Fluid Kinematics

Fluid flow can be described with the Eulerian and Lagrangian methods. These two approaches give different views of the same moving fluid. They are useful in science and engineering because the best method depends on the problem being studied.

The Eulerian method looks at fixed points in space. At each location, it measures fluid properties such as velocity, pressure, and temperature as the fluid moves past. This stationary view is useful when studying how a fluid interacts with a solid object.

Fluid flow can be grouped by direction and by how it changes over time. The simplest case is one-dimensional flow. In this type, properties such as velocity and pressure change along only one axis. Water moving through a straight pipe is a common example, because changes in other directions are very small.

Two-dimensional flow changes in two directions. It varies in both length and height, so the analysis is more complex than one-dimensional flow. Air moving over a flat surface, such as a...

Streamlines, streaklines, and pathlines are three ways to describe fluid motion. Each one shows flow from a different angle. Together, they help students compare how a fluid moves in steady and unsteady flow.

A streamline is a line that stays tangent to the fluid’s velocity vector at each point. That means the fluid velocity points along the streamline. Streamlines give an instant picture of the flow field, so they are useful for showing the overall direction of flow in a fluid system. In...

Fluid analysis often uses two linked ideas: the control volume approach and the system approach. Both help describe mass, energy, and momentum transfer, but they focus on different things. One follows a region in space. The other follows a fixed mass of fluid over time.

The control volume approach looks at a stationary area in space through which fluid moves. That area is bounded by a control surface, which is the outer edge of the region. A pipe with water flowing through it is a clear...

Velocity and acceleration help describe how a fluid particle moves in steady and unsteady flow. A fluid particle follows a pathline, and its velocity depends on both position and time. Acceleration is found by differentiating velocity with respect to time, so it shows how the particle’s motion changes.

In a flow field, acceleration can be written using three perpendicular components. These components show how velocity changes over time in different spatial directions. This gives a general way...

Reynolds transport theorem links a fluid system to a control volume. It helps explain how the time rate of change of a property can be tracked in fluid dynamics.

The theorem uses extensive properties, such as mass, velocity, acceleration, temperature, and momentum. These properties depend on the size of the system. Their intensive forms are the values per unit mass.

The total amount of an extensive property in a system at any instant is the sum of the amounts carried by each tiny fluid...

A pressurized water fire extinguisher uses fluid dynamics to create a fast stream of water. The water is stored at a much higher pressure inside the extinguisher than the surrounding air. When the extinguisher is activated, that pressure difference forces water to flow out quickly.

Bernoulli's equation helps predict the exit speed of the water. This equation links pressure and velocity. As pressure drops, velocity increases. In the extinguisher, the high internal pressure is converted into the...