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Transient 1D Inviscid fluid flow


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\rho \left(  \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial l} \right)=
-\frac{\partial p}{\partial l}  + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}



Steady-state 1D inviscid fluid flow



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\frac{d p}{d l} =
-\rho \, u \, \frac{d u}{d l}  + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}



Bernoulli equation for steady=
Steady-state 1D inviscid fluid flow of incompressible fluid with no friction


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\frac{p(l)}{\rho} +  \frac{u^2}{2} -  g \cdot z(l)   = \rm const


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