The Bernoulis equation is according to which law

The energy balance then changes into Bernoulli equation

The Bernoulli equation

 

 

If there is no friction, the principle of maintaining the mechanical Energy:

 

 

By relating the energy to the unit of volume, we move on to energy density or pressures:

 

 



 

The total pressure is the sum of Back pressure,Gravity pressureandstatic pressure pSt..

 

If the density is a function of the pressure, then more generally applies

 

 

 

For an ideal gas, the relationship between pressure and density in the isothermal case is described by Boyle’s law:

 

Boyle’s Law

 

 

With the molar volume VM. and the molar mass µ is obtained

 

or.

 

Under normal conditions (not standard conditions) the following applies:

 

T0

VM0

p0

r0(Air)

0 ° C = 273.15 K

22.4 l

1,01325.105 Pa

1.29 kg / m3

 

The following applies to an ideal gas: At a given temperature, the density of a gas is proportional to its pressure.

 

 

In the following we are interested in the pressure in a non-flowing liquid or gas column, i.e. with v = 0 the following applies:

 

 

For an incompressible liquid with ptotal (h = 0) = p0 then applies to the static pressure:

 


The static pressure of a column of liquid decreases with increasing height.

In the case of a gas (as an approximation of an ideal gas) at constant temperature (isothermal stratification):

 

 

The calculation of the integral in the Bernoulli equation gives:

 

 

At the height h = 0, let the pressure ptotal = pSt. = p0 and the density r0. From this it follows for the constant of integration pc = p0/ e. The barometric altitude formula results for the altitude dependence of the static pressure: