The transition from laminar flow to  is usually told interms of Reynolds numbers. The Reynolds number is $Re=UL/\nu$ where $U$ is the speed, $L$ is dimensional length and $\nu$ is the viscosity. Even if we say the Reynold's number tells us whether the flow is turbulent or not, I have never seen a unique $Re$ that differentiates laminar from turbulence. My question is then, is the cause of turblence perfectly known? is it velocity, length or viscosity that highly determines the flow condition? Is there a unique Reynold's number that separates laminar flow from turbulent?
In high Reynolds numbers we have turbulent flow. This is because the inertial forces are much greater than the viscous forces. I understand inertial forces to be actually the fictional forces due to the momentum of the moving fluid. And viscous to be the forces that drag each layers together. But why when inertial forces are too high than the viscous forces, there is turbulence? Why don't the molecules just continue to move laminarly due to their momentum? I can assume the viscous forces are not very strong in high speeds (in high inertial forces) to keep them together to form a laminar flow? But again, why they result in irrational movement after the effect of viscous forces is not anymore considerable? As a mechanical analogue, if I have balls attached together and make them travel linearly, and remove their between them attachment, they can continue to travel linearly. But what happens in fluid molecules that turbulence is created?
Show that AB is singular if A is singular Actually I need to show that $\det(AB) = \det(A)\det(B)$ if $A$ is a singular matrix.  The determinant of $A$ is $0$ if $A$ is singular, so $\det(AB)$ has to be $0$ as well, but I have problems showing that $AB$ is singular if $A$ is singular. How can I show that? Can't boot XP after Ubuntu Installation, how to fix? I installed Ubuntu and after the installation, i can't boot to XP. When i choose XP from the Grub menu, I got black screen for like 30 sec, and then it returns to the Grub menu.  Thanks! How do I find this conditional expectation? I’ve had this issue for months but in the last couple of days it’s got very very bad.  When my phone runs out of battery it needs like 2–3 days to turn back on. At the beginning of this problem the phone would need about 1h. Every time when my phone goes off again the time to switching on goes up.  What does this all look like? Well, when my phone died I put it on the charger, then the logo appears and goes off. When it goes off, a black screen pops out with a little white line on in it, then it turns on back to Apple logo. It keeps doing this until it turns on which is 1 or 2 even now 3 days.  I tried to restore it and also update it but nothing happens, literally nothing happened. Class is not key value coding-compliant I am seeing quite a few conversions which have as source "accounts.google.com" (almost 40%).  AFAIK, in the new Universal Analytics as soon as a user has a Referrer set a new session is started. So if a user is getting on my page, and creates an account using social auth (e.g. Google accounts) when being redirected back, will this create a new session? I guess this would explain that there are many conversions coming from accounts.google.com - is it safe to enter accounts.google.com into the Referral Exclusion List? And more - what about Facebook logins, those would show up as facebook.com, but i probably don't want to exclude facebook.com as referrer?  Any ideas how to deal with UA referrers and social logins? I have got a new installation of windows recently. Now when I do unpin items from taskbar that were there (IE, Edge, Explorer), they do come back after restart. A pinned chrome does not disappear though e.g.  Anything to fix this issue?  P.S. Just created a new user, and he has the same problem  P.P.S. Sign out is enough to get it back, no full restart needed How do I achieve this kind of light star effect? I'm kinda new to Blender. Currently playing around with version 2.8 to practice some rendering. Is there a way to achieve this 'light-star' effect for the blooming objects with the emission? If there is an alternative way then it's fine too. See these images below for references. Thanks in advance: How do the Flashes breathe utilizing their super speed? The air pressure would be extreme. Do they run in a pressurized bubble? Implementation of "show" for function How do I create a PDO parameterized query with a LIKE statement? Here's my attempt at it:  $query = $database-&gt;prepare('SELECT * FROM table WHERE column LIKE "?%"');  $query-&gt;execute(array('value'));  while ($results = $query-&gt;fetch())  {     echo $results['column']; } Bold code in a question Frequently when I ask a question I have to include quite a bit of code for reference purposes.    It would be nice to be able to bold the important lines in the code.  For example this code:  &lt;DataTrigger Value="True"&gt;     &lt;DataTrigger.Binding&gt;         &lt;MultiBinding Converter="{StaticResource DisableWorkItemConverter}"&gt;             &lt;Binding ElementName="MainForm" Path="PickedWorkItemID"/&gt;             &lt;Binding Path="Id"/&gt;         &lt;/MultiBinding&gt;     &lt;/DataTrigger.Binding&gt;     &lt;Setter Property="IsEnabled" Value="False"/&gt;     &lt;Setter Property="IsSelected" Value="False"/&gt; &lt;/DataTrigger&gt;   Is not way long, but the important part (as seen in ) is the second to last line.  However, if I try to bold it, it ends up looking like this:  &lt;DataTrigger Value="True"&gt;     &lt;DataTrigger.Binding&gt;         &lt;MultiBinding Converter="{StaticResource DisableWorkItemConverter}"&gt;             &lt;Binding ElementName="MainForm" Path="PickedWorkItemID"/&gt;             &lt;Binding Path="Id"/&gt;         &lt;/MultiBinding&gt;     &lt;/DataTrigger.Binding&gt;     &lt;Setter Property="IsEnabled" Value="False"/&gt;     **&lt;Setter Property="IsSelected" Value="False"/&gt;** &lt;/DataTrigger&gt;   Not what I was going for.  It would be nice to be able to draw attention to specific lines of code when needed.    (One suggestion of a different color background sounds nice too (ie a yellow background to draw the eye to the relevant code.)  If there is some other way to bold in code please let me know. I am trying to install Ubuntu 16.04 LTS on a Dell XPS 13 (9350). The laptop came with Windows 10 pre-installed. I am installing from a pendrive but I think the issue would be the same if I used e.g. a USB DVD drive.   