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Natural Science Forum / Physics / Acoustics / December 2003pressure vs velocity potential ?
For different books and articles, the wave equations and their solutions are representated by sound pressure field. But there are also many articles refering those equtaions and solutions in term of velocity potential. (Basically, these two quanties are linked by a constant.) I would like to ask : 1. What's the difference between using pressure field and velocity potential in defining problems? 2. What's the advantage for each of the representations ? Regrads, MJ In the referenced article, "Man J" <manj.wong@polyu.edu.hk> writes: >For different books and articles, the wave equations and their solutions are >representated by sound pressure field. But there are also many articles [quoted text clipped - 5 lines] >1. What's the difference between using pressure field and velocity potential >in defining problems? It depends on the kind of problem you're doing, but the biggest difference will be in stating boundary conditions. The relationship is p = d\phi/d t >2. What's the advantage for each of the representations ? Working in terms of pressure is a little simpler for many problems, but can make imposing boundary conditions harder than using the velocity potential. A potential representation can also allow you to solve problems with non-uniform mean flows, by computing the full time dependent potential (aerodynamic and acoustic) all together.  Signature`The above passage is carefully calculated to deprave the cultivated reader. ' No MS attachments: http://www.fsf.org/philosophy/no-word-attachments.html Home page: http://staff.bath.ac.uk/ensmjc/ Carley, thx .... Also want to ask, what're the main differences in stating boundary conditions ?? E.g. 1. B.C. for a hard surface, should we say dP/dn = 0 or d(phi)/dn = 0 ? ( n is the normal vector) 2. Does the "Sommerfeld far field condition" be defined in pressure field or potential field ? Regards, MJ ¤¤¼¶¼g... > In the referenced article, "Man J" <manj.wong@polyu.edu.hk> writes: > >For different books and articles, the wave equations and their solutions are [quoted text clipped - 19 lines] > solve problems with non-uniform mean flows, by computing the full time > dependent potential (aerodynamic and acoustic) all together. In the referenced article, "Man J" <manjj@hotmail.com> writes: >Carley, thx .... > [quoted text clipped - 4 lines] >1. B.C. for a hard surface, should we say dP/dn = 0 or d(phi)/dn = 0 ? ( n >is the normal vector) For a hard surface it makes no difference. When you have a finite impedance (relationship between velocity and pressure), it can be easier to work with the potential. >2. Does the "Sommerfeld far field condition" be defined in pressure >field or potential field ? It makes no difference in this case; you can use either. Signature`The above passage is carefully calculated to deprave the cultivated reader. ' No MS attachments: http://www.fsf.org/philosophy/no-word-attachments.html Home page: http://staff.bath.ac.uk/ensmjc/ > For different books and articles, the wave equations and their > solutions are representated by sound pressure field. But there are [quoted text clipped - 4 lines] > potential in defining problems? > 2. What's the advantage for each of the representations ? For many situations, it probably does not matter which formulation is used. For some problems, it may be more convenient to use one formulation or the other, in which case one uses whichever is more convenient. In other situations, there may be distinct advantages to one formulation over the other. For example, in the structural acoustics problem (e.g., elastic structure coupled with acoustic fluid) using finite element modeling of both structure and fluid, one can obtain symmetric matrices with a velocity potential formulation, but not with a pressure formulation. > For different books and articles, the wave equations and their solutions are > representated by sound pressure field. But there are also many articles [quoted text clipped - 10 lines] > Regrads, > MJ I am not an expert on this, but according to my textbooks, the velocity potential is an abstract entity that can be used to get both sound pressure and the particle velocity vector. d (phi) p = rho0 * --------- dt and _ v = - grad (phi) or seen as separate x, y and z components: d (phi) vx= -------- dx d (phi) vy= -------- dy d (phi) vz= -------- dz So it appears to me that the velocity potential would be an elegant way of managing both the pressure and the velocity (vector). |
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