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Google Drive
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Google Drive
The web version of Google Drive
Type of site
File hosting service
Owner
Google
Website
www.google.com/drive/
Registration
Required
Users
800 million (March 2017)
Launched
April 24, 2012; 5 years ago (2012-04-24)
Google Drive is a file storage and synchronization service developed by Google. Launched on April 24, 2012, Google Drive allows users to store files in the cloud, synchronize files across devices, and share files. In addition to a website, Google Drive offers apps with offline capabilities for Windows and macOS computers, and Android and iOS smartphones and tablets. Google Drive encompasses Google Docs, Sheets and Slides, an office suite that permits collaborative editing of documents, spreadsheets, presentations, drawings, forms, and more. Files created and edited through the office suite are saved in Google Drive.
Google Drive offers users 15 gigabytes of free storage, with 100 gigabytes, 1 terabyte, 2 terabytes, 10 terabytes, 20 terabytes, and 30 terabytes offered through optional paid plans. Files uploaded can be up to 5 terabytes in size. Users can change privacy settings for individual files and folders, including enabling sharing with other users or making content public. On the website, users can search for an image by describing its visuals, and use natural language to find specific files, such as "find my budget spreadsheet from last December". The website and Android app offer a Backups section to see what Android devices have data backed up to the service, and a completely overhauled computer app released in July 2017 allows for backing up specific folders on the user's computer. A Quick Access feature can intelligently predict the files users need.
Google Drive is a key component of G Suite, Google's monthly subscription offering for businesses and organizations. As part of select G Suite plans, Drive offers unlimited storage, advanced file audit reporting, enhanced administration controls, and greater collaboration tools for teams.
Following the launch of the service, Google Drive privacy policy was heavily criticized by some members of the media. Google has one set of Terms of Service and Privacy Policy agreements that cover all of its services, meaning that the language in the agreements grants the company broad rights to reproduce, use, and create derivative works from content stored on Google Drive. While the policies also confirm that users retain intellectual property rights, privacy advocates raised concerns that the licenses grant Google the rights to use the information and data to customize advertising and other services Google provides. In contrast, other members of the media noted that the agreements were no worse than those of competing cloud storage services, but that the competition uses "more artful language" in the agreements, and also stated that Google needs the rights in order to "move files around on its servers, cache your data, or make image thumbnails".
As of March 2017[update], Google Drive has 800 million active users, and as of September 2015, it has over one million organizational paying users. As of May 2017[update], there are over two trillion files stored on the service.
Contents
[hide]
1 Platforms
1.1 Computer apps
1.2 Mobile apps
1.3 Website interface
2 Storage
2.1 Individual user account storage
2.2 G Suite storage
2.3 Storage scheme revisions
3 Features
3.1 Sharing
3.2 Third-party apps
3.3 File viewing
3.4 File limits
3.5 Quick Access
3.6 Search
3.7 Backups
3.8 Metadata
3.9 Accessibility to the visually impaired
3.10 Save to Google Drive browser extension
3.11 Mobile apps
3.12 Encryption
4 Professional editions
4.1 Google Drive for Work
4.2 Google Drive for Education
4.3 Team Drives
5 Docs, Sheets and Slides
6 Reception
6.1 Features
6.2 Ownership and licensing
7 Growth
8 Downtime issues
9 See also
10 References
11 External links
Platforms[edit]
Google Drive
Google Drive's Android app
Stable release(s) [±]
macOS & Windows (Backup & Sync)
3.36.6721.3394 / September 7, 2017; 50 days ago (2017-09-07)[1]
Android
2.7.372.10.30 / October 4, 2017; 23 days ago (2017-10-04)[2]
iOS
4.2017.39509 / October 4, 2017; 23 days ago (2017-10-04)[3]
Written in
Python (back-end), Objective-C (Mac client), wxPython (Windows client)[4]
Operating system
Windows, macOS, Chrome OS, Android, iOS
License
Freeware
Website
www.google.com/drive/
Google Drive was introduced on April 24, 2012 with apps available for Windows, macOS, and Android, as well as a website interface, with an iOS app under development.[5] The iOS app was released in June 2012.[6]
Computer apps[edit]
Google Drive is available for PCs running Windows 7 or later, and Macs running OS X Lion or later.[7]
Google indicated in April 2012 that work on Linux software was underway,[8] but there was no news on this as of November 2013.[9]
In April 2012, Google's then-Senior Vice President Sundar Pichai said that Google Drive would be tightly integrated with Chrome OS version 20.[10]
In October 2016, Google announced that, going forward, it will drop support for versions of the computer software older than 1 year.[11]
In June 2017, Google announced that a new app called Backup and Sync would replace the existing separate Google Drive and Google Photos desktop apps, creating one unified app on desktop platforms.[12][13] Originally intended for release on June 28, its release was delayed[14] until July 12.[15][16][17]
In September 2017, Google announced that it will discontinue the Google Drive desktop app in March 2018 and end support in December 2017.[18]
Mobile apps[edit]
Google Drive is available for Android smartphones and tablets running Android 4.1 "Jelly Bean" or later,[19] and iPhones and iPads running iOS 8 or later.[20]
In August 2016, Google Drive ended support for Android devices running Android 4.0 "Ice Cream Sandwich" or older versions,[21] citing Google's mobile app update policy, which states: "For Android devices, we provide updates for the current and 2 previous Android versions." According to the policy, the app will continue to work for devices running older Android versions, but any app updates are provided on a best-efforts basis. The policy also states a notice will be given for any planned end of service.[22]
Website interface[edit]
Google Drive has a website that allows users to see their files from any Internet-connected computer, without the need to download an app.