Dude, where's my hard drive?  I am blocked because the installation program cannot find 8.6Gb of free space on my hard drive despite the fact that there are hundreds of Gb free according to Windows. Digging a bit into the problem, it seems that Ubuntu cannot see my hard disk at all.    This is the output of GParted:    I am not sure what that drive mounted at /cdrom is, but it seems the only device that exists in the system that is not a RAM disk or a loop device:   Content of /proc/partitions:   ubuntu@ubuntu:~$ cat /proc/partitions   major minor  #blocks  name     1        0      65536 ram0     1        1      65536 ram1     1        2      65536 ram2     1        3      65536 ram3     1        4      65536 ram4     1        5      65536 ram5     1        6      65536 ram6     1        7      65536 ram7     1        8      65536 ram8     1        9      65536 ram9     1       10      65536 ram10     1       11      65536 ram11     1       12      65536 ram12     1       13      65536 ram13     1       14      65536 ram14     1       15      65536 ram15     7        0     130048 loop0     7        1    1104188 loop1     8        0    1970239 sda     8        1    1953439 sda1   Summary of fdisk -l:   ubuntu@ubuntu:~$ sudo fdisk -l |grep Disk Disk /dev/ram0: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram1: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram2: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram3: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram4: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram5: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram6: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram7: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram8: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram9: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram10: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram11: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram12: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram13: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram14: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram15: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/loop0: 127 MiB, 133169152 bytes, 260096 sectors Disk /dev/loop1: 1.1 GiB, 1130688512 bytes, 2208376 sectors Disk /dev/sda: 1.9 GiB, 2017525248 bytes, 3940479 sectors Disklabel type: dos Disk identifier: 0x00000000   Result of fdisk of the only non-loop non-RAM device (not sure this is relevant):   ubuntu@ubuntu:~$ sudo fdisk -l |grep -A 50 sda Disk /dev/sda: 1.9 GiB, 2017525248 bytes, 3940479 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x00000000  Device     Boot Start     End Sectors  Size Id Type /dev/sda1  *      129 3907007 3906879  1.9G  c W95 FAT32 (LBA)   I am blocked at this point. Any help will be much appreciated.   Additional information (following comments):   Running dmesg |grep -i sata shows (among others) eight lines that suggest some kind of error:   ata1: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata2: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata3: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata4: SATA link down (SStatus 0 SControl 0) ata5: SATA link down (SStatus 0 SControl 0) ata6: SATA link down (SStatus 0 SControl 0) ata7: SATA link down (SStatus 0 SControl 0) ata8: SATA link down (SStatus 0 SControl 0)  I have "Restarted" windows instead of only "Shutdown" it to avoid problems with "fast startup", following some recommendations I have read of other users having problems installing Linux on Windows 10 laptops.ago   Regarding SATA, the BIOS says: "SATA Operation: RAID ON". The other two options available are "Disabled" and "AHCI".    I have followed the instructions of these two pages from Dell: , . Moving set of polygons in ArcGIS Pro? I am very new to mapping and I have loaded a set polygons from a shapefile into ArcGIS Pro. They appear correctly however they have clearly lost (or didn't have in the first place), their longitudinal and latitudinal information as they are currently placed in the middle of the ocean, which I believe is the 0 lat, 0 long position.  I can manually move these polygons but it won't let me save the moves, so when I click 'select', it moves back to the original location. Both of the 'save' and 'discard' buttons are greyed out and cannot be clicked. If I click 'finish' on the move tool then it will snap back to the original location too.  Does anybody have any ideas? Does a finally block always get executed in Java? Considering this code, can I be absolutely sure that the finally block always executes, no matter what something() is?  try {       something();       return success;   }   catch (Exception e) {        return failure;   }   finally {       System.out.println("I don't know if this will get printed out"); } Questions with ignored tags still visible in iOS app I have set to ignore [php] tag and chose to hide questions in preferences:        But I still see questions tagged [php] in the iOS app.         Seems the app can't distinguish options for ignored tags.   App Version: 1.6.5.3 Device: iPad Air 2 (Wi-Fi) OS Version: Version 10.3.1 (Build 14E304) Best way to specify whitespace in a String.Split operation How long will foods that have "Best by: XX-XX-XX" on the product last past that date?  I have tried looking online, and all I can find is anecdotal evidence, which isn't very assuring for me since there seems to be no specific "x food will expire y weeks after its best by date".  Is there a rule of thumb or some guide out there that can tell me how long a "best by" food will last? Or is it safe to assume that they never expire, since it's not actually labelled on the product? Assume $T \in \mathbb{R}^{d\times d}$. Let $\rho(T)$ be the spectral radius of $T$ and $\rho \ge 0$. Prove that  $\rho(T) &lt; \rho$ if and only if there exists a $P \succ 0$ satisfying $T^TPT - \rho^2 P \prec 0$.  I can prove the Necessity: If $P = I$, for any $x \in \mathbb{R}^d$,   \begin{equation} x^T T^T P T x - \rho^2 x^T P x = \| Tx \|^2 - \rho^2 \| x\|^2 &lt; 0 \end{equation} so $T^T PT - \rho^2 P \prec 0$  I get stuck in proving the Sufficiency. HUD is not working after upgrade My HUD is not working after I upgraded from 11.04 (and or 11.10).  It prompts for command and it tries loading for 4 seconds then gives up.