Glossary
Bernoulli's Equation
An expression of the conservation of mechanical energy for ideal fluid flow along a streamline, relating pressure, fluid speed, and height.
Example:
Airplane wings are designed using Bernoulli's equation to create lift, as faster air flow over the curved top surface results in lower pressure.
Conservation of Mechanical Energy (in Fluid Flow)
The principle that in an ideal fluid system, the sum of pressure energy, kinetic energy, and gravitational potential energy per unit volume remains constant along a streamline.
Example:
The conservation of mechanical energy explains why water speeding up as it falls from a dam experiences a corresponding drop in pressure or height.
Continuity Equation
A fundamental principle in fluid dynamics stating that for an incompressible fluid in steady flow, the product of the cross-sectional area and fluid velocity remains constant along a streamline.
Example:
Using the continuity equation, engineers can predict how fast water will flow through different sections of a pipe system, ensuring consistent delivery.
Cross-sectional Area
The area of a two-dimensional slice taken perpendicular to the direction of fluid flow in a pipe or channel.
Example:
When you squeeze a garden hose, you decrease its cross-sectional area, making the water spray out faster.
Fluid Speed
The rate at which a fluid element moves through a given point in a system.
Example:
The fluid speed of water in a narrow river section is typically much higher than in a wide, calm lake.
Gravitational Potential Energy (in Fluids)
The energy stored in a fluid due to its position in a gravitational field, which is higher for fluid at greater elevations.
Example:
Water stored in a high-altitude reservoir has significant gravitational potential energy that can be converted into kinetic energy to generate hydroelectric power.
Ideal Fluid
A theoretical fluid characterized by being incompressible, having steady flow, and being non-viscous (no internal friction).
Example:
While no real fluid is perfectly ideal, treating water as an ideal fluid often provides good approximations for many practical problems in introductory physics.
Incompressible Fluids
Fluids whose density remains constant regardless of changes in pressure or temperature, meaning their volume does not significantly change under compression.
Example:
Water is often treated as an incompressible fluid in many physics problems, simplifying calculations for flow in pipes.
Inviscid Flow
Fluid flow where the fluid has no viscosity, meaning there is no internal friction or resistance to flow.
Example:
In inviscid flow, a fluid would move without any energy loss due to friction between its layers or with the pipe walls.
Mass Flow Rate
The mass of fluid passing through a given cross-sectional area per unit of time, calculated as density times area times velocity.
Example:
The mass flow rate of blood through the aorta is crucial for delivering oxygen efficiently throughout the body.
Pressure Difference
The variation in pressure between two points in a fluid, which drives fluid flow from regions of high pressure to low pressure.
Example:
Water flows out of a faucet because the pressure difference between the inside of the pipe and the outside air pushes it out.
Steady-State Flow
A type of fluid flow where the fluid properties (like velocity, pressure, and density) at any given point in space do not change over time.
Example:
The continuous, unchanging flow of water through a well-designed irrigation system represents steady-state flow.
Streamline
An imaginary line in a fluid flow whose tangent at any point gives the direction of the fluid velocity at that point.
Example:
Smoke rising smoothly from an incense stick initially forms clear streamlines before becoming turbulent.
Torricelli's Theorem
A theorem derived from Bernoulli's equation that calculates the exit velocity of a fluid from an opening in a container based on the height difference between the fluid surface and the opening.
Example:
Using Torricelli's theorem, you can predict how fast water will gush out of a hole at the bottom of a water bottle.
Volume Flow Rate
The volume of fluid passing through a given cross-sectional area per unit of time, often denoted by Q.
Example:
A fire hose delivers a high volume flow rate of water to quickly extinguish large fires.