The website received a visual overhaul in 2014 that gave it a completely new look and improved performance. It also simplified some of the most common tasks, such as clicking only once on a file to see recent activity or share the file, and added drag-and-drop functionality, where users can simply drag selected files to folders, for improved organization.[23][24]
A new update in August 2016 changed several visual elements of the website; the logo was updated, search box design was refreshed, and the primary color was changed from red to blue. It also improved the functionality to download files locally from the website; users can now compress and download large Drive items into multiple 2 GB .zip files with an improved naming structure, better Google Forms handling, and empty folders will now be included in the .zip, thereby preserving the user's folder hierarchy.[25][26]
Storage[edit]
Individual user account storage[edit]
Google gives every user 15 GB of free Drive storage space, which is shared across files in Google Drive, messages and attachments in Gmail, and pictures and videos in Google Photos.[27] Google Docs, Sheets and Slides files do not count towards the storage limit.[28] An unlimited number of photos at maximum 16 megapixels and videos at maximum 1080p resolutions are stored for free using the "High quality" setting in Google Photos. Using the "Original quality" setting uses Google Drive quota.[29]
Users can purchase additional space through either a monthly or yearly payment. The option of yearly payments was introduced in December 2016, and is limited to the 100 GB or 1 TB storage plans. Furthermore, the yearly payments offer a discount.[30]
As of 2017[update], these are the storage plans offered by Google:[31]
Storage
Price (US$)
15 GB Free
100 GB $1.99 per month ($19.99 per year with 16% discount)
1 TB $9.99 per month ($99.99 per year with 17% discount)
2 TB $19.99 per month
10 TB $99.99 per month
20 TB $199.99 per month
30 TB $299.99 per month
Storage purchases renew automatically at the end of the subscription period. Users can upgrade their storage plan anytime, with the new storage tier taking effect immediately. If the auto-renewal fails, a 7-day grace period is offered for users to update their payment information. When the storage subscription expires or is cancelled, storage limit is set back to the 15 GB free level at the end of the subscription period. Users can still access all their content, but will not be able to add anything beyond the storage limit, which means:[32]
Users cannot add new files to Google Drive, with the exception of Google Docs, Sheets, or Slides files, which do not take up space. Synchronization between Drive and the local device will stop.
Users with the "Original quality" setting in Google Photos cannot upload new photos or videos.
Any incoming emails in Gmail will be returned to the sender.
Varying levels of free additional storage are offered on the purchase of specific Android devices from Motorola and HTC, and for various devices from Kensington, Asus, LG, and Panasonic.[33]
G Suite storage[edit]
Main article: G Suite
Google offers 30 GB of Drive storage for all G Suite Basic customers, and unlimited storage for those using G Suite Business or G Suite for Education, as long as there are at least 5 members. Associations with less than 5 members get 1 TB per user.[34]
Storage scheme revisions[edit]
Before the introduction of Google Drive, Google Docs initially provided 15 GB of storage free of charge.[citation needed] On April 24, 2012, Google Drive was introduced with free storage of 5 GB. Storage plans were revised, with 25GB costing $2.49/month, 100GB costing $4.99/month and 1TB costing $49.99/month.[5]
Originally, Gmail, Google Docs and Picasa had separate allowances for free storage and a shared allowance for purchased storage.[citation needed] Between April 2012 and May 2013, Google Drive and Google+ Photos had a shared allowance for both free and purchased storage, whereas Gmail had a separate 10 GB storage limit, which increased to 25 GB on the purchase of any storage plan.[citation needed]
In September 2012, Google announced that a paid plan would now cover total storage, rather than the paid allocation being added to the free; e.g. a 100 GB plan allowed a total of 100 GB rather than 115 GB as previously.[35]
In May 2013, Google announced the overall merge of storage across Gmail, Google Drive and Google+ Photos, allowing users 15 GB of unified free storage between the services.[27]
In March 2014, the storage plans were revised again and prices were reduced by 80% to $1.99/month for 100 GB, $9.99/month for 1TB, and $99.99/month for 10 TB.[36] This was much cheaper than competitors Dropbox and OneDrive offered at the time.[37] The 25 GB and 200 GB plans were discontinued and the 2 TB, 4 TB, 8 TB and 16 TB plans were replaced with 10 TB, 20 TB and 30 TB. Users were automatically upgraded to the new pricing scheme.
In most cases during these changes, users could continue with their existing plans as long as they kept their accounts active and did not make any adjustments to the plan. However, if the account lapsed for any reason, users had to choose from current plans.
Features[edit]
Sharing[edit]
Google Drive incorporates a system of file sharing in which the creator of a file or folder is, by default, its owner. The owner can regulate the public visibility of the file or folder. Ownership is transferable. Files or folders can be shared privately with particular users having a Google account, using their @gmail.com email addresses. Sharing files with users not having a Google account requires making them accessible to "anybody with the link". This generates a secret URL for the file, which may be shared via email or private messages. Files and folders can also be made "public on the web", which means that they can be indexed by search engines and thus can be found and accessed by anyone. The owner may also set an access level for regulating permissions. The three access levels offered are "can edit", "can comment" and "can view". Users with editing access can invite others to edit.
Third-party apps[edit]
A number of external web applications that work with Google Drive are available from the Chrome Web Store. To add an app, users are required to sign into the Chrome Web Store, but the apps are compatible with all supported web browsers. Some of these apps are first-party, such as Google Docs, Sheets and Slides. Drive apps operate on the online files, and can be used to view, edit and create files in various formats, edit images and videos, fax and sign documents, manage projects, create flowcharts, etc. Drive apps can also be made the default for handling file formats supported by them. Some of these apps also work offline on Google Chrome and Chrome OS.[38][39]
All of the third-party apps are free to install. However, some have fees associated with continued usage or access to additional features. Saving data from a third-party app to Google Drive requires authorization the first time.[40]
The Google Drive software development kit (SDK) works together with the Google Drive user interface and the Chrome Web Store to create an ecosystem of apps that can be installed into Google Drive. In February 2013, the "Create" menu in Google Drive was revamped to include third-party apps, thus effectively granting them the same status as Google's own apps.[41][42]
In March 2013, Google released an API for Google Drive that enables third-party developers to build collaborative apps that support real-time editing.[43][44]
File viewing[edit]
The Google Drive viewer on the web allows the following file formats to be viewed:[45]
Native formats (Docs, Sheets, Slides, Forms, Drawings)
Image files (.JPEG, .PNG, .GIF, .TIFF, .BMP, .WEBP)
Video files (.WEBM, .MPEG4, .3GPP, .MOV, .AVI, .MPEG, .MPEGPS, .WMV, .FLV, .OGG)
Audio formats (.MP3, .M4A, .WAV, .OGG)
Text files (.TXT)
Markup/Code (.CSS, .HTML, .PHP, .C, .CPP, .H, .HPP, .JS)
Microsoft Word (.DOC and .DOCX)
Microsoft Excel (.XLS and .XLSX)
Microsoft PowerPoint (.PPT and .PPTX)
Adobe Portable Document Format (.PDF)
Apple Pages (.PAGES)
Adobe Illustrator (.AI)
Adobe Photoshop (.PSD)
Autodesk AutoCad (.DXF)
Scalable Vector Graphics (.SVG)
PostScript (.EPS, .PS)
Fonts (.TTF)
XML Paper Specification (.XPS)
Archive file types (.ZIP, .RAR, tar, gzip)
.MTS files
Raw Image formats
Files in other formats can also be handled through third-party apps that work with Google Drive, available from the Chrome Web Store.[38]
File limits[edit]
Files uploaded, but not converted to Google Docs, Sheets, or Slides formats, may be up to 5 TB in size. There are also limits, specific to file type, listed below:[45][46]
Documents (Google Docs)
Up to 1.02 million characters, regardless of the number of pages or font size. Document files converted to .gdoc Docs format cannot be larger than 50 MB. Images inserted cannot be larger than 50 MB, and must be in either .jpg, .png, or non-animated .gif formats.
