Why is oil called more viscous than water when we slip on oil more than we do on water If we were to throw some water on the floor then walk over it we may or may not slip but it wouldn't that be difficult to walk. If we repeat the same thing with oil we it would be harder to walk as me spread our legs and apply a force component of force tangential to the surface of the floor does this not mean that the layers of oil have less friction between them than compared to water.So why is oil said to be more viscous?  Another example is hair oil if we keep water in out palm it's not that slippery but  with oil it's slippery even after we apply it to our hair. I've read some answers on reddit about this but I wasn't able to understand much.
Why is oil a better lubricant than water? How come mineral oil is a better lubricant than water, even though water has a lower viscosity?    When two surfaces slide over each other with a gap filled with a fluid, the different layers of the fluid are dragged at different speeds. The very top layer touching the top metal surface will have the same speed as the surface itself, while the bottommost layer is stationary. The speed in the layers between is distributed linearly and there exist friction forces between those layers that slow the movement. Those frictional forces should be reduces however, if a fluid with a lower viscosity is chosen.   How come this is not so?   Does it have to do with water's polarity, so that it sticks to surfaces in a different way than oil?
Find the value of:$$\frac{\sqrt{45} + \sqrt{18}} {\sqrt{7+2\sqrt{10}}}$$      I need help solving this question. Every reply is appreciated.  Thanks! asp.net mvc put controllers into a separate project If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian? I know that any group satisfying $x^2=1$ for all $x$ is abelian. Is the same true if $x^3=1$? I don't think it is, but I can't find a basic counterexample. How do I return a variable from Google Maps JavaScript geocoder callback? launch app, capture stdout and stderr in c++ What is the best way to identify outliers in multivariate data? Suppose I have a large set of multivariate data with at least three variables. How can I find the outliers? Pairwise scatterplots won't work as it is possible for an outlier to exist in 3 dimensions that is not an outlier in any of the 2 dimensional subspaces.  I am not thinking of a regression problem, but of true multivariate data. So answers involving robust regression or computing leverage are not helpful.  One possibility would be to compute the principal component scores and look for an outlier in the bivariate scatterplot of the first two scores. Would that be guaranteed to work? Are there better approaches? PHP: Split string into array, like explode with no delimiter Using JQuery and Prototype in the same page Several of my pages use both JQuery and Protoype. Since I upgraded to version 1.3 of JQuery this appears to be causing problems, because both libraries define a function named '$'.  JQuery provides a function noConflict() which relinquishes control of $ to other libraries that may be using it. So it seems like I need to go through all my pages that look like this:  &lt;head&gt;           &lt;script type="text/javascript" src="/obp/js/prototype.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript" src="/obp/js/jquery.js"&gt;&lt;/script&gt; &lt;/head&gt;   and change them to look like this:  &lt;head&gt;           &lt;script type="text/javascript" src="/obp/js/prototype.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript" src="/obp/js/jquery.js"&gt;&lt;/script&gt;     &lt;script type="text/javascript"&gt;         jQuery.noConflict();         var $j = jQuery;     &lt;/script&gt; &lt;/head&gt;   I should then be able to use '$' for Prototype and '$j' (or 'jQuery') for JQuery. I'm not entirely happy about duplicating these 2 lines of code in every relevant page, and expect that at some point somebody is likely to forget to add them to a new page. I'd prefer to be able to do the following    Create a file jquery-noconflict.js which "includes" jquery.js and the 2 lines of code shown above Import jquery-noconflict.js (instead of jquery.js) in all my JSP/HTML pages   However, I'm not sure if it's possible to include one JS file in another, in the manner I've described? Of course an alternate solution is simply to add the 2 lines of code above to jquery.js directly, but if I do that I'll need to remember to do it every time I upgrade JQuery. $A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$ I'm trying to prove that if $A\neq 0$ is a commutative ring and there is an injective $A$-module homomorphism $A^m\hookrightarrow A^n$ then $m\leq n$ must necessarily hold.    This is exercise 2.11 from Atiyah and MacDonald's Introduction to Commutative Algebra, but unfortunately all the solutions available online are either very sparse with regard to this question or seem to use (to my surprise) a generalized version of Cramer's rule. Is there perhaps some other "cleaner" approach to solving this problem? I want to be able to  write the following in LaTeX      We make the further assumption that \begin{equation} \label{eqn:assumption} There is a bounded linear operator     $B:X\to X^*$ such that $B^*=B$ and the operator $JB$ is an extension of $T'(0)$\end{equation}   and get a nice output, in such a way that this whole chunk of text along with the math can be referenced later. Of course I can write text inside the equation environment using \text{}, but when I tried this the spacing was all wrong. Can anyone suggest a solution to this? Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. How to run both Intel and Nvidia graphics card driver on dual monitor setup? I'm trying to get Intel and Nvidia graphics card working together with two monitors. One monitor should use the Intel card and the other the Nvidia card. Of course, I want to use only one keyboard and one mouse to switch between both screens. Bumblebee didn't work for me.  I don't want to use the xserver-xorg-video-all package because I need the Nvidia card for gaming and I can't use only one graphics card because I need one for KVM virtualisation and the other one for my Linux desktop  So I tried to install the drivers and to configure the Xserver manually. The Nvidia driver is working and I get a video output. But I don't get a video output with the Intel card.  I followed   The config files: Set a global policy for floats positioning I have a document with many floats (figures, specifically).  I want to be able to change the global floats positioning policy from htbp to just h (or even H with the floats package).  For my-own reasons, I don't want to do this by appending the [h] argument to each float env.  One option that I can think of is using a macro:  \newcommand{\mypos}{h} % or htbp \begin{figure}[\mypos]...   I also prefer not to do that - It is cumbersome.  Is there a way to set the global float positioning argument globally? Add Virtualbox Shortcut in Unity Launcher to boot to a VM How to pass parameters in batch file and zip the file using 7z.exe? I need to create a batch file as per below requirements  1) pass path1 &amp; path2 while running the batch file  exl: testrun.bat E:\ERP\test1.txt E:\ERP\header.txt  2) Need to store these command line paths values in batch file  exl: var1=E:\ERP\test1.txt var2=E:\ERP\header.txt  3) zip the path1 using PKZIPW.exe or 7z.exe and create new o/p zip file  exl: 7z.exe u -tzip E:\Erp\Test1.zip var1  4) copy path2 in newly created o/p file  exl: copy /b var2+test1.zip E:\Erp\Final_output.zip What really causes light/photons to appear slower in media? I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm interested in - I want to go deeper than that. We know that the real speed of light is actually not changing, the decrease in speed is just apparent. Material is mostly empty, the light will still travel with $c$ in the spacing. The rare atoms will disturb the light in some way. So I am interested in how the atoms affect the light. Photon absorption-emission theory Some textbooks that I read explain it in a way kind of like this: In a material the photons are absorbed by atom and then re-emitted a short time later, then they travel a short distance to the next atom and get absorbed&amp;emitted again and so on. How quickly the atoms in a material can absorb and re-emit the photon and how dense the atoms decides the apparent speed of light in that material. So the light appears slower because it has a smaller “drift speed”. Interference theory But recently I realize an alternative explanation: Atoms respond to the light by radiating electromagnetic wave. This “new light” interferes with the “old light” in some way that results in delayed light (advanced in phase), this can easily be shown by using simple phasor diagram. Consequently effectively the light covers a smaller phase each second, which gives the impression of a lower phase velocity. However the group velocity is changing in a complicated way. I think that the first explanation does not explain the change in phase velocity of light. if we consider light travelling into a slab of negative refractive index non-dispersive material, let’s say the light is directed perpendicular to the slab. The phase velocity’s direction will be flipped, but group velocity’s direction in the material will not change. Only the second explanation can explain the flipped phase velocity direction. I guess that the velocity that we get in the first explanation is actually belongs to the group velocity. It makes sense to me that the front most of the photon stream determines the first information that the light delivers. So the question is What really cause the phase velocity of light to be decreased?  &quot;drift velocity&quot; of photons (they aren't the same photons, they are re-emitted all the time) phase difference between absorbed and emitted light something else  And also, I still don't really understand detailed explanation of the absorption-emission process for small light's wavelength (for large lambda compare to the atoms spacing, the photons will be absorbed by the phonons). The dispersion relation that we know is continuous and also some material is non-dispersive, therefore the absorption process must occur in all frequency for a certain range. So definitely it doesn't involve the atomic transition, otherwise it will be quantized. My guess is that the relevant absorption process gets smooth out by the dipole moment. What makes the spectrum continuous? EDIT: link for dispersion relation: Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $ Problem with Refsection When did Tom Riddle get his new face? Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? How to check if windows has automatic updates waiting from the command line? If a Windows server (2k3/2k8) is set to "download but not install" updates, is there a way to check from the command line.. perhaps a log file or something I can check with powershell, to see if there are any updates actually waiting to be installed? I'm trying to prevent having to manually log on to each server to check, even though they want the "trigger" pulled manually. We have an automation system in place I can use (CA Autosys) - just not sure what to have it look for.