This question relates to drag cofficients. This should be rather basic, but I cannot find a reference for the Frontal area (Fa) of a square cylinder (i.e., a box) oriented normal to airflow. It seems instinctive that the Fa should be the Length * Height of the windward side of the box. However, at best, texts give a little picture of a horizontal box (i.e., length oriented horizontally) where they call out length and depth…implying Fa = L * D and not L * H (where height would be the width).
In my case, my box is oriented vertically where Length = Height. As such, it seems instinctive that Fa = L * W.
Regardless, I need a reference - preferably a fluids text book I can (mostlikely) find in university library.
It’s so simple, perhaps the authors (which seem to copy from each other…esp the figures) have overlooked it?
The frontal area is usually* the projected area normal to flow. If you need (ie need to move from 95 to 99%) a text book saying Ap = "Area projected normal to flow you could use Perry page 6-50, it’ll be in the Knovel library/Database.
*I don’t want to say this. But if you are in a situation where you are using some sort of effective diameter, the text should say explicitly what area they want you to use. The only reason I left the asterisk in is because what I have said is what I would assume unless I had a reason to assume differently. Is the area for a particular correlation? If you are unsure, you would have to go back and check the derivation.
I’m 99% certain it is what I’ve said, unless there is something in the literature or on the table you are pulling your Cd values that implies differently.
Thanks, Zany! I assume you mean Perry’s Handbook of Chemical Engineering? As for your asterisk, I’m not sure what you’re saying. Yes, of course the text SHOULD explain how to find the effective diameter (or whatever you want to call it), but my text was selected by a bunch of self-serving thiefs who only had their own greedy profits in mind when selecting our fluids text. (I’m a ME, but I haven’t had to think about square cylinders in ages, and I probably took the Fa formula for granted way back when.) The more I try and use my text as a reference, the worse of a reference I see it is!
I’m not quite sure what your question is. ZZZ is right that you’ll be using the projected area (I usually refer to it as the cross sectional area). Remember that you’re going to be having some skin drag as well; I’m not sure how closely using the C[sub]d[/sub] of a cylinder will model a box, since there is going to be edge effects that and some other funky stuff going on at the corners of the box. It will probably be within an acceptable area, though.
Is the third dimension (the one you and I would call depth) included in the formula you’re trying to use? It’s important, as Wiki gives the C[sub]d[/sub] of a long cylinder as 0.82 while a short one is 1.15.
In short, I’m not sure where you’re going to be able to find a fluids text that shows how to compute an area; maybe a geometry book?
It’s not complete yet, but WikiBooks will be a good reference in a few years. I use it often for controls; it seems to be a higher quality than the encyclopedia.
Ye Olde Schaum’s Outline of Fluid Mechanics (mine dates to 1962 :eek: )derives the drag equation for fluids in some of the exercises given in the book. I don’t think you can find this one in the library, but perhaps in the bookstore? I don’t think it’s very expensive.
The drag on the body you describe is related to width x length, although the book simply calls it “area”. Schaum’s relates the drag coefficient to the Reynolds number, and there is a spiffy chart in the back which gives coefficients of drag for various shapes, indexed by R.
Found one on Amazon, it’s around thirteen dollars new, eight dollars used: Schaum’s Outline. Well worth the money; I still use mine from time to time. They have other titles of Schaum’s also.
Thanks for your thoughts, but to clarify: In some fluids books, you can find the term “Frontal Area” (Fa) and examples with cylinders with the length (often called “b”) and diameter (d) called out in a little diagram…such that Fa = b*d. Yes, this works out to the projected area if one were to slice the cyliner along its longitudinal axis (assuming the cylinder is oriented such that the aristream is normal to its longitudinal axis).
Now, if you’ve seen such a figure, then you’ve probably seen a chart of other geometries including a “square cylinder” (i.e., box) where the max Cd value is typically 2.05 (per many references). But, the little figure shown in such a chart will use arrowheads between dimension lines calling out the length as “b” and the depth as “d” to specfically call attention to the length and depth of the box. This strongly imples that the terms “b” and “d” are now length and depth, respectively. Surely, this is misleading. It would stand to reason that, applying the same nomenclature, Fa = b*width for a box. I believe such a chart with this same figure appears in Marks’ Handbook for Mechanical Engineers, for one.
In short, I am not looking for a reference on how to find area…such as a geometry book. I am looking for a fluids reference that clearly calls this area “The projected area” or “The cross-sectional” so that there is no confusion that it could be any other way of figuring area. Unfortunately, books that call it “frontal area” or simply “area” do not help my cause.
Alternately, I’d settle for a reference that defines a closely-related term called “Effective Projected Area” also known as “EPA”. Some civil engineers were taught to apply the EPA value which is the product of Fa * Cd for any given geometry.
Thanks for the thought. I believe I own one, and I’ll have to see if they provide anything more pinpointedly specific that simply calling it “area”. They may even provide a better figure (in a chart of Cd values) that may give support to what I am seeking…even if the text is not explicit enough. I’ll check it out. - Jinx