Spreadsheets (Google Sheets)
Up to 2 million cells.
Presentations (Google Slides)
Presentation files converted to .gslides Slides format cannot be larger than 100 MB. Images inserted cannot be larger than 50 MB, and must be in either .jpg, .png, or non-animated .gif formats.
Quick Access[edit]
Introduced in the Android app in September 2016, Quick Access uses machine learning to "intelligently predict the files you need before you've even typed anything".[47][48] The feature was announced to be expanded to iOS and the web in March 2017,[49] though the website interface received the feature in May.[50]
Search[edit]
Search results can be narrowed by file type, ownership, visibility, and the open-with app. Users can search for images by describing or naming what is in them. For example, a search for "mountain" returns all the photos of mountains, as well as any text documents about mountains.[51] Text in images and PDFs can be extracted using optical character recognition.[52] In September 2016, Google added "natural language processing" for searching on the Google Drive website, enabling specific user search queries like "find my budget spreadsheet from last December".[53] In February 2017, Google integrated Drive and the Google Search app on Android, letting users search for keywords, switch to an "In Apps" tab, and see any relevant Drive files.[54][55][56]
Backups[edit]
In December 2016, Google updated the Android app and website with a "Backups" section, listing the Android device and app backups saved to Drive. The section lets users see what backups are stored, the backups' sizes and details, and delete backups.[57]
In June 2017, Google announced that a new app, "Backup and Sync", would be able to synchronize any folder on the user's computer to Google.[12][13] The app was released on July 12, 2017.[15][16][17]
Metadata[edit]
A Description field is available for both files and folders that users can use to add relevant metadata. Content within the Description field is also indexed by Google Drive and searchable.[58]
Accessibility to the visually impaired[edit]
In June 2014, Google announced a number of updates to Google Drive, which included making the service more accessible to visually impaired users. This included improved keyboard accessibility, support for zooming and high contrast mode, and better compatibility with screen readers.[23]
Save to Google Drive browser extension[edit]
Google offers an extension for Google Chrome, Save to Google Drive, that allows users to save web content to Google Drive through a browser action or through the context menu. While documents and images can be saved directly, webpages can be saved in the form of a screenshot (as an image of the visible part of the page or the entire page), or as a raw HTML, MHTML, or Google Docs file. Users need to be signed into Chrome to use the extension.[59]
Mobile apps[edit]
The main Google Drive mobile app supported editing of documents and spreadsheets until April 2014, when the capability was moved to separate, standalone apps for Google Docs, Sheets, and Slides.[60][61] The Google Drive app on Android allows users to take a photo of a document, sign, or other text and use optical character recognition to convert to text that can be edited.[62] In October 2014, the Android app was updated with a Material Design user interface, improved search, the ability to add a custom message while sharing a file, and a new PDF viewer.[63][64]
Encryption[edit]
Before 2013, Google did not encrypt data stored on its servers. Following information that the United States' National Security Agency had "direct access" to servers owned by multiple technology companies, including Google,[65] the company began testing encrypting data in July,[66] and enabled encryption for data in transit between its data centers in November.[67] However, as of 2015, Google Drive does not provide client-side encryption.[68]
Professional editions[edit]
See also: G Suite
Google Drive for Work[edit]
Google Drive for Work is a business version, a part of G Suite (formerly Google Apps for Work), announced at the Google I/O conference on June 25, 2014 and made available immediately. The service features unlimited storage, advanced file audit reporting and eDiscovery services, along with enhanced administration control and new APIs specifically useful to businesses. Users can upload files as large as 5 TB.[69] A press release posted on Google's Official Enterprise Blog assured businesses that Google will encrypt data stored on its servers, as well as information being transmitted to or from them. Google will deliver 24/7 phone support to business users and has guaranteed 99.9% uptime for its servers.[70]
In September 2015, Google announced that Google Drive for Work would be compliant with the new ISO/IEC 27018:2014 security and privacy standard, which confirmed that Google would not use data in Drive for Work accounts for advertising, enabled additional tools for handling and exporting data, more transparency about data storage, and protection from third-party data requests.[71]
In March 2017, Google introduced Drive File Stream, making it possible for G Suite customers on Windows and macOS computers to search their Drive folders and download specific files on-demand rather than downloading all files during installation, potentially preventing large amounts of data from "gobbling up your hard drive". Additionally, the feature will guess what files users need in the future and download those files as well.[72][73]
Google Drive for Education[edit]
Google Drive for Education was announced on September 30, 2014. It was made available for free to all Google Apps for Education users. It includes unlimited storage and support for individual files up to 5TB in size, in addition to full encryption.[74]
Team Drives[edit]
In September 2016, Google announced Team Drives, a new way for teams to collaborate. Sharing and file ownership are managed for the entire team rather than one individual, and new users instantly get access to all files and information.[75] In November, Google opened an Early Adopter Program, allowing G Suite Business and G Suite for Education customers to sign up, although Google noted that some functionality isn't yet supported by Team Drives.[76]
Docs, Sheets and Slides[edit]
Main article: Google Docs, Sheets and Slides
An example of a document in Google Docs
Google Docs, Google Sheets and Google Slides constitute a free, web-based office suite offered by Google and integrated with Google Drive. It allows users to create and edit documents, spreadsheets, and presentations online while collaborating in real-time with other users. The three apps are available as web applications, as Chrome apps that work offline, and as mobile apps for Android and iOS. The apps are compatible with Microsoft Office file formats. The suite also consists of Google Forms, Google Drawings and Google Tables (beta). While Forms and Tables are only available as web applications, Drawings is also available as a Chrome app. The suite is tightly integrated with Google Drive, and all files created with the apps are by default saved to Google Drive.
