"A continuity equation or transport equation is an equation that describes the transport of some quantity."
Expresses the conservation of mass principle applied to fluid flow, stating that the mass entering and leaving a system must be equal.
Conservation of Mass: The principle that states that mass cannot be created or destroyed, but can be transformed from one form to another, as applied to fluid mechanics.
Continuity Equation: An equation that describes the relationship between the flow rate, velocity, and cross-sectional area of a fluid moving through a pipe or other confined space.
Reynolds Transport Theorem: A mathematical theorem that relates the rate of change of a conserved property (such as mass or momentum) with respect to time to the flow of that property through the boundary of a control volume.
Velocity Field: A mathematical description of the velocity of a fluid at various points in space and time.
Flow Measurement Techniques: Techniques used to measure the flow rate or velocity of a fluid, such as Pitot tubes, flow meters, and ultrasonic Doppler velocimetry.
Incompressible Flows: Flows in which the density of the fluid remains constant, regardless of changes in pressure or temperature, such as the flow of water in a pipe.
Compressible Flows: Flows in which the density of the fluid varies with changes in pressure or temperature, such as the flow of air around an airplane wing.
Bernoulli's Equation: An equation that relates the pressure, velocity, and elevation of a fluid in a steady flow regime, and is derived from the conservation of energy.
Non-Newtonian Flows: Flows in which the relationship between the applied stress and the resulting deformation of the fluid is not linear, such as the flow of blood, polymers, or sludge.
Dimensional Flows: Flows in which the velocity and pressure vary only in two spatial dimensions, such as the flow of fluid around a flat plate.
Dimensional Flows: Flows in which the velocity and pressure vary in all three spatial dimensions, such as the flow of air around a car or airplane.
Turbulent vs. Laminar Flows: Two different types of fluid flows with distinct patterns of velocity and pressure variations, usually characterized by their Reynolds number and flow regime.
Continuity Equation: This equation states that the mass of a fluid is conserved in a closed system, meaning that the mass entering the system must be equal to the mass leaving the system.
Incompressible Continuity Equation: This equation applies to fluids that cannot be compressed, such as liquids. It states that the volume flow rate (Q) must be constant throughout the entire system.
Non-Incompressible Continuity Equation: This equation applies to fluids that can be compressed, such as gases. It states that the mass flow rate (m) must be conserved in a closed system.
Steady State Continuity Equation: This equation applies to systems that are in a steady state, meaning that the flow rates and conditions in the system do not change over time. It states that the volumetric flow rate is constant throughout the system.
Unsteady State Continuity Equation: This equation applies to systems that are not in a steady state, meaning that the flow rates and conditions in the system are changing over time. It states that the mass flow rate entering the system must be equal to the mass flow rate leaving the system at any given point in time.
Three-Dimensional Continuity Equation: This equation applies to systems that are three-dimensional, meaning that the flow can occur in any direction. It states that the mass flow rate in any given direction must be conserved.
Inviscid Continuity Equation: This equation applies to fluids that have no viscosity, meaning that the flow is frictionless. It states that the mass or volume flow rate must be conserved, depending on the type of fluid.
Navier-Stokes Continuity Equation: This equation is a general equation that applies to all fluids, including those with viscosity. It states that the mass or volume flow rate must be conserved in a closed system.
"Continuity equations are a stronger, local form of conservation laws."
"Mass, energy, momentum, electric charge and other natural quantities can be described using continuity equations."
"A weak version of the law of conservation of energy states that energy can neither be created nor destroyed."
"Energy can only move by a continuous flow."
"The continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries."
"Yes, continuity equations can include 'source' and 'sink' terms, which allow them to describe quantities that are often but not always conserved, such as the density of a molecular species which can be created or destroyed by chemical reactions."
"In an everyday example, there is a continuity equation for the number of people alive; it has a 'source term' to account for people being born, and a 'sink term' to account for people dying."
"Any continuity equation can be expressed in an 'integral form' (in terms of a flux integral), which applies to any finite region, or in a 'differential form' (in terms of the divergence operator) which applies at a point."
"Continuity equations underlie more specific transport equations such as the convection-diffusion equation, Boltzmann transport equation, and Navier-Stokes equations."
"Flows governed by continuity equations can be visualized using a Sankey diagram." Note: The remaining questions don't have direct answers in the provided paragraph. They may require additional information or explanation.