I am new in this place, am studying civil engineering in Spain,Madrid, and is something I do not understand in a theoretical exposition of the velocity/force potential.(adsbygoogle = window.adsbygoogle || []).push({});

They suppose that the external force that it acts in each point of the fluid and the speed, derive from scalar , so they admit a potential :

[tex]\frac{\vec{F}}{m}= - \vec{\nabla} U[/tex]

[tex]\vec{V}= \vec{\nabla} \Omega[/tex]

If the acceleration depends on the coordinates of the point and the time [tex]\vec{a} ( u',v',w') = f(x,y,z,t)[/tex] :

[tex]u'= \frac{du}{dt}= \frac{\partial u}{\partial x} \frac{\partial x}{\partial t} +\frac{\partial u}{\partial y } \frac{\partial y}{\partial t} + \frac{\partial u}{\partial z}\frac{\partial z}{\partial t} + \frac{\partial u}{\partial t}[/tex] and thus with the other coordinates of the acceleration

And here my doubt comes, I do not understand as they obtain to this expression:

[tex]u'= \frac{\partial^2 \Omega}{\partial x^2} \frac{\partial \Omega}{\partial x} +\frac{\partial^2 \Omega}{\partial x \partial y} \frac{\partial \Omega}{\partial y} + \frac{\partial^2 \Omega}{\partial x \partial z}\frac{\partial \Omega}{\partial z} + \frac{\partial^2 \Omega}{\partial x \partial t}[/tex]

if somebody can help to understand it me, would be thanked for. Thank you very much

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fluid Mechanics question,velocity potential

**Physics Forums | Science Articles, Homework Help, Discussion**