Reception[edit]
Features[edit]
In a review of Google Drive after its launch in April 2012, Dan Grabham of TechRadar wrote that the integration of Google Docs into Google Drive was "a bit confusing", mainly due to the differences in the user interfaces (UI) between the two, where Drive offers a "My Drive" section with a specific "Shared with me" view for shared documents. He stated that "We think the user interface needs a lot more work. It's like a retread of Google Docs at the moment and Google surely needs to do work here". He considered uploading files "fairly easy", but noted that folder upload was only supported through the Google Chrome web browser. The lack of native editing of Microsoft Office documents was "annoying". Regarding Google Drive's computer apps, he stated that the option in Settings to synchronize only specific folders was "powerful". He wrote that Drive was "a great addition to Google armoury of apps and everything does work seamlessly", while again criticizing the interface for being "confusing" and that the file view was "not quite intuitive enough" without file icons. Grabham also reviewed the mobile Android app, writing that "it's a pretty simple app that enables you to access your files on the move and save some for offline access should you wish", and praised Google Docs creation and photo uploading for being "easy". He also praised that "everything is easily searchable".[77]
A review by Michael Muchmore of PC Magazine in February 2016 praised the service as "truly impressive" in creating and editing files, describing its features as "leading" in office-suite collaboration. He added that "Compatibility is rarely an issue", with importing and exporting options, and that the free storage of 15 gigabytes was "generous". However, he also criticized the user interface for being confusing to navigate, and wrote that "Offline editing isn't simple".[78]
Ownership and licensing[edit]
Immediately after its announcement in April 2012, Google faced criticism over Google Drive privacy. In particular, privacy advocates have noted that Google has one unified set of Terms of Service and Privacy Policy agreements for all its products and services. In a CNET report, Zack Whittaker noted that "the terms and service have come under heavy fire by the wider community for how it handles users' copyright and intellectual property rights". In a comparison of Terms of Service agreements between Google Drive and competing cloud storage services Dropbox and OneDrive, he cited a paragraph stating that Google has broad rights to reproduce, use, and create derivative works from content stored on Google Drive, via a license from its users. Although the user retains intellectual property rights, the user licenses Google to extract and parse uploaded content to customize advertising and other services that Google provides to the user, and to promote the service. Summarized, he wrote that "According to its terms, Google does not own user-uploaded files to Google Drive, but the company can do whatever it likes with them".[79] In a highly critical editorial of the service, Ed Bott of ZDNet wrote that language in the agreements contained "exact same words" as Dropbox used in a July 2011 Privacy Policy update that sparked criticism and forced Dropbox to update its policy once again with clarifying language, adding that "It's a perfect example of Google's inability to pay even the slightest bit of attention to anything that happens outside the Googleplex".[80] Matt Peckham of Time criticized the lack of unique service agreements for Drive, writing that "If any Google service warrants privacy firewalling, it’s Google Drive. This isn’t YouTube or Calendar or even Gmail——the potential for someone’s most sensitive data to be snooped, whether to glean info for marketing or otherwise, is too high. [...] Google ought to create a privacy exception that “narrows the scope” of its service terms for Google Drive, one that minimally states the company will never circulate the information generated from searching within [sic] your G-Drive data in any way."[81]
In contrast, a report by Nilay Patel of The Verge stated that "all web services should be subject to harsh scrutiny of their privacy policies—but a close and careful reading reveals that Google's terms are pretty much the same as anyone else's, and slightly better in some cases", pointing to the fact that Google "couldn't move files around on its servers, cache your data, or make image thumbnails" without proper rights. In comparing the policies with competing services, Patel wrote that "it's clear that they need the exact same permissions—they just use slightly more artful language to communicate them".[82]
Growth[edit]
On November 12, 2013, Google announced that Google Drive had 120 million active users, a figure that the company was releasing for the first time.[83]
On June 25, 2014 at the Google I/O developer conference, Sundar Pichai announced that Google Drive now had 190 million monthly active users, and that it was being used by 58% of the Fortune 500 companies as well as by 72 of the top universities.[84]
On October 1, 2014, at its Atmosphere Live event, it was announced that Google Drive had 240 million monthly active users. The Next Web noted that this meant an increase of 50 million users in just one quarter.[85]
On September 21, 2015, it was announced that Google Drive had over one million organizational paying users.[86]
In March 2017, Google announced that Google Drive had 800 million active users.[87][88]
In May 2017, a Google executive stated at a company event that there were over two trillion files stored on Google Drive.[89][90]
Downtime issues[edit]
Although Google has a 99.9% uptime guarantee for Google Drive for G Suite customers,[91] Google Drive has suffered downtimes for both consumers and business users. During significant downtimes, Google's App Status Dashboard gets updated with the current status of each service Google offers, along with details on restoration progress. Notable downtimes occurred in March 2013,[92] October 2014,[93] and January 2016.[94][95]
When the January 2016 outage was resolved, a Google spokesperson told The Next Web:[95]
At Google we recognize that failures are statistically inevitable, and we strive to insulate our users from the effects of failures. As that did not happen in this instance, we apologize to everyone who was inconvenienced by this event. Our engineers are conducting a post-mortem investigation to determine how to make our services more resilient to unplanned network failures, and we will do our utmost to continue to make Google service outages notable for their rarity.
