Bernoulli's principle states that air molecules moving with high velocity create an area of low pressure which in turn causes an object to fly, but how does high velocity cause low pressure?
So, if we have a large pipe which is constricted in the middle, the fluid in the middle section  will move faster. Why is it so? What dictates that liquid that an X amount of it must pass on the other side regardless of the size of the encasement?  The only reason I could think about is because that the initial pressure which causes the movement somehow is being transferred to a smaller area, but that makes no sense.
Why do objects move when you apply a force that's equal in magnitude to the friction? If the friction on an object is 200 N and you apply 200 N, it seems, the forces should immediately cancel each other out since the friction and your applied force go in opposite directions, leaving you with an object that is motionless. Yet, from what I've read, that's not the case. I feel like I'm misunderstanding something. Could it be I'm wrong about needing to apply 200 N initially? Might the amount of force I actually need be greater, but instantaneously decrease to 200 N? Floating sidebar can get too long and obscure footer Sometimes, when you create a question which returns a lot of similar questions, it makes the height of the floating "Similiar Questions" box too big to fit on the page. As a result, it blocks some of the footer on the right hand side. It's actually doing it as I type this question.  I think a max height based on the view port - footerHeight should fix it. How can author deal with late reviews? Another problem I personally struggle with in peer-review publication process is the situation when review takes really, really, really long. The precise definition of "long" is probably very area-specific: for example a paper in Maths will probably took longer to review than one in Physics. Many well-established journals and major publishers, sadly, prefer not to specify the "rules of the game" precisely, particularly how long the review process should normally take. Fortunately, I quite often serve as a referee with the very same journals and know the amount of time I am given to write a review. Unfortunately, when I am an author, I do not observe these deadlines to be always met. For example, a notable U.S. publisher would ask a reviewer to send a review in 2 months; but in practice a first review of my paper once took as long as 8 months.  As a rule of thumb, I usually start writing to editors with questions about "the status of my paper" in X+1 months time, when X is a deadline time for a reviewer to submit a review. This strategy is not particularly successful &mdash; what I usually get is a recommendation to be more patient. Since there is no "official" deadline time announced, there is no formal ground for complaints here.  Of course, such delays lead to a whole bunch of funny situations, particularly if a preprint is put online (e.g., on arXiv) and the results are presented in some conferences. Follow-ups with no official paper to cite, grant applications in which you can not justify by a solid publication, good research but bad bibliometrics or CV, to name just a few.   Could you recommend an efficient way to deal with this problem? A map $f:S^n\rightarrow S^n$ satisfying $f(x)=f(-x)$ for all $x\in S^n$ is said to be an even map. Show that if $f:S^n\rightarrow S^n$ is an even map, then $\deg f=0$ when $n$ is even and $\deg f$ is even when $n$ is odd. Moreover show that when $n$ is odd, there exist even maps of any given even degree.   My Try:  So $f=(-I)\circ f$. Then $\deg f=\deg (-I)\times \deg f$. If $n$ is even $\deg (-I)=-1$. Hence, $2\deg f=0$, so $\deg f=0$. But how do I show the results when $n$ is odd. No clue at all. This problem is in Hatchers book (A very complicated text). There is a hint but I do not understand it. Can somebody help me to proceed? How to install Blender from the official website I installed Blender from official Ubuntu repository but its version is always behind the version available from the official Blender website.  I'm aware that I can launch the program within the downloaded folder, but i want to replace the install version with a new version downloaded from the website?   It must be present in the unity launcher.  I'm also aware of the available PPA's that are available, however I just want to install Blender manually.  Thanks in advance How gently could a comet/asteroid/meteorite “hit” Earth? How to automatically keep user remembered in Devise How to redirect output of wget as input to unzip? I have to download a file from this . The file download is a zip file which I will have to unzip in the current folder.  Normally, I would download it first, then run the unzip command.  $ wget http://www.vim.org/scripts/download_script.php?src_id=11834 -O temp.zip $ unzip temp.zip   But in this way, I need to execute two commands, wait for the completion of first one to execute the next one, also, I must know the name of the file temp.zip to give it to unzip.  