What is H in Bernoulli's equation

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




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






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, the following applies (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: