# The gas laws

The kinetic energy of the molecules increases with increasing temperature. The important effects of this fact are given in Boyle’s law and Charles’ law, which state that the volume of a perfect gas varies inversely with absolute pressure and directly with absolute temperature, respectively.

The total effect is more properly stated by the equation of state:

P = pR T Equ2.1

Where:

P = pressure

P = density

R = gas constant

T = absolute temperature

In the design of the majority of fan systems, the gas may be considered as incompressible without introducing significant error. The normal boundary, between the assumption that the gas is incompressible or that it is compressible, as accepted in ISO 5801 is for pressures up to 2 kPa. In many calculations, therefore, the air density may be considered constant and the absolute pressure is directly proportional to the absolute temperature.

Since an ideal gas is assumed to be composed of molecules, which are very small perfect spheres, and the collisions of these

 Av Figure 2.1 Definition of viscosity

Molecules with one another and solid boundaries are assumed to be elastic, an ideal gas can only exert pressure normal to a surface. Thus, no frictional force exists in any ideal gas, even if strong velocity gradients exist. All gases, however, consist of molecules, which do not behave as elastic spheres, and thus no gas is truly ideal. Real gases are capable of exerting pres­sure parallel to the surface of a body, which is moving with re­spect to the gas. The magnitude of the force parallel to the sur­face is used to define an important property of real gases — viscosity. The effects of viscosity on the behaviour of real gases causes resistance to flow; the resistance is proportional to the velocity gradients, which exist in the gas.

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