Glossary
Bernoulli's Equation
A principle in fluid dynamics that relates pressure, fluid velocity, and height, representing the conservation of energy for an ideal fluid in steady flow.
Example:
When designing an airplane wing, engineers use Bernoulli's Equation to understand how the faster airflow over the curved top surface creates lower pressure, generating lift.
Continuity Equation
A mathematical expression of mass conservation for fluids, stating that the product of the cross-sectional area and fluid velocity is constant at any two points in a pipe ($A_1v_1 = A_2v_2$).
Example:
If water flows from a wide pipe into a narrow one, the Continuity Equation predicts that the water's velocity will increase in the narrower section.
Cross-sectional Area
The area of a two-dimensional slice taken perpendicular to the direction of fluid flow, typically circular for pipes.
Example:
When calculating the flow through a cylindrical pipe, the Cross-sectional Area is found using the formula , where 'r' is the pipe's radius.
Flow Rate
The volume of fluid passing a specific point per unit of time, calculated as the product of the fluid's speed and the cross-sectional area of the container.
Example:
If a garden hose has a Flow Rate of 0.5 liters per second, it means half a liter of water exits the hose every second.
Fluid Dynamics
The branch of physics that studies the motion of fluids (liquids and gases) and the forces acting on them.
Example:
Understanding how water flows through a pipe or air moves around an airplane wing involves the principles of Fluid Dynamics.
Incompressible Fluids
Fluids whose density remains constant regardless of changes in pressure or volume, making them ideal for applying the continuity equation without significant error.
Example:
Most liquids, like water, are considered Incompressible Fluids for practical purposes in fluid dynamics problems.
Mass Conservation (in fluids)
A fundamental principle stating that the total mass of a fluid within a closed system remains constant over time, meaning mass cannot be created or destroyed.
Example:
When water flows from a wide river into a narrower channel, the principle of Mass Conservation ensures that the same amount of water mass passes through both sections per unit time.
Mass Flow Rate
The mass of fluid passing through a system per unit time, which remains constant in a closed system unless mass is added or removed.
Example:
A pump moving 2 kg/s of water is demonstrating a Mass Flow Rate of 2 kilograms per second.
Pressure (in fluid flow)
The force exerted by a fluid per unit area, which is inversely related to fluid velocity in a horizontal flow according to Bernoulli's principle.
Example:
In a narrow section of a pipe where water flows faster, the Pressure exerted by the water on the pipe walls will be lower than in a wider section.