**Hydrodynamics **

Hydrodynamics is a major branch of the physics discipline which studies the motion of liquids. A fluid in its simplest definition, is a body of matter that can flow. A fluid can be considered a liquid, which has definite volume and free surface, or it can be considered a gas, which expands to fill a container. The main forces that allow fluids to move are pressure differences, surface stress, and gravity.

There are many types of fluid flow. Determining the type of flow is essential to solving a problem involving moving fluids. Fluid flow can either be laminar or turbulent. Laminar flow deals with slow moving fluids traveling in regular, smooth paths. Laminar flows have thin layers and move parallel to each other. Turbulent flow, on the other hand, is more irregular and the speed of the fluid continuously changes in strength and direction. For example, a river may be turbulent, though undercurrents may undergo little movement. The Reynolds number (Re) is a quantity without dimensions, which can be used to predict flow patterns through a ratio of inertial forces to viscous forces within a fluid.

Hydrodynamic problems can be addressed by applying one or more physical principles: continuity (mass conservation), momentum, and energy. Continuity is often the most basic of equation and is usually applied to reduce unknown variables. Mass is unable to be created or destroyed. Continuity states that the total mass entering the control volume must equal the total mass exiting the control volume. This statement is true of fluid flow that is steady or incompressible.

The principle of momentum is based on Newton’s Laws of Motion. Newton’s Second Law states that the acceleration of an object is dependent on the force acting upon the object and the mass of the object. A greater force causes an increased acceleration of the object, but an increased object mass decreases the acceleration of the object. Newton’s Third Law declares that the force that is exerted on a contained fluid is equal and opposing to the force exerted by the containment of the fluid.

Energy can simply be considered the capacity for doing work. Energy exists in three forms: potential energy, kinetic energy, and pressure energy. Kinetic energy is utilized by a moving body. Potential energy is stored relative to its position. Pressure energy is stored in a fluid based on the force exerted on it. The pressure energy principle uses as an equation which is also known as the Bernoulli equation to analyze a hydrodynamic system. In other words, change of energy equals the work achieved plus the heat input. Bernoulli’s equation associates a relationship between height, pressure, and velocity at two points along a streamline. This equation should only be used for ideal fluids or fluids without changes in energy.

Scientists from many different fields make use of hydrodynamics. It is an important area of study for technological advances including rocket engines, oil pipelines, reservoir management, and air conditioning systems. It also provides a basis for studying weather patterns, tectonic plates, and even the circulation of blood in the human body.

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