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# Equations in Fluid Mechanics

## Equations used in fluid mechanics - like Bernoulli, conservation of energy, conservation of mass, pressure, Navier-Stokes, ideal gas law, Euler equations, Laplace equations, Darcy-Weisbach Equation and more.

### The Bernoulli Equation

• The Bernoulli Equation - A statement of the conservation of energy in a form useful for solving problems involving fluids. For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point.

### Euler Equations

• In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. They correspond to the Navier-Stokes equations with zero viscosity, although they are usually written in the form shown here because this emphasizes the fact that they directly represent conservation of mass, momentum, and energy.

### Laplace's Equation

• The Laplace Equations describes the behavior of gravitational, electric, and fluid potentials.

### Ideal Gas Law

• The Ideal Gas Law - For a perfect or ideal gas the change in density is directly related to the change in temperature and pressure as expressed in the Ideal Gas Law.
• Properties of Gas Mixtures - Special care must be taken for gas mixtures when using the ideal gas law, calculating the mass, the individual gas constant or the density.
• The Individual and Universal Gas Constant - The Individual and Universal Gas Constant is common in fluid mechanics and thermodynamics.

### Navier-Stokes Equations

• The motion of a non-turbulent, Newtonian fluid is governed by the Navier-Stokes equations. The equation can be used to model turbulent flow, where the fluid parameters are interpreted as time-averaged values.

### Mechanical Energy Equation

• The Mechanical Energy Equation - The mechanical energy equation in Terms of Energy per Unit Mass, in Terms of Energy per Unit Volume and in Terms of Energy per Unit Weight involves Heads.

## Related Topics

• ### Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

• ### Bernoulli Equation

Conservation of energy in a non-viscous, incompressible fluid at steady flow.
• ### Conservation of Mass

The Law of Conservation of Mass states that mass can neither be created or destroyed.
• ### Fluid Flow - Equation of Continuity

The Equation of Continuity is a statement of mass conservation.

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## Citation

• The Engineering ToolBox (2003). Equations in Fluid Mechanics. [online] Available at: https://www.engineeringtoolbox.com/fluid-mechanics-equations-d_204.html [Accessed Day Month Year].

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4.19.9

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