BERNOULLI’S EQUATION

PRERNA FOR IAS

BERNOULLI’S EQUATION

1. Bernoulli’s Equation

Bernoulli’s Equation is a fundamental principle in fluid mechanics that relates pressure, velocity, and height in a flowing fluid. It states that the total mechanical energy of a fluid remains constant along a streamline. The equation explains how changes in speed affect pressure and is widely used in engineering.

2. Volume Flow Rate

Volume flow rate is the volume of fluid passing through a cross-sectional area per unit time. It is represented by the formula Q = A × v, where A is the area and v is the fluid velocity. It helps measure fluid movement in pipes, rivers, pumps, and hydraulic systems.

3. Incompressible Liquids

An incompressible liquid is a fluid whose density remains nearly constant during flow. Although the shape of the fluid may change while moving through pipes or channels, its volume remains the same. Water is commonly treated as incompressible in fluid mechanics, simplifying calculations and engineering applications.

4. Continuity Equation

The Continuity Equation expresses the conservation of mass in fluid flow. For an incompressible fluid, the product of cross-sectional area and velocity remains constant, represented as A₁V₁ = A₂V₂. When the pipe narrows, velocity increases; when the pipe widens, velocity decreases. It is widely applied in hydraulics.

5. Work in Fluid Flow

Work in fluid flow is performed when pressure forces move a fluid from one location to another. The work done depends on the pressure difference and the volume of fluid displaced. This concept helps explain energy transfer in flowing liquids and forms an important part of Bernoulli’s derivation.

6. Work-Energy Theorem in Fluids