My question is about a toy hovercraft - a balloon connected to a CD. I need to know about something. How does cross section of the pipe affect the time that the toy hovercraft hovers above the surface?
Poiseuille's law states that the rate of flow of water is proportionate to $r^4$ where $r$ is the radius of the pipe. I don't see why.  Intuitively I would expect rate of flow of fluid to vary with $r^2$ as the volume of a cylinder varies with $r^2$ for a constant length. The volume that flows past a point is equal to rate of flow fluid, and thus it should vary with $r^2$.  I cannot understand the mathematical proof completely. Is there an intuitive explanation for this?
My organization is looking at developing mobile applications, we have a wealth of web development resources. There are many factors to consider in making the decision of how to develop this application such as Cost(s), platform support, performance, and maintainability.   But, I have not found any research that actually backs up the assumptions that users prefer the experience of a native app over a hybrid mobile web app (A hybrid app is a HTML5 app distributed in an embedded web view using PhoneGap, etc.).   Some  that native apps are more performant and have a better user experience, but why? Have there been any user surveys or analytics that indicate this user preference towards native? Use Listing in newenvironment I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. How do you debug PHP scripts? Isn't the const modifier here unnecessary? I've been struggling with this all day today. I imagine it's not very hard, but my algebra skills are terrible. So, how can I show that if $m&gt;n$ and $a$ is a positive integer, then $$a^{2^n}+1 \mid a^{2^m}-1.$$ I just can't get a coherent picture of what I'm supposed to do. If this too (see yesterday's question) boils down to the Unique Factorization Theorem, I would be very grateful for any intuition on how to think about this! Single service account running all SQL Servers Is there any negative performance impact for using the same service account and agent account to run SQL Server and SQL Agent respectively for all SQL server instances running at a small company of say 35 servers? The biggest database is 0.5 GB. any suggestions are welcome. Thank you. White background with filmic blender Bridged interfaces and VLAN tags Why is it better to use "#!/usr/bin/env NAME" instead of "#!/path/to/NAME" as my shebang? I notice that some scripts which I have acquired from others have the shebang #!/path/to/NAME while others (using the same tool, NAME) have the shebang #!/usr/bin/env NAME.  Both seem to work properly.  In tutorials (on Python, for example), there seems to be a suggestion that the latter shebang is better.  But, I don't quite understand why this is so.  I realize that, in order to use the latter shebang, NAME must be in the PATH whereas the first shebang does not have this restriction.  Also, it appears (to me) that the first would be the better shebang, since it specifies precisely where NAME is located.  So, in this case, if there are multiple versions of NAME (e.g., /usr/bin/NAME, /usr/local/bin/NAME), the first case specifies which to use.  My question is why is the first shebang preferred to the second one? Many anime do not follow the manga history and are made shorter. However there are a few that do follow it or try to finish the history with the manga like the big three (Naruto, Bleach, One Piece), Death Note, and FMA Brotherhood. But others finish the anime without the real ending like FMA, Ouran High School, Pandora Hearts, Tsubasa Reservoir Chronicle. Why is this so? Is it because of the high cost? Or the lack of popularity? I've got a PDF that is automatically generated from a certain piece of software, that I want to include in the report I'm writing. I'm using pdfpages which gets the job done elegantly, but the problem is, the PDF has a lot of white space around the actual content (which is a graphics) and I always have to do some tedious post-processing of the automatically generated document so that it fits well in my report. Changing the output of the software to eliminate the white space is not an option (or at least, would be much more trouble than it's worth).  I checked the pdfpages , but wasn't able to find an option that does that. Ideally, I'd like to be able to set margins from each direction, and the PDF is then cropped accordingly and included.  What other options do I have to control what portion of the included PDF is visible in the final document? What is the point of the Red Thread/Tape around evidence or newspaper clippings? I have seen in a lot-lot of movies that the person who searches for a crime or another person creates a web of red tape or wire around the newspapers and evidence he acquires. I never guessed its usefulness and am therefore asking why do they do it?  Here is an illustration I created: $F(x)$ versus $F[x]$ where $F$ is a field Should one downvote answers to off-topic questions? It annoys me when people post answers to obviously off-topic questions like , especially after those questions have already received several close votes. Migrations seem to happen rather infrequently these days, so there's probably no reputation to gain for questions that are likely to be closed. And although sure, the answer may help the OP, it also encourages bad behavior (posting off-topic questions.)  Is it appropriate to downvote these answers?   Personally, I think I could make a case for both sides. What is the scientific name of this evergreen plant? This plant is found in India. It is an evergreen plant. Would love to know the scientific name. How to wipe and install ubuntu? Can you use an alias in the WHERE clause in mysql? I need to use an alias in the WHERE clause, but It keeps telling me that its an unknown column. Is there any way to get around this issue? I need to select records that have a rating higher than x. Rating is calculated as the following alias:  sum(reviews.rev_rating)/count(reviews.rev_id) as avg_rating How to install packages to external drive (and run them)? I am running Xenial 16.04 and looking to install packages to an external drive - my computer has a 32gb SSD so it would be very useful to me to be able to use an external drive.  In a quick search I found a framework called  which seems to be designed to package all dependencies for a program (chromium, GIMP, some python packages, etc), but haven't had time to look into it.   seems to be looking for the same solution I am.   Thanks, Chris What's the current state of LaTeX3 (2020)? There are a few questions on this forum asking about why Latex3 is taking so long to come out. However, all of these are from the early 2010s. I'm just wondering what the current state of the project is and whether it's ready (or nearly ready) for prime time? Do small title edits constitute trivial edits?