I am trying to reduce water pressure by changing pipe size. I want to make a slow peaceful fountain spray.The end of the water line will be pointed straight up so will the weight of the water play into the water pressure. Does the length of the tube going straight up effect water pressure?
Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm diameter pipe, what will be the pressure generated by water?
What should I do, as my submitted paper is still under review after 1 year? For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable? I recently read the well known theorem that for a group $G$ and $H$ a normal subgroup of $G$, then $G$ is solvable if and only if $H$ and $G/H$ are solvable. In my book, only the fact that $G$ is solvable implies $H$ is solvable was proven. I was able to show that if $H$ and $G/H$ are solvable, then so is $G$, but I can't quite show that $G$ is solvable implies $G/H$ is solvable.   My idea was this. Since $G$ is solvable, there exists a normal abelian tower $$ G=G_0\supset G_1\supset\cdots\supset G_r=\{e\}. $$ I let $K_i=G_i/(H\cap G_i)$, in hopes of getting a sequence $$ G/H\supset K_1\supset\cdots\supset K_r=\{e\}. $$ My hunch is that the above is also a normal abelian tower. However, I'm having trouble verifying that $K_{i+1}\unlhd K_i$ and that $K_i/K_{i+1}$ is abelian.  Writing $H_i=H\cap G_i$, I take $gH_{i+1}\in K_{i+1}$ for some $g\in G_{i+1}$. If $g&#39;H_i\in K_i$, then I want to show $g&#39;H_igH_{i+1}g&#39;^{-1}H_i$ is still in $K_{i+1}$, but manipulating the cosets threw me off. I also tried to use either the second or third isomorphism theorems to show that $K_i/K_{i+1}$ is abelian, but I'm not clear on how to apply it exactly. I'd be grateful to see how this result comes through. Thank you. Can I switch the User-Agent header for only a single web site? I get it after updating in Synaptic Manager  I recently did a clean install of Ubuntu 17.04 from 16.10.  error message:-  W: Download is performed unsandboxed as root as file '/var/cache/apt/archives/partial/samba-libs_2%3a4.5.8+dfsg-0ubuntu0.17.04.1_i386.deb' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) How does RAID 1 determine which drive should act as the source for a rebuild? Here's my scenario -- both drives were working perfectly fine. I removed one of the drives for a while (building a new PC, didn't think I was going to use RAID anymore but changed my mind). I actually switch the SATA type to AHCI and was operating for about a week on the new system before deciding to re-enable RAID and reinstall the drive I had removed.   It's currently rebuilding, but I'm curious how it knows which one is the source and which one is out-of-date? my circuit is shown on the picture. the problem is the output of the mosfet does't work as desired. For example, If I use Vin=100V and the duty cycle is 50%, the output is Vout=19V.  Anyway, the output is not even near to the desired value. can you help, please? Is "mens" a valid word? I've been living in Ireland for almost a year now and I start noticing they use the word "mens" a lot. I can see it used in:   Shops, to denote the area where you can find men's clothes In sport, when they talk about "mens team".    My guess is just that they are lazy about the use of quotes, so that mens should actually be men's. However, there may be some rule I'm not aware of. So, is "mens" only limited to Irish English? When I'm allowed to use it? Why are the United States often referred to as America? How does an accelerating charge radiate electromagnetic waves? Cauchy condensation test The following is Cauchy condensation test:  If $b_n \ge 0$ and $b_n \ge b_{n+1}$ then $\sum b_n$ converges if and only if $\sum 2^n b_{2^n}$ converges.  Is the following modified Cauchy condensation test possible:  Let $N \in \mathbb N$. Then if $b_n \ge 0$ and $b_n \ge b_{n+1}$ then $\sum b_n$ converges if and only if $\sum N^n b_{N^n}$ converges? Java code needs a system.out.println statement to run Looking for a short story about an artist and a forger Back in the late 1970s to early 1980s, I read a short story about an artist and a forger.  Between the two of them, they managed to start a revolution that brought down a corrupt dictatorship.  It was science fiction:   The dictatorship was interplanetary, maybe interstellar.   The artist used some kind of advanced technology to make his art works.   Plot:  The artist is one of the best (if not the best) at what he does.  The dictator wants the artist to make what amounts to a family portrait in whatever medium it is he works in.  Think of it like painting - you create the image manually (not a photograph) but it is much more than just a flat image.    The artist doesn't like the dictator - maybe on general principles, maybe because he knows the dictator personally - and refuses to make the "portrait."  The dictator has the artist arrested, and will only let the artist free again if he makes the portrait.  The artists makes the portrait.  He does the work while in the prison or jail.  That's where the forger comes into things. The forger is also in jail for something or other.  The forger makes copies of art works.  He of course recognizes the artist, and knows what the artist works with.  The forger can somehow see what the artist is working on.  The artist finishes the portrait.  At first the dictator is thrilled.  It looks exactly the way he wanted it.  