Is it possible to redirect output of wget to unzip? Something like  $ unzip &lt; `wget http://www.vim.org/scripts/download_script.php?src_id=11834`   But it didn't work.      bash: wget   http://www.vim.org/scripts/download_script.php?src_id=11834   -O temp.zip: ambiguous redirect   Also, wget got executed twice, and downloaded the file twice. If I wanted to just view, sort, and organize (via tags or folders or both), what programs are geared toward doing this quickly?  I know I could do this in most any photo editor, but it's not ideal for reviewing hundreds of images. I've also seen people use the image previewers built into their computer's OS, but that can't be the best option either.  What program would you suggest instead?  Extra info on the program is appreciated, i.e. OS requirements and cost. Finding maximal sublist of linearly independent vectors I would like to use multiple .bib files for my article, such as file1.bib, file2.bib. However, I would like my references not to be separated (such as &quot;Primary sources&quot;, &quot;Secondary sources&quot;, etc.). These bibliographies just need to be merged into one. One way to do this is to copy-paste these .bib files into one .bib file, and this would solve the problem. However, I would like to keep it split into several .bib files, by topic (file1.bib contains articles on topic1, file2.bib contains articles on topic2, and so on). I tried to do \bibliographystyle{alpha}  \bibliography{file1} \bibliography{file2}  but this just gives me the same bibliography twice! If $G$ is a compact topological group, how to show that a finite index subgroup of $G$ is open ? I really don't know where/how to start...  PS : I precise that by "compact" I mean that it is hausdorff and that any recovering of $G$ by open sets has a finite sub-recovering (sorry if I wasn't unclear) What are the differences between "-" and "--" in commands? I often see a single dash - or double dash -- followed by linux commands or other installed linux programs.   What are the differences between single dash and double dashes?  Is it just about abbreviation?  For example, -v means --verbose most of the time. In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? Multiple AES Key Derivation from a master key How to read high voltages on microcontroller? commandButton/commandLink/ajax action/listener method not invoked or input value not set/updated Mid 2012 MBP shuts down claiming no power with charge at 30% or 40% or more I have two mid 2012 MBPs. Sometime last year they both started randomly shutting down and showing the 'please plug me in to power' image when trying to start them up. That would be fine if the batter was at 1% or less but this happens when the battery is at anywhere from 30% to as high as 48% full. The power cycle info says 500 cycles or so. Both of them do this. They are both patched current, always. I asked Apple they suggested NVRAM PRAM and SMC reset, as expected, which had no effect. Any ideas? Is it implied that Porpetina and Queenie Goldstein are Jewish? How do I efficiently get "the most recent corresponding row"? I have a query pattern that must be very common, but I don't know how to write an efficient query for it.  I want to look up the rows of a table that correspond to "the most recent date not after" the rows of another table.  I have a table, inventory say, which represents the inventory I hold on a certain day.  date       | good | quantity ------------------------------ 2013-08-09 | egg  | 5 2013-08-09 | pear | 7 2013-08-02 | egg  | 1 2013-08-02 | pear | 2   and a table, "price" say, which holds the price of a good on a given day  date       | good | price -------------------------- 2013-08-07 | egg  | 120 2013-08-06 | pear | 200 2013-08-01 | egg  | 110 2013-07-30 | pear | 220   How can I efficiently get the "most recent" price for each row of the inventory table, i.e.  date       | pricing date | good | quantity | price ---------------------------------------------------- 2013-08-09 | 2013-08-07   | egg  | 5        | 120 2013-08-09 | 2013-08-06   | pear | 7        | 200 2013-08-02 | 2013-08-01   | egg  | 1        | 110 2013-08-02 | 2013-07-30   | pear | 2        | 220   I know one way of doing this:  select inventory.date, max(price.date) as pricing_date, good from inventory, price where inventory.date &gt;= price.date and inventory.good = price.good group by inventory.date, good   and then join this query again to inventory. For large tables even doing the first query (without joining again to inventory) is very slow.  However, the same problem is quickly solved if I simply use my programming language to issue one max(price.date) ... where price.date &lt;= date_of_interest ... order by price.date desc limit 1 query for each date_of_interest from the inventory table, so I know there is no computational impediment.  I would, however, prefer to solve the whole problem with a single SQL query, because it would allow me to do further SQL processing on the result of the query.  Is there a standard way to do this efficiently? It feels like it must come up often and that there should be a way to write a fast query for it.  I'm using Postgres, but an SQL-generic answer would be appreciated.