Effect of temperature and pressure on density

Although air is not quite a ‘perfect gas’ it does obey the gas law within reason­able limits, so we can say that

P = RT P

It is often convenient to express the density in terms of the ratio of the density at some height p to the value at standard sea-level conditions p0. This ratio p/p0 is usually denoted by the Greek letter cr, and is called the relative density.

EXAMPLE 2.1

If the temperature at sea-level in the temperate ISA is 15°C, and the lapse rate is 6.5°C per km, find the temperature and density at 6 km altitude where the pressure is 47 200 N/m2. The gas constant R = 287 J/kg K.

SOLUTION

First we must convert all temperatures to absolute (Kelvin). Sea-level tempera­ture is

273 + 15 = 288 K.

Temperature at 6000 m is 288 + 6.5 X 6 = 249 К The gas law states that

— = RT or p = – Ё-

p K1

so the density at 6 km is

An important property of air in so far as it affects flight is its viscosity. This is a measure of the resistance of one layer of air to movement over the neigh­bouring layer; it is rather similar to the property of friction between solids. It is owing to viscosity that eddies are formed when the air is disturbed by a body passing through it, and these eddies are responsible for many of the phenomena of flight. Viscosity is possessed to a large degree by fluids such as treacle and certain oils, and although the property is much less noticeable in air, it is none the less of considerable importance.