# Euler's Momentum Theory

1. May 20, 2005

### ProxRB

Thank you for taking a look at my hopeless plight. As a part my Calculus project, I am trying to define tornados, or any particular feature of a tornado, using calculus, or basically linking tornados and calculus any way I can. In my research, I came across Neil B. Ward’s The Exploration of Certain Features of Tornado Dynamics Using a Laboratory Model. Ward states:

“3. Application of Euler’s Momentum Theory

“The interpretation of the observations of vortices produced with laboratory system is facilitated through an application of the momentum theory (Milne-Thomson, 1960) which pertains to fluid flow into and out of a volume, V, enclosed by a surface, S. The theorem states that:

<img src='http://img.villagephotos.com/p/2005-5/1014872/1.JPG' width=436 height=46 >

“Where
<img src='http://img.villagephotos.com/p/2005-5/1014872/n.JPG' width=17 height=18 > is the inward unit vector normal to the surface,
<img src='http://img.villagephotos.com/p/2005-5/1014872/p.JPG' width=18 height=19 > is the static pressure*,
<img src='http://img.villagephotos.com/p/2005-5/1014872/ro.JPG' width=18 height=19 > is the fluid density,
<img src='http://img.villagephotos.com/p/2005-5/1014872/f.JPG' width=18 height=19 > is the external force per unit mass, including gravity,
<img src='http://img.villagephotos.com/p/2005-5/1014872/t.JPG' width=15 height=14 > is the time and <img src='http://img.villagephotos.com/p/2005-5/1014872/q.JPG' width=17 height=22 > is the fluid velocity

*Static pressure p as in the Bernoulli equation,

<img src='http://img.villagephotos.com/p/2005-5/1014872/2.JPG' width=258 height=51 >” (pg 3, The Exploration of Certain Features of Tornado Dynamics Using a Laboratory Model)

Now, my question is essentially, what does Euler’s Momentum Theory mean, what is it referring to, and what is Ward describing in the use of this theorem, what does it describe in terms of tornados?

Thank you again

Last edited by a moderator: Apr 21, 2017
2. May 20, 2005

### Staff: Mentor

It looks like those are meant to be images of symbols used in some equation. Either take a crack at writing the symbols directly or just give the link where you found the original statement.