Ejection dynamics of a simple liquid from individual carbon nanotube nozzles

Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:

A fire extinguisher that uses pressurized water relies on fluid dynamics principles to generate a high-velocity stream capable of suppressing flames. The water is stored at a much higher pressure inside the extinguisher than the surrounding atmosphere. This pressure difference forces the water to flow rapidly when the extinguisher is activated, and the behavior of the water as it exits the nozzle can be understood using fundamental equations of fluid dynamics.
The key to understanding how the...

Capillarity describes the movement of liquid in small spaces without external forces acting on it. The capillarity is driven by surface tension and adhesive interactions between the liquid and surrounding solid surfaces. This effect is often seen in narrow tubes, porous materials, and fine particles.
Surface tension is crucial to capillarity. It results from cohesive forces between liquid molecules at the liquid-air boundary, forming a skin that resists external forces. When the capillary tube...

There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...