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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.

I came here looking for a better understanding of body forces for my fluids class and,... no dice. eximo (talk) 01:13, 7 February 2008 (UTC)[reply]

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.

What major mistakes? Adding v^2 is a major mistake, a force in general doesn't need to depend on acceleration. -Ben pcc (talk) 03:20, 26 May 2008 (UTC)[reply]

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 (F_net = 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.

(GLeeDads (talk) 03:20, 6 February 2009 (UTC))[reply]

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.

--GLeeDads (talk) 21:22, 6 March 2009 (UTC)[reply]

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)[reply]

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)[reply]

There is a paragraph in the qualitative definition section which says,

"A body force is distinct from a contact force in that the force does not require contact for transmission. Thus, common forces associated with pressure gradients and conductive and convective heat transmission are not body forces as they require contact between systems to exist. Radiation heat transfer, on the other hand, is a perfect example of a body force."

I have bolded the last statement because it looks like it's probably incorrect, which seems plausible given that it is uncited and others seem to think this article is generally rather bad right now. It would make sense to say that radiation is a body force if not requiring contact between the objects was all that was necessary to make something a body force. Thus, it seems plausible that someone added this after seeing the preceding sentence (and/or a similar one elsewhere) and noted that radiation does not require contact between objects made of "matter" to transfer heat, unlike conduction and convection, and so decided to note it.

I have two main problems with this statement:

Firstly, radiation heat transfer is not a force at all on a macroscopic scale, although I suppose it does involve a whole bunch of random "forces" pushing on particles in the two objects to slow down particles in the cooling object and speed them up in the heating object (on average relative to the center-of-momentum frame of reference of each object). The concept of body forces versus surface forces seems very much to be a macroscopic concept likely to occur in continuum mechanics or other classical theories but not in statistical mechanics or quantum physics, so I think it's fair to say that heat transfer, in and of itself, is not a force. If this reasoning holds, then the wording of this statement, at the very least, is wrong.

Secondly, for objects that are opaque to the type of radiation being considered, the macroscopic forces resulting from radiation pressure (which acts on objects emitting, absorbing, or reflecting the radiation) behaves like a surface force, not like a body force: For opaque objects, radiation is effectively only emitted at the surface of the object, because any internally emitted radiation (of the type considered) is immediately absorbed, producing no net change in momentum (or temperature). Similarly, for opaque objects, all absorption and reflection of radiation also happens at the surface, because no radiation (of the kind under consideration) can penetrate any deeper than that.

The only situation in which it makes sense to call radiation pressure a body force is when objects that are semitransparent to the relevant types of radiation are considered. In this situation, emission, absorption, and reflection, and therefore momentum transfer, i.e. force, is distributed throughout the body and not just at the surface. Even this situation is a somewhat unusual type of body force, though, since the radiation attenuates exponentially as it passes through the semitransparent material. Thus, the force exerted on each part of the semitransparent body is dependent on the length of the path(s) the radiation took to get there (as well as the specific opacity of the parts it passed through if the object is not homogeneous with regard to opacity). I don't think this prevents it from being a body force, and I even think that other, perhaps more clear-cut, types of body force, like forces from static electromagnetic fields, may sometimes have properties somewhat like this (e.g., due to differences in permittivity and permeability); however, when we combine this with the fact that many if not most objects are effectively (though perhaps not totally) opaque to most of the radiation involved in the radiation heat transfer situations usually considered and the fact that radiation pressure is usually negligible anyway, I think it's quite dubious to call this "a perfect example of a body force", even if we were to replace "radiation heat transfer" with "radiation pressure" or "forces associated with radiation pressure".

Also, I personally don't know what forces related to conductive heat transfer there are, but I don't doubt that there are some.DubleH (talk) 22:02, 23 January 2021 (UTC)[reply]