In an outage that affected all of Google's services for 5 minutes in August 2013, CNET reported that global Internet traffic dropped 40%.[96]
See also[edit]
Comparison of file hosting services
Comparison of file synchronization software
Comparison of online backup services
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Jump up ^ Epstein, Mike (March 13, 2014). "Google Drive's new prices make Dropbox, OneDrive seem like ripoffs". Digital Trends. Retrieved October 22, 2016.
^ Jump up to: a b "Use Google Drive apps". Drive Help. Google. Retrieved October 30, 2016.
Jump up ^ Chitu, Alex (April 25, 2012). "Chrome and Google Drive's Third-Party Apps". Retrieved October 30, 2016.
Jump up ^ Ogasawara, Todd (February 22, 2013). "Google Drive Third-Party Apps: An Introduction". InformationWeek. UBM Tech. Retrieved October 30, 2016.
Jump up ^ Garnier, Nicolas (February 8, 2013). "Elevate your apps in Google Drive". Google Developers Blog. Google. Retrieved October 30, 2016.
Jump up ^ Protalinski, Emil (February 8, 2013). "Google Drive's Create menu now lets you add and access third-party, Drive-enabled apps". The Next Web. Retrieved October 30, 2016.
Jump up ^ Cairns, Brian (March 19, 2013). "Build collaborative apps with Google Drive Realtime API". Google Developers Blog. Google. Retrieved October 30, 2016.
Jump up ^ Souppouris, Aaron (March 19, 2013). "Google Drive now allows third-party apps to edit docs in realtime". The Verge. Vox Media. Retrieved October 30, 2016.
^ Jump up to: a b "Files you can store in Google Drive". Drive Help. Google. Retrieved October 22, 2016.
Jump up ^ "Insert or delete images or videos". Docs editors Help. Google. Retrieved October 22, 2016.
Jump up ^ Meyer, Cayden (September 29, 2016). "Save time with Quick Access in Drive". The Keyword Google Blog. Google. Retrieved February 22, 2017.
Jump up ^ Davenport, Corbin (September 29, 2016). "Google Drive adds Quick Access feature, guesses what file you might want". Android Police. Retrieved February 22, 2017.
Jump up ^ Novet, Jordan (March 9, 2017). "Google revamps Drive with File Stream and expanded Quick Access, launches Gmail add-ons". VentureBeat. Retrieved March 10, 2017.
Jump up ^ Hager, Ryne (May 18, 2017). "The Quick Access feature in Google Drive for Android is coming to Drive on the web". Android Police. Retrieved May 19, 2017.
Jump up ^ Garnier, Nicolas (February 27, 2013). "How to make files searchable in Google Drive". G Suite Developers Blog. Google. Retrieved November 12, 2016.
Jump up ^ "Convert PDF and photo files to text". Drive Help. Google. Retrieved March 20, 2017.
Jump up ^ Smith, Josh (September 20, 2016). "What you love about Google Search—now for Drive". The Keyword Google Blog. Google. Retrieved November 12, 2016.
Jump up ^ Lopez, Napier (February 23, 2017). "Android users can now find Google Drive files right in Search". The Next Web. Retrieved March 27, 2017.
Jump up ^ Ravenscraft, Eric (February 24, 2017). "You Can Now Use Google to Search Your Drive Files On Android". Lifehacker. Univision Communications. Retrieved March 27, 2017.
Jump up ^ Chang, Lulu (February 24, 2017). "You can now find your Google Drive files directly through the Android Google app". Digital Trends. Retrieved March 27, 2017.
Jump up ^ El Khoury, Rita (December 8, 2016). "[Update: Available on Android] Google Drive Backups tab starts showing up, gives you a glimpse into your device and app backups". Android Police. Retrieved January 16, 2017.
Jump up ^ Steelman, Rebecca (June 14, 2011). "Tips & Tricks: Using the description field in your documents list". Google Drive Blog. Google. Retrieved March 20, 2017.
Jump up ^ "Save to Google Drive". Chrome Web Store. Google. Retrieved July 29, 2014.
Jump up ^ Levee, Brian (April 30, 2014). "New mobile apps for Docs, Sheets and Slides - work offline and on the go". Official Google Blog. Google. Retrieved January 16, 2017.
Jump up ^ Petrovan, Bogdan (April 30, 2014). "Google launches standalone Docs, Sheets, and Slides apps for Android". Android Authority. Retrieved January 16, 2017.
Jump up ^ Kan, Reuben (April 27, 2011). "Introducing the new Google Docs app for Android". Google Mobile Blog. Google. Retrieved January 16, 2017.
Jump up ^ "New version of the Google Drive app for Android". G Suite Updates. Google. October 29, 2014. Retrieved January 16, 2017.
Jump up ^ Spradlin, Liam (October 21, 2014). "A Look At Google Drive's Material Design In Android 5.0 Lollipop". Android Police. Retrieved January 16, 2017.
Jump up ^ Greenwald, Glenn; MacAskill, Ewen (June 7, 2013). "NSA Prism program taps in to user data of Apple, Google and others". The Guardian. Guardian Media Group. Retrieved June 10, 2017.
Jump up ^ McCullaugh, Declan (July 17, 2013). "Google tests encryption to protect users' Drive files against government demands". CNET. CBS Interactive. Retrieved June 10, 2017.
Jump up ^ Gallagher, Sean (November 6, 2013). "Googlers say “F*** you” to NSA, company encrypts internal network". Ars Technica. Condé Nast. Retrieved June 10, 2017.
Jump up ^ McNamara, Tom (July 8, 2015). "How to make Google Drive more secure". CNET. CBS Interactive. Retrieved June 10, 2017.
Jump up ^ Bishop, Bryan (June 25, 2014). "Google announces Drive for Work with unlimited storage at $10 a month". The Verge. Vox Media. Retrieved October 23, 2016.
Jump up ^ Johnston, Scott (June 25, 2014). "Unlimit your business with Google Drive for Work". Official Google Cloud Blog. Google. Retrieved November 12, 2016.
Jump up ^ Crandall, Marc (September 21, 2015). "Google Apps for Work adopts ISO 27018 cloud privacy standard". Official Google Cloud Blog. Google. Retrieved October 28, 2016.
