Fluid dynamics

Fluid dynamics is the motion of fluids (liquids and gases). It is one of the oldest studies of physics. It is studied by physicists, mathematicians, and engineers. Mathematics can describe how fluids move using mathematical formulas called equations. The fluid dynamics of gases are called aerodynamics.

Understanding how fluids behave helps us understand things like flight or ocean currents. Fluid dynamics can be used to understand weather, because clouds and air are fluids. Fluid dynamics can also be used to understand how aeroplanes fly through the air or how ships and submarines move through water.

Computer programs can use the mathematical equations of fluid dynamics to model and predict the actions of moving fluids. Computers have helped us understand fluid dynamics very much, and some people study how to model or simulate fluids only with a computer. Studying how fluid dynamics can be done with computers is called computational fluid dynamics (or CFD for short).

Important equations

The equations that govern fluid flow are simple to think about but very hard to solve. Usually, computers must be used to calculate fluid dynamics.

In real life, fluids are many molecules that collide with other objects. These molecules are "discrete", which means that they are individual molecules. However, discrete molecules are very hard to study. In fluid dynamics, these molecules follow "continuum assumption". This means that all fluids are "continuous", or acts as one large object, instead of many small molecules. This also means that things like the density, pressure, temperature, and flow velocity can be measured and changes from one area of fluid to the other.

Fluid dynamics is based on 3 fundamental rules. These are also the 3 conservation laws. Conservation laws are based off classical mechanics. However, quantum mechanics and general relativity can change the way that fluids move. The first conservation law is conservation of mass. Conservation of mass means that mass is never created nor destroyed. Mass only moves from one place to another. This gives the mass conservation equation. Sometimes this may not apply such as a flow involving a chemical reaction. The second conservation law is conservation of energy. Conservation of energy is also the first law of thermodynamics. In this law, energy is never created or destroyed. Energy only changes its form. For example, kinetic energy can turn into potential energy. The last conservation law is conservation of momentum. This is also Newton's Second Law. The law says that Force = rate of change of momentum. Momentum is mass times velocity. Conservation of momentum makes fluids harder to study.

In Newtonian fluids, the Navier–Stokes equations are equations that describe fluids. The fluids have to follow 3 rules to use these equations.The first rule is that the fluid is continuously dense. The second rule is that the fluid is not ionized. The third rule is that the fluid has a small flow velocity. A "small" flow velocity just means its velocity is a lot slower than the speed of light. The Navier–Stokes equations are non-linear differential equations that explain the momentum and "flow" of the fluid. It describes the fluid's movement based on velocity and pressure gradients. These unsimplified equations are very difficult to solve and do not have a closed-form solution. This means that a computer has to solve these equations. They are usually solved in computational fluid dynamics. However, these equations can be simplified, which makes the equations easier to solve.

To solve the equations, information is needed about the fluid's "equation of state". The equation of state is the thermodynamic properties (usually pressure and temperature) of the fluid. For example, the "Ideal Gas Law" relates pressure, temperature, and density in fluids. This equation is:

${\displaystyle p={\frac {\rho R_{u}T}{M}}}$

In this equation, p is pressure, ρ is density, and T is the absolute temperature, R_u is the gas constant and M is molar mass.

Related pages

• Fluid mechanics
• Superfluidity

Further reading

• Acheson, D. J. (1990). Elementary Fluid Dynamics. Clarendon Press. ISBN 0-19-859679-0.
• Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. ISBN 0-521-66396-2.
• Chanson, H. (2009). Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows. CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 478 pages. ISBN 978-0-415-49271-3.
• Clancy, L. J. (1975). Aerodynamics. London: Pitman Publishing Limited. ISBN 0-273-01120-0.
• Lamb, Horace (1994). Hydrodynamics (6th ed.). Cambridge University Press. ISBN 0-521-45868-4. Originally published in 1879, the 6th extended edition appeared first in 1932.
• Milne-Thompson, L. M. (1968). Theoretical Hydrodynamics (5th ed.). Macmillan. Originally published in 1938.
• Shinbrot, M. (1973). Lectures on Fluid Mechanics. Gordon and Breach. ISBN 0-677-01710-3.
• Nazarenko, Sergey (2014), Fluid Dynamics via Examples and Solutions, CRC Press (Taylor & Francis group), ISBN 978-1-43-988882-7
• Encyclopedia: Fluid dynamics Scholarpedia

Other websites

• National Committee for Fluid Mechanics Films (NCFMF), containing films on several subjects in fluid dynamics (in RealMedia format)
• Gallery of fluid motion, "a visual record of the aesthetic and science of contemporary fluid mechanics," from the American Physical Society
• List of Fluid Dynamics books Archived 2024-12-11 at the Wayback Machine