# Continuity Equation, Continuity Equation of Fluid, Fluid Dynamics (For CBSE, ICSE, IAS, NET, NRA 2022)

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# Continuity Equation

• The continuity equation describes the transport of some quantities like fluid or gas.
• This equation explains how a fluid conserves mass in its motion.
• Many physical phenomena like energy, mass, momentum, natural quantities, and electric charge are conserved using the continuity equations.
• It provides very useful information about the flow of fluids and its behavior during its flow in a pipe or hose, the hose, a flexible tube, whose diameter decreases along its length has a direct consequence.
• The volume water flowing through the hose must be equal to the flow rate on the other end.

## Continuity Equation of Fluid

• The Volume of Fluid Moving through the Pipe at Any Point Can Be Quantified in Terms of the Volume Flow Rate, which is Equal to the Area of the Pipe at That Point Multiplied by the Velocity of the Fluid.
• This Volume Flow Rate Must Be Constant Throughout the Pipe, Therefore You Can Write the Equation of Continuity for Fluids (Also Known as the Fluid Continuity Equation) as:

This Equation Tells That as the Cross-Section of the Pipe Gets Smaller, the Velocity of the Fluid Increases, and as the Cross-Section Gets Larger, the Fluid Velocity Decreases

## Fluid Dynamics

• Fluid dynamics is βthe branch of applied science that is concerned with the movement of liquids and gases,β according to the American Heritage Dictionary.
• It is one of two branches of fluid mechanics, which is the study of fluids and how forces affect them.
• Scientists across several fields study fluid dynamics.
• It provides methods for studying the evolution of stars, ocean currents, weather patterns, plate tectonics and even blood circulation.
• Some important technological applications of fluid dynamics include rocket engines, wind turbines, oil pipelines and air conditioning systems.

### Continuity Equation in S- Coordinates

Nothing that

it becomes:

Here, is the vertical velocity relative to the z coordinate system. Introducing the dia-surface velocity component, , defined as the volume flux across the moving -surfaces per unit horizontal area:

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