Jump up ^ Vogenthaler, Alex (March 9, 2017). "Introducing new, enterprise-ready tools for Google Drive". The Keyword Google Blog. Google. Retrieved March 10, 2017.
Jump up ^ Whitwam, Ryan (March 9, 2017). "Drive File Stream for G Suite lets you access all your files without using all your disk space". Android Police. Retrieved March 10, 2017.
Jump up ^ Summers, Nick (September 30, 2014). "Google unveils Drive for Education with free, unlimited storage and 'Classroom' integration". The Next Web. Retrieved October 23, 2016.
Jump up ^ "New Early Adopter Programs: Team Drives and a new Hangouts video meetings experience". G Suite Updates. Google. September 29, 2016. Retrieved January 4, 2017.
Jump up ^ "Google Team Drives Early Adopter Program now accepting applications". G Suite Updates. Google. November 21, 2016. Retrieved January 4, 2017.
Jump up ^ Grabham, Dan (April 27, 2012). "Hands on: Google Drive review". TechRadar. Future plc. Retrieved March 18, 2017.
Jump up ^ Muchmore, Michael (February 23, 2016). "Google Drive". PC Magazine. Ziff Davis. Retrieved March 18, 2017.
Jump up ^ Whittaker, Zack (May 29, 2014). "Who owns your files on Google Drive?". CNET. CBS Interactive. Retrieved October 30, 2016.
Jump up ^ Bott, Ed (April 24, 2012). "Google clones Dropbox: lock, stock, and privacy gaffe". ZDNet. CBS Interactive. Retrieved March 19, 2017.
Jump up ^ Peckham, Matt (April 26, 2012). "Will Google Drive Snoop Inside Your Data? Google Needs to Be Clearer". Time. Time Inc. Retrieved March 19, 2017.
Jump up ^ Patel, Nilay (April 25, 2012). "Is Google Drive worse for privacy than iCloud, Skydrive, and Dropbox?". The Verge. Vox Media. Retrieved October 30, 2016.
Jump up ^ Perez, Sarah (November 12, 2013). "Gmail Users No Longer Need To Download Attachments, As Google Drive Gets Baked Into The Inbox". TechCrunch. AOL. Retrieved October 30, 2016.
Jump up ^ Kokalitcheva, Kia (June 25, 2014). "Google Drive now has 190M users & a brand new tablet app for presentations". VentureBeat. Retrieved October 30, 2016.
Jump up ^ Protalinski, Emil (October 1, 2014). "Google announces 10% price cut for all Compute Engine instances, Google Drive has passed 240M active users". The Next Web. Retrieved October 30, 2016.
Jump up ^ Johnston, Scott (September 21, 2015). "Making Google Drive the safest place for all your work". Medium. Retrieved October 28, 2016.
Jump up ^ Lardinois, Frederic (March 9, 2017). "Google updates Drive with a focus on its business users". TechCrunch. AOL. Retrieved May 10, 2017.
Jump up ^ Dignan, Larry (March 9, 2017). "Google plans to leverage G Drive for broader enterprise footprint, team management and collaboration". ZDNet. CBS Interactive. Retrieved March 10, 2017.
Jump up ^ Price, Rob (May 6, 2017). "Google Drive now hosts more than 2 trillion files". Business Insider. Axel Springer SE. Retrieved May 10, 2017.
Jump up ^ Humphries, Matthew (May 8, 2017). "Google Drive Passes 2 Trillion Files Stored". PC Magazine. Ziff David. Retrieved May 10, 2017.
Jump up ^ "Reliability". Google Cloud Help. Google. Retrieved December 11, 2016.
Jump up ^ Perez, Sarah (March 18, 2013). "Google Drive Experiencing Outage (UPDATE: Google Says Resolved)". TechCrunch. AOL. Retrieved December 11, 2016.
Jump up ^ Woods, Ben (October 27, 2014). "Google Drive and Docs are down for some users, company is investigating [Update: Fixed now!]". The Next Web. Retrieved December 11, 2016.
Jump up ^ Griffin, Andrew (January 26, 2016). "Gmail, Google Drive down: Many Google services hit by widespread outage". The Independent. Retrieved December 11, 2016.
^ Jump up to: a b Woods, Ben (January 26, 2016). "Google Drive and Gmail are down for some users around the world (Update: They’re back!)". The Next Web. Retrieved December 11, 2016.
Jump up ^ Svetlik, Joe (August 19, 2013). "Google goes down for 5 minutes, Internet traffic drops 40%". CNET. CBS Interactive. Retrieved December 11, 2016.
External links[edit]
Google Drive section of Google's The Keyword updates blog
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Hagen–Poiseuille equation
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In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838[1] and Gotthilf Heinrich Ludwig Hagen,[2] and published by Poiseuille in 1840–41 and 1846.[1]
The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen–Poiseuille equation.
Contents
[hide]
1 Equation
2 Relation to Darcy–Weisbach
3 Derivation
3.1 Liquid flow through a pipe
3.2 Viscosity
3.3 Faster lamina
3.4 Slower lamina
3.5 Putting it all together
3.6 Poiseuille's law
3.7 Startup of Poiseuille flow in a pipe[8]
4 Poiseuille flow in annular section[9]
5 Plane Poiseuille flow
6 Poiseuille flow in non-circular cross-sections[10]
7 Poiseuille's equation for compressible fluids
8 Electrical circuits analogy
9 Medical applications – intravenous access and fluid delivery
10 See also
11 Notes
12 References
13 External links
Equation[edit]
In standard fluid-dynamics notation:[3][4][5]
Δ P = 8 μ L Q π R 4 {\displaystyle \Delta P={\frac {8\mu LQ}{\pi R^{4}}}}
where:
ΔP is the pressure difference between the two ends,
L is the length of pipe,
μ is the dynamic viscosity,
Q is the volumetric flow rate,
R is the pipe radius.
