# The Bernoulis equation is according to which law

## The energy balance then changes into __Bernoulli equation__

__Bernoulli equation__

The Bernoulli equation

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

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

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The total pressure is the sum of **Back pressure**_{},**Gravity pressure**_{}and**static pressure** p_{St.}.

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

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

__Boyle’s Law__

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With the molar volume V_{M.} and the molar mass µ is obtained

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or.

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

T | V | p | r |

0 ° C = 273.15 K | 22.4 l | 1,01325 | 1.29 kg / m |

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:

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For an incompressible liquid with p_{total }(h = 0) = p_{0} then applies to the static pressure:

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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):

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The calculation of the integral in the Bernoulli equation gives:

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At the height h = 0, let the pressure p_{total} = p_{St.} = p_{0} and the density r_{0}. From this it follows for the constant of integration p_{c} = p_{0}/ e. The barometric altitude formula results for the altitude dependence of the static pressure:

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