Fluid Mechanics
lesson
intermediate
Fluid Mechanics: Bernoulli's Equation & Applications
Understanding Bernoulli's principle, its derivation, and practical applications in pipe flow and hydraulic systems.
Fluid Mechanics: Bernoulli's Equation & Applications β Quick Overview
Get a quick, plain-language overview of this topic.
Bernoulli's Equation
For steady, incompressible, inviscid flow along a streamline:
$$\frac{p}{\rho g} + \frac{v^2}{2g} + z = \text{constant}$$
Where:
- p = pressure
- Ο = fluid density
- v = flow velocity
- z = elevation head
- g = gravitational acceleration
Key Assumptions
- Steady flow
- Incompressible fluid
- No viscous losses
- Flow along a streamline
Applications
- Venturi meters β flow measurement in pipes
- Pitot tubes β velocity measurement
- Orifice flow β culverts and drainage structures
- Pump and turbine analysis
Modified Bernoulli with Head Loss
For real flow with friction losses: $$H_1 = H_2 + h_L$$
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