The equation does not hold close to the pipe entrance.[6]:3
The equation fails in the limit of low viscosity, wide and/or short pipe. Low viscosity or a wide pipe may result in turbulent flow, making it necessary to use more complex models, such as Darcy–Weisbach equation. If the pipe is too short, the Hagen–Poiseuille equation may result in unphysically high flow rates; the flow is bounded by Bernoulli's principle, under less restrictive conditions, by
Q max = π R 2 2 Δ P ρ . {\displaystyle Q_{\max }{}=\pi R^{2}{\sqrt {\frac {2\Delta P}{\rho }}}.}
Relation to Darcy–Weisbach[edit]
Normally, Hagen-Poiseuille flow implies not just the relation for the pressure drop, above, but also the full solution for the laminar flow profile, which is parabolic. However, the result for the pressure drop can be extended to turbulent flow by inferring an effective turbulent viscosity in the case of turbulent flow, even though the flow profile in turbulent flow is strictly speaking not actually parabolic. In both cases, laminar or turbulent, the pressure drop is related to the stress at the wall, which determines the so-called friction factor. The wall stress can be determined phenomenologically by the Darcy–Weisbach equation in the field of hydraulics, given a relationship for the friction factor in terms of the Reynolds number. In the case of laminar flow:
Λ = 64 R e , R e = ρ v d μ , {\displaystyle \Lambda ={\frac {64}{\mathrm {Re} }},\quad \mathrm {Re} ={\frac {\rho vd}{\mu }},}
where Re is the Reynolds number, ρ is the fluid density, v is the mean flow velocity, which is half the maximal flow velocity in the case of laminar flow. It proves more useful to define the Reynolds number in terms of the mean flow velocity because this quantity remains well defined even in the case of turbulent flow, whereas the maximal flow velocity may not be, or in any case, it may be difficult to infer. In this form the law approximates the Darcy friction factor, the energy (head) loss factor, friction loss factor or Darcy (friction) factor Λ in the laminar flow at very low velocities in cylindrical tube. The theoretical derivation of a slightly different form of the law was made independently by Wiedman in 1856 and Neumann and E. Hagenbach in 1858 (1859, 1860). Hagenbach was the first who called this law the Poiseuille's law.
The law is also very important in hemorheology and hemodynamics, both fields of physiology.[7]
Poiseuille's law was later in 1891 extended to turbulent flow by L. R. Wilberforce, based on Hagenbach's work.
Derivation[edit]
Main article: Hagen–Poiseuille flow from the Navier–Stokes equations
The Hagen–Poiseuille equation can be derived from the Navier–Stokes equations. Although more lengthy than directly using the Navier–Stokes equations, an alternative method of deriving the Hagen–Poiseuille equation is as follows.
Liquid flow through a pipe[edit]
a) A tube showing the imaginary lamina. b) A cross section of the tube shows the lamina moving at different speeds. Those closest to the edge of the tube are moving slowly while those near the center are moving quickly.
Assume the liquid exhibits laminar flow. Laminar flow in a round pipe prescribes that there are a bunch of circular layers (lamina) of liquid, each having a velocity determined only by their radial distance from the center of the tube. Also assume the center is moving fastest while the liquid touching the walls of the tube is stationary (due to the no-slip condition).
To figure out the motion of the liquid, all forces acting on each lamina must be known:
The pressure force pushing the liquid through the tube is the change in pressure multiplied by the area: F = −A ΔP. This force is in the direction of the motion of the liquid. The negative sign comes from the conventional way we define ΔP = Pend − Ptop < 0.
Viscosity effects will pull from the faster lamina immediately closer to the center of the tube.
Viscosity effects will drag from the slower lamina immediately closer to the walls of the tube.
Viscosity[edit]
Two fluids moving past each other in the x direction. The liquid on top is moving faster and will be pulled in the negative direction by the bottom liquid while the bottom liquid will be pulled in the positive direction by the top liquid.
When two layers of liquid in contact with each other move at different speeds, there will be a shear force between them. This force is proportional to the area of contact A, the velocity gradient in the direction of flow Δvx/Δy, and a proportionality constant (viscosity) and is given by
F viscosity, top = − μ A Δ v x Δ y . {\displaystyle F_{\text{viscosity, top}}=-\mu A{\frac {\Delta v_{x}}{\Delta y}}.}
The negative sign is in there because we are concerned with the faster moving liquid (top in figure), which is being slowed by the slower liquid (bottom in figure). By Newton's third law of motion, the force on the slower liquid is equal and opposite (no negative sign) to the force on the faster liquid. This equation assumes that the area of contact is so large that we can ignore any effects from the edges and that the fluids behave as Newtonian fluids.
Faster lamina[edit]
Assume that we are figuring out the force on the lamina with radius r. From the equation above, we need to know the area of contact and the velocity gradient. Think of the lamina as a ring of radius r, thickness dr, and length Δx. The area of contact between the lamina and the faster one is simply the area of the inside of the cylinder: A = 2πr Δx. We don't know the exact form for the velocity of the liquid within the tube yet, but we do know (from our assumption above) that it is dependent on the radius. Therefore, the velocity gradient is the change of the velocity with respect to the change in the radius at the intersection of these two laminae. That intersection is at a radius of r. So, considering that this force will be positive with respect to the movement of the liquid (but the derivative of the velocity is negative), the final form of the equation becomes
F viscosity, fast = − 2 π r μ Δ x d v d r | r {\displaystyle F_{\text{viscosity, fast}}=-2\pi r\mu \,\Delta x\,\left.{\frac {dv}{dr}}\right|_{r}}
where the vertical bar and subscript r following the derivative indicates that it should be taken at a radius of r.
Slower lamina[edit]
Next let's find the force of drag from the slower lamina. We need to calculate the same values that we did for the force from the faster lamina. In this case, the area of contact is at r + dr instead of r. Also, we need to remember that this force opposes the direction of movement of the liquid and will therefore be negative (and that the derivative of the velocity is negative).
