Bernoulli’s Theorem
Bernoulli's Theorem is a fundamental principle in fluid dynamics that describes the behavior of a moving fluid. It is based on the conservation of energy for flowing fluids and can be applied to incompressible, non-viscous fluids in steady flow. The theorem states that:
"For an incompressible, non-viscous fluid flowing in a streamline, the total mechanical energy (sum of pressure energy, kinetic energy, and potential energy) remains constant along any streamline."
Key Concepts:
Pressure Energy: The energy due to the pressure exerted by the fluid.
Kinetic Energy: The energy due to the motion of the fluid.
Potential Energy: The energy due to the height of the fluid in a gravitational field.
Applications:
Airplanes: Bernoulli’s principle explains how an increase in the speed of air over the wings of an aircraft leads to lower pressure on top, helping generate lift.
Venturi Effect: In a pipe with varying cross-sectional areas, the fluid’s velocity increases in narrower sections, leading to a decrease in pressure.
Assumptions:
The fluid is incompressible (its density doesn't change).
The flow is steady (no abrupt changes in speed or direction).
The fluid is non-viscous (no internal friction).
The flow is along a streamline (in a specific path without mixing between different paths of flow).
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