Homentrop

Homentrop is a term from fluid mechanics and describes an isentropic flow:

${\displaystyle {\frac {\mathrm {D} s}{\mathrm {D} t}}=0,}$

in which the specific entropy , d. H. the entropy per mass particle is homogeneously distributed: ${\displaystyle s}$

${\displaystyle \nabla s=0}$

with the Nabla operator ${\displaystyle \nabla .}$

In other words: the entropy is evenly distributed, both over time and in space. Homentrop therefore also includes the simplifications frictionless and no heat conduction .

Another condition for homentropia is:

${\displaystyle \mathrm {d} p=a^{2}\cdot \mathrm {d} \rho }$

With

• the pressure and ${\displaystyle p}$
• the density ${\displaystyle \rho .}$

The speed of sound is defined in this way: ${\displaystyle a}$

${\displaystyle \Leftrightarrow a^{2}=\left({\frac {\partial p}{\partial \rho }}\right)_{s}}$

Bernoulli's equation

For a homentropic and incompressible flow, the relationship between pressure and velocity between two points can be calculated using Bernoulli's equation :

${\displaystyle {\frac {\partial \Phi }{\partial t}}+{\frac {1}{2}}\;\nabla \Phi \;\nabla \Phi +{\frac {p}{\rho }}+\psi =C(t)}$