Speed potential

Speed potential (そくど potential British: Velocity potential) [¹] [²] is used for the analysis of the whirlpoolless flow in hydrodynamics. I call a flow with speed potential a potential style.

Speed potential Φ is a scalar field satisfying the next expression.

${\displaystyle {\boldsymbol {u}}=\operatorname {grad} \Phi}$

But u is speed of the fluids, and there is no whirlpool and is clogged up

${\displaystyle \operatorname {rot} {\boldsymbol {u}}=\nabla \times {\boldsymbol {u}}={\boldsymbol {0}}}$

I satisfy を. I can put this for the vector analysis

${\displaystyle \operatorname {rot} (\operatorname {grad} \Phi) ={\boldsymbol {0}}}$

I use の property (I refer to ナブラ # the second floor differential calculus).

Unlike general potential, I am careful about a definition of the speed potential not having a minus sign.

Property

• If a domain is a single connection, speed potential Φ is a many-valued function if it is single-valued function, a multiplex connection.
• Speed u and the streamline are at right angles to the equivalence side of speed potential Φ (equipotential surface), and differential calculus of normal direction n of the speed potential gives speed:

  ${\displaystyle {\frac {\partial \Phi }{\partial n}}={\boldsymbol {n}}\cdot \operatorname {grad} \Phi ={\boldsymbol {n}}\cdot {\boldsymbol {u}}=u}$ 

• For the whirlpoolless flow of the incompressible fluid, speed potential Φ becomes the harmony function.

References

1. ^ Tomomasa Tatsumi "hydrodynamics" 培風館, 1982. ISBN 4-563-02421-X. 
2. ^ Isao Imai "hydrodynamics" (the first part) kimono Hanafusa, 1997. ISBN 4-7853-2314-0. 

Allied item

• Double bare speed potential

It is acquired by "https://ja.wikipedia.org/w/index.php?title= speed potential &oldid=47496259"

This article is taken from the Japanese Wikipedia Speed potential

This article is distributed by cc-by-sa or GFDL license in accordance with the provisions of Wikipedia.

Wikipedia and Tranpedia does not guarantee the accuracy of this document. See our disclaimer for more information.

In addition, Tranpedia is simply not responsible for any show is only by translating the writings of foreign licenses that are compatible with CC-BY-SA license information.