{2}\rho v_1^2+\rho gh_1=P_2+\frac{1}{2}\rho v_2^2+\rho gh_2$$

### Terminologies

- P → Pressure energy per unit volume.

- ρ → Density of fluid.

- v → Fluid velocity.

- h → Height above reference level.

- g → Acceleration due to gravity.

### Conditions / Special Cases

Bernoulli equation is valid when:

- Fluid is incompressible.

- Flow is steady.

- Flow is non-viscous.

### Usage

- Used in fluid flow, pipes, and aerodynamic problems.