Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...

When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers of the solid known as shearing resistance. However, when the force is removed, the shearing forces restore the original shape of the solid. Other deformation forces also cause temporary changes in shape if the forces are not beyond a threshold magnitude. Solids tend to retain their shape, making the study of their rest and motion easier. Beyond...

When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:

Fluids differ from solids primarily in their molecular structure and stress response. Solids have tightly packed molecules with strong intermolecular forces, maintaining their shape and resisting deformation. In contrast, fluids have molecules spaced farther apart with weaker forces, allowing them to flow and deform easily.
Fluids, which include both liquids and gases, are substances that deform continuously under shearing stress. For example, water and oil are liquids with molecules that can...

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...

Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent spots,...