Glossary
Bernoulli's Equation
A mathematical expression of energy conservation for an ideal fluid, relating its pressure, velocity, and height at two different points along a streamline.
Example:
Engineers use Bernoulli's Equation to calculate the pressure drop in a pipe as water flows faster through a narrower section.
Bernoulli's Principle
A direct consequence of the conservation of energy, stating that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
Example:
The lift on an airplane wing is explained by Bernoulli's Principle, where faster air above the wing results in lower pressure.
Continuity Equation
A statement of mass conservation for fluids, indicating that for an incompressible fluid, the volume flow rate must remain constant through a pipe of varying cross-sectional area.
Example:
The Continuity Equation explains why water speeds up when a wide river flows into a narrow gorge.
Energy Conservation (for fluids)
The principle stating that the total energy within an ideal fluid system remains constant, transforming between pressure, kinetic, and potential energy forms.
Example:
In a closed pipe system, the total energy of the water, including its pressure, speed, and height, remains constant due to Energy Conservation.
Fluid Density (ρ)
The mass per unit volume of a fluid, indicating how much mass is packed into a given space. It is denoted by the Greek letter rho (ρ).
Example:
Oil has a lower Fluid Density than water, which is why it floats on top.
Fluid Dynamics
The branch of physics that studies the motion of fluids (liquids and gases) and the forces acting on them.
Example:
Understanding Fluid Dynamics is crucial for designing efficient airplane wings and optimizing water flow in pipes.
Fluid Velocity (v)
The speed and direction of a fluid's motion at a specific point. It is a vector quantity.
Example:
The Fluid Velocity of water exiting a garden hose increases when you partially cover the opening with your thumb.
Height (h)
The vertical position of a point in a fluid relative to a chosen reference level, influencing its gravitational potential energy.
Example:
The Height of water in a tank affects the speed at which it leaks from a hole at the bottom.
Incompressible Fluid
A fluid whose density remains constant regardless of changes in pressure. This is a common simplifying assumption in fluid dynamics problems.
Example:
For most practical purposes in AP Physics 2, water is considered an Incompressible Fluid.
Kinetic Energy (in fluids context)
The energy a fluid possesses due to its motion, directly proportional to its mass and the square of its velocity.
Example:
A fast-moving river has significant Kinetic Energy that can be harnessed to generate electricity.
Negligible Viscosity
A condition where the internal friction within a fluid is so minimal that it can be disregarded in calculations, simplifying fluid dynamics problems.
Example:
When analyzing the flow of air over an airplane wing, we often assume Negligible Viscosity for initial calculations.
Potential Energy (in fluids context)
The energy a fluid possesses due to its position in a gravitational field, proportional to its mass, gravity, and height.
Example:
Water stored in a reservoir at a high elevation has considerable Potential Energy before it flows downhill.
Power (in fluids context)
The rate at which work is done on or by a fluid system, or the rate at which energy is transferred. It is measured in Watts (W).
Example:
The Power output of a hydroelectric dam indicates how quickly it can convert the potential energy of water into electrical energy.
Pressure (in fluids)
The force exerted perpendicularly per unit area by a fluid. It is a scalar quantity measured in Pascals (Pa).
Example:
The Pressure at the bottom of a swimming pool is greater than at the surface due to the weight of the water above.
Streamline Flow
A type of fluid flow characterized by smooth, parallel layers without turbulence, where the velocity at any given point remains constant over time.
Example:
Smoke rising smoothly from an incense stick on a calm day exhibits Streamline Flow.
Volume Flow Rate (V or Q)
The volume of fluid that passes a given cross-sectional area per unit time. It is calculated as the product of fluid velocity and cross-sectional area.
Example:
A fire hose delivers a high Volume Flow Rate of water to quickly extinguish a blaze.
Work (in fluids context)
The energy transferred to or from a fluid system by a force acting over a distance, often related to changes in its kinetic or potential energy.
Example:
A pump does Work on water to lift it from a well to an elevated storage tank.