College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
The equation of continuity states that the mass flow rate of a fluid must remain constant from one cross-section of a pipe to another, assuming steady, incompressible flow. Mathematically, it is expressed as $A_1v_1 = A_2v_2$, where $A$ is the cross-sectional area and $v$ is the fluid velocity.
congrats on reading the definition of equation of continuity. now let's actually learn it.
The equation of continuity applies to incompressible fluids, meaning their density remains constant.
It is derived from the principle of conservation of mass in fluid dynamics.
In a pipe with varying cross-sectional areas, if the area decreases, the velocity of the fluid increases and vice versa.
This principle helps explain phenomena like why water speeds up when it flows through a narrow section of a hose.
The units for both sides of the equation are consistent: if area is in square meters (m²) and velocity in meters per second (m/s), then the product gives cubic meters per second (m³/s), representing volumetric flow rate.
Review Questions
How does the velocity of an incompressible fluid change when it moves from a wider section to a narrower section of a pipe?
What fundamental conservation principle underlies the equation of continuity?
If you know the cross-sectional areas and velocities at two points in a streamline flow, how can you verify that they satisfy the equation of continuity?
Related terms
Incompressible Flow: A type of fluid flow where the fluid density remains constant throughout.
Volumetric Flow Rate: The volume of fluid that passes through a given surface per unit time, typically measured in cubic meters per second (m³/s).
Bernoulli's Principle: \( An increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy \). Often used alongside the equation of continuity to analyze fluid behavior.