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:

The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...

When an object is placed in a fluid, it either floats or sinks. All objects in a fluid experience a buoyant force. For example, a metal ball sinks, while a rubber ball floats. Similarly, a submarine can sink and float by adjusting its buoyancy.  The concept of buoyancy raises several interesting questions. For instance, where does this buoyant force come from? How much buoyant force is required to make an object sink or float? Do objects that sink get any support at all from the fluid? 
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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,...

Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform Flow
Uniform flow...