Lecture on Bernoulli's Equation

Introduction

Bernoulli's Equation: A fundamental principle in fluid dynamics.
Describes relationship between pressure, velocity, and elevation of a flowing fluid.
Published by Daniel Bernoulli in 1738.
Used to explain phenomena such as lift in airplanes and fluid drainage rate.

Static Pressure: Pressure P of the fluid.
Dynamic Pressure: Function of fluid density (Rho) and velocity (V); represents kinetic energy per unit volume.
Hydrostatic Pressure: Pressure due to gravity; involves gravitational acceleration (G) and elevation (H).
Conservation of energy: Sum of pressure energy, kinetic energy, and potential energy remains constant along a streamline.

Flow Through Pipes: Change in pressure as fluid moves through varying diameters.
- Assumptions: incompressible fluid, equal mass flow rate at different points.
- Continuity Equation: Conservation of mass; relates cross-sectional area and velocity.
- Increase in velocity leads to decrease in pressure (Bernoulli's Principle).
Airfoil Lift: Difference in fluid velocity over and under a wing creates pressure difference, generating lift.
Bunsen Burners: Gas flow at high velocity creates low pressure, drawing air in for combustion.
Flow Measurement Devices:
- Pitot-static Tube: Measures airspeed by comparing stagnation pressure and static pressure.
- Venturi Meter: Measures flow rate through pressure drop across converging section of pipe.
Gravity-fed Systems: Calculating flow speed of liquid from containers like a beer keg.

Assumptions in Derivation:
- Laminar and steady flow.
- Inviscid flow (negligible shear forces).
- Incompressible fluid behavior.
Adapted versions exist for unsteady and compressible flows.

Bernoulli's Principle is a vital tool for engineers.
Recognizing scenarios where it applies helps solve various fluid dynamics problems.