As time goes by, though, the people looking at the picture see that it represents the vileness and corruption of the dictator.  The more you look at it, the more of the evilness of the dictator you see in it.  That is the genius of the artist, and whatever medium he is using.  Once you notice the hidden levels of the portrait, you can't unsee them and you see more and more of it as you look.  I think the effect carries over into reality as well.  Once you've seen the dictator's corruption in the portrait you also begin to see it in the dictator and his works as well.  This of course seriously pisses off the dictator, who has the artist killed and the portrait destroyed.  While in prison, the forger watched as the artist created his masterpiece, and recognized it for the subversive thing it is.  He also recognized it as the ultimate rebellion from the artist - the artist knows what will be seen, and that he will be killed for it.  All of that inspires the forger to do something more meaningful with his life than make forgeries for the money.  The forger is released from prison.  He saw the completed portrait, and knows how it was made.  He begins making forgeries of the portrait - like, hundreds if not thousands of them.  These are distrubuted throughout the nation/empire.  The people realize what evil is controlling them once they see it in the copies of the portrait, and eventually a revolution rises and brings down the dictatorship.  It was probably older than the 1970s.  I expect earlier than 1960.  Any ideas? Say you have the infinitely continued fraction: $$x+\cfrac{1}{x^2+\cfrac{1}{x^3+\cfrac{1}{x^4+\ddots}}}$$ When $x=1$, you can see that it's $$1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\ddots}}}$$ which converges upon the golden ratio $\phi = 1.61803398875...$. What if I were to plug in $x=2$? $$2+\cfrac{1}{4+\cfrac{1}{8+\cfrac{1}{16+\ddots}}}$$ Using a caluclator, it seems to converge upon the irrational number: $2.24248109286...$ Is there any way I can represent this irrational number algebraically? C++ warning: deprecated conversion from string constant to ‘char*’ [-Wwrite-strings] How to get number of affected rows in sqlalchemy? I have one question concerning Python and the sqlalchemy module. What is the equivalent for cursor.rowcount in the sqlalchemy Python? Writing a string array to text file separated by new line character Here is the script to create my tables:   CREATE TABLE clients (    client_i INT(11),    PRIMARY KEY (client_id) ); CREATE TABLE projects (    project_id INT(11) UNSIGNED,    client_id INT(11) UNSIGNED,    PRIMARY KEY (project_id) ); CREATE TABLE posts (    post_id INT(11) UNSIGNED,    project_id INT(11) UNSIGNED,    PRIMARY KEY (post_id) );   In my PHP code, when deleting a client, I want to delete all projects posts:  DELETE  FROM posts INNER JOIN projects ON projects.project_id = posts.project_id WHERE projects.client_id = :client_id;   The posts table does not have a foreign key client_id, only project_id. I want to delete the posts in projects that have the passed client_id.  This is not working right now because no posts are deleted. Allow me to add my own "top questions" too! I know, I know, the site should be more heavily weighted to answering, but sometimes, how and what people ask is important too! For example I recently asked  which I think is a fairly good question. Clearly I'm going to avoid questions where I've asked something very simple, but I know of a user or two who are implementing their own C standard libraries and the depth of those questions is important/ought to be on show.  Of course, the argument I can just look at their profile holds, but that awesome q/a might have been from a year or so ago in which case finding it is difficult. Durrett Example 1.9 - Pairwise independence does not imply mutual independence? The example in question is from Rick Durrett's "Elementrary Probability for Applications", and the setup is something like this:     Let $A$ be the event "Alice and Betty have the same birthday", $B$ be the event "Betty and Carol have the same birthday", and $C$ be the event "Carol and Alice have the same birthday".   Durrett goes on to demonstrate that each pair is independent, since for example,   $P(A \cap B) = P(A)P(B)$.   However, he concludes that $A, B$, and $C$ are not independent, since   $P(A \cap B \cap C) = \frac{1}{365^2} \neq \frac{1}{365^3} = P(A)P(B)P(C)$.  I understand the reasoning here, and that one can generally show that arbitrary events $X$ and $Y$ are not independent by showing that $P(X\cap Y) \neq P(X)P(Y)$.   I am a little new to probability, though, and don't understand why exactly $P(A \cap B \cap C) = \frac{1}{365^2}$.   My progress so far:   I do see why $P(A) = P(B) =P(C) = \frac{1}{365}$, and thus why $P(A)P(B)P(C) = \frac{1}{365^3}$.  It seems like the sample space $\Omega = \{ (a, b, c) \mid a,b,c \in [365] \}$ -- i.e., all of the possible triples of numbers from 1 to 365, where 1 denotes January 1st, 2 denotes January 2nd, etc. From that, I can conclude $|\Omega| = 365^3$, but I'm not sure where to go from here.   It seems like once a single birthday is chosen, the rest are completely determined if they're all equal to each other - is this a good direction to go in? What is the maximum value of $n$ if $n + 5$ divides $n^5 + 5$, $n$ being a natural number? I tried to solve by binomial theorem but it failed.