|WikiProject Physics||(Rated Start-class, Low-importance)|
I had always thought "body-force" was the ratio of force to mass, not volume i.e. for gravitational force it is "g" or "g cos(angle)" if there is an angle between the direction of flow and the direction the gravity force acts.
There are some major mistakes on this page, or lack of information maybe. I changed the equation F=rho*a to F=rho*velocity squared*area as is shown in the fluids books.
Erm, that makes no sense. I mean, look at the units, that's not even force per mass. There are differing definitions of body force, mind you, and I have indeed seen force per mass in one context; force per volume is more common, and I've seen it both in fluid and solid mechanics classes and books. I've clarified the article why force per volume is favorable.
I'm about to be quite critical of this article in its present form. I hope my comments are useful and I hope nobody takes offense.
The basic definition in the first paragraph is a pretty standard statement of the definition of body force. But there are problems with most of the rest of the article. Here are points to look at:
1. A body force is usually defined simply a type of force (a force that acts throughout the body, not just at the surface), not as a different type of physical quantity. So it is not a force per unit volume. A force per unit volume would usually be called a "force density". A body force would just have dimensions of force. Force densities are commonly used in continuum mechanics. I have never encountered the term "body force" being used to describe a "force density" and continuum mechanics is one of the things I do for a living. So I don't know where this confusion would have come from. Perhaps engineers use the terminology differently? (I'm a physicist)
2. I'm afraid it is completely wrong to say that a centripetal force is a body force. The term "centripetal force" simply refers to any (real, not fictitious) force that pushes/pulls an object towards the center of a circle. Saying a force is "centripetal" is conceptually not much different from saying that it is "upward", or "to the right". In other words it is simply a statement about the direction the force acts in. A centripetal force can be any type of force (normal, gravitational, tension, electrical, magnetic, etc., etc.) and so it might or might not be a body force.
3. The forces mentioned (centrifugal, coriolis) which arise due to looking at the system in a non-inertial frame are "fictitious forces". This, at least, deserves some brief explanation if they are to be included in a list along with real physical forces. I would not encourage puting them in the same list with real forces, though, since conceptually they are something quite different.
4. A pressure gradient is not a force. A net force will be *exerted* on an object that is in a pressure gradient (for example, this is what buoyancy is). But the agent of this force (i.e. the thing exerting the force) is the fluid that the object is immersed in. The fluid only exerts contact forces and these, by definition, cannot be body forces since contact forces are always surface forces. I find this error interesting since I was reading a book called "Physics for Geologists" recently and the author made a convoluted (and wrong) argument that buoyancy must be a body force. So I wonder if this is some widespread misconception. A pressure gradient *does* act on a fluid and is a force per unit volume (a force density) that can accelerate the fluid. But again, I don't think this article is supposed to be about force density.
5. The f = rho*a is dimensionally correct for a force per unit volume. But, like I say above, what is usually meant by body force (at least by physicists) is not a force per unit volume. Also, if one were calculating the acceleration of a solid object subject to a body force one would normally write it as a = integral (f/rho)dV so that the quantities that depend on position in the body (f and rho) appear on one side of the equation while the quantity that is the same everywhere in the body (a) appears on the other. When writing Newton's 2nd Law for a fluid (e.g. the Navier-Stokes equation or Euler equation depending on what approximations are being used) this becomes more complicated since dv/dt breaks up into a partial derivative w.r.t. time and another term containing the velocity gradient.
6. The statement "any acceleration that a body undergoes will cause a body force given by..." is very problematic. Forces cause accelerations, not vice versa. There is a sense in which that statement could be understood to be true for fictitious forces that we invoke to cause Newton's 2nd law to still work in a non-inertial frame. But I would never encourage anyone to think of it in that way because of risk of serious confusion. The core conceptual content of Newton's 2nd Law (Fnet = ma) is that accelerations are caused by forces. Thinking about it the other way around generally results in extremely incorrect predictions.
The comment by another poster about changing the equation to f = rho*velocity squared*area is puzzling since that would not be dimensionally correct for either a force or a force per unit volume.
There is a Wikipedia stub on force density and I think some of the content of this page ought to move there. But some of this content is simply incorrect. It looks like the term "body force" being applied to forces per unit volume must be done in some set of texts somewhere but I'm not aware of them, which is why I suspect this is an engineerism (I'm not saying there is anything wrong with the terminology used by engineers. I'm just saying that I may not be aware of it). Doing a quick search I see the term "body force density" being used in some physics publications. So maybe someone needs to investigate that and then insert some comment that the term is used differently in different fields if that turns out to be the case.
I'm loathe to make these edits myself because I'm not sure of the netiquet around it and also it looks like there is someone who's made this article a personal project, so maybe I'll leave it to them. But students in my class might be stumbling across this page soon because of a question I put on an assignment, so if edits haven't been made on this page within a few days I will probably do some of my own.
I've made edits along the lines of the points I raised above. I haven't been able to come up with examples of the term "body force" being used synonymously with "force density". If anyone can come up with examples of this usage, perhaps in the engineering literature, then I think some comment should be inserted alerting readers to the fact that the term is used differently in different disciplines.
I'd like to point out that f = rho*velocity squared*area is a valid force. It has the units of force if you work it out right. Keep in mind, in aerodynamics F=c_l*1/2*rho*V^2*area. Since the coefficient of lift and drag are unit less the other terms must equal to a force unit. This is just an example to validate my statement. You can look up the aerodynamics article or google it if you don't believe it. Otherwise I completely agree with your statements above. Iron_Engineer (talk) 07:22, 1 July 2009 (UTC)
Hey I linked this page from fluid statics and upon checking it out would like to help improve it. I'm just starting to look at the article though. Could someone explain need to include the following line in the intro paragraph: The fictitious forces associated with a non-inertial reference frame may be viewed as body forces. I understand you are referencing Coriolis and centripetal affects, but the term fictitious force is not widespread and in my opinion adds confusion to what should be a straightforward opening paragraph for a relatively simple topic. I'm not going to get into a debate about whether the term fictitious force is relevant or not, as I'm sure many physicists and possibly engineers as well utilize it. I'm making the statement that even though I am a graduate student in mechanical engineering and fully versed in dynamics, this term confused me as I had never heard of it. If you want to maintain it as an example, just place it in a paragraph in the article. But since this should be a very fundamental topic, why risk alienating readers who may not have heard of this, since even on the fictitious forces talk page there is ongoing debate about the term's validity. Iron_Engineer (talk) 07:18, 1 July 2009 (UTC)