F viscosity, slow = 2 π ( r + d r ) μ Δ x d v d r | r + d r {\displaystyle F_{\text{viscosity, slow}}=2\pi (r+dr)\mu \,\Delta x\left.{\frac {dv}{dr}}\right|_{r+dr}}
Putting it all together[edit]
To find the solution for the flow of a laminar layer through a tube, we need to make one last assumption. There is no acceleration of liquid in the pipe, and by Newton's first law, there is no net force. If there is no net force then we can add all of the forces together to get zero
0 = F pressure + F viscosity, fast + F viscosity, slow {\displaystyle 0=F_{\text{pressure}}+F_{\text{viscosity, fast}}+F_{\text{viscosity, slow}}}
or
0 = Δ P 2 π r d r − 2 π r μ Δ x d v d r | r + 2 π ( r + d r ) μ Δ x d v d r | r + d r . {\displaystyle 0=\Delta P2\pi r\,dr-2\pi r\mu \,\Delta x\left.{\frac {dv}{dr}}\right|_{r}+2\pi (r+dr)\mu \,\Delta x\,\left.{\frac {dv}{dr}}\right\vert _{r+dr}.}
First, to get everything happening at the same point, use the first two terms of a Taylor series expansion of the velocity gradient:
d v d r | r + d r = d v d r | r + d 2 v d r 2 | r d r . {\displaystyle \left.{\frac {dv}{dr}}\right|_{r+dr}=\left.{\frac {dv}{dr}}\right|_{r}+\left.{\frac {d^{2}v}{dr^{2}}}\right|_{r}\,dr.}
The expression is valid for all laminae. Grouping like terms and dropping the vertical bar since all derivatives are assumed to be at radius r,
0 = Δ P 2 π r d r + 2 π μ d r Δ x d v d r + 2 π r μ d r Δ x d 2 v d r 2 + 2 π μ ( d r ) 2 Δ x d 2 v d r 2 . {\displaystyle 0=\Delta P2\pi r\,dr+2\pi \mu \,dr\,\Delta x{\frac {dv}{dr}}+2\pi r\mu \,dr\,\Delta x{\frac {d^{2}v}{dr^{2}}}+2\pi \mu (dr)^{2}\,\Delta x{\frac {d^{2}v}{dr^{2}}}.}
Finally, put this expression in the form of a differential equation, dropping the term quadratic in dr.
− 1 μ Δ P Δ x = d 2 v d r 2 + 1 r d v d r {\displaystyle -{\frac {1}{\mu }}{\frac {\Delta P}{\Delta x}}={\frac {d^{2}v}{dr^{2}}}+{\frac {1}{r}}{\frac {dv}{dr}}}
It can be seen that both sides of the equations are negative: there is a drop of pressure along the tube (left side) and both first and second derivatives of the velocity are negative (velocity has a maximum value at the center of the tube, where r = 0). Using the product rule, the equation may be rearranged to:
− 1 μ Δ P Δ x = 1 r d d r ( r d v d r ) . {\displaystyle -{\frac {1}{\mu }}{\frac {\Delta P}{\Delta x}}={\frac {1}{r}}{\frac {d}{dr}}\left(r{\frac {dv}{dr}}\right).}
The right-hand side is the radial term of the Laplace operator ∇2, so this differential equation is a special case of the Poisson equation. It is subject to the following boundary conditions:
v ( r ) = 0 at r = R {\displaystyle v(r)=0\quad {\mbox{ at }}r=R} — "no-slip" boundary condition at the wall
d v d r = 0 at r = 0 {\displaystyle {\frac {dv}{dr}}=0\quad {\mbox{ at }}r=0} — axial symmetry.
Axial symmetry means that the velocity v(r) is maximum at the center of the tube, therefore the first derivative dv/dr is zero at r = 0.
The differential equation can be integrated to:
v ( r ) = − 1 4 μ r 2 Δ P Δ x + A ln  ( r ) + B . {\displaystyle v(r)=-{\frac {1}{4\mu }}r^{2}{\frac {\Delta P}{\Delta x}}+A\ln(r)+B.}
To find A and B, we use the boundary conditions.
First, the symmetry boundary condition indicates:
d v d r = − 1 2 μ r Δ P Δ x + A r = 0 at r = 0. {\displaystyle {\frac {dv}{dr}}=-{\frac {1}{2\mu }}r{\frac {\Delta P}{\Delta x}}+{\frac {A}{r}}=0\quad {\mbox{ at }}r=0.}
A solution possible only if A = 0. Next the no-slip boundary condition is applied to the remaining equation:
v ( R ) = − 1 4 μ R 2 Δ P Δ x + B = 0 {\displaystyle v(R)=-{\frac {1}{4\mu }}R^{2}{\frac {\Delta P}{\Delta x}}+B=0}
so therefore
B = 1 4 μ R 2 Δ P Δ x . {\displaystyle B={\frac {1}{4\mu }}R^{2}{\frac {\Delta P}{\Delta x}}.}
Now we have a formula for the velocity of liquid moving through the tube as a function of the distance from the center of the tube
v = 1 4 μ Δ P Δ x ( R 2 − r 2 ) {\displaystyle v={\frac {1}{4\mu }}{\frac {\Delta P}{\Delta x}}(R^{2}-r^{2})}
or, at the center of the tube where the liquid is moving fastest (r = 0) with R being the radius of the tube,
v m a x = 1 4 μ Δ P Δ x R 2 . {\displaystyle v_{max}={\frac {1}{4\mu }}{\frac {\Delta P}{\Delta x}}R^{2}.}
Poiseuille's law[edit]
To get the total volume that flows through the tube, we need to add up the contributions from each lamina. To calculate the flow through each lamina, we multiply the velocity (from above) and the area of the lamina.
Q ( r ) d r = 1 4 μ | Δ P | Δ x ( R 2 − r 2 ) 2 π r d r = π 2 μ | Δ P | Δ x ( r R 2 − r 3 ) d r {\displaystyle Q(r)\,dr={\frac {1}{4\mu }}{\frac {|\Delta P|}{\Delta x}}(R^{2}-r^{2})2\pi r\,dr={\frac {\pi }{2\mu }}{\frac {|\Delta P|}{\Delta x}}(rR^{2}-r^{3})\,dr}
Finally, we integrate over all lamina via the radius variable r.
Q = π 2 μ | Δ P | Δ x ∫ 0 R ( r R 2 − r 3 ) d r = | Δ P | π R 4 8 μ Δ x {\displaystyle Q={\frac {\pi }{2\mu }}{\frac {|\Delta P|}{\Delta x}}\int _{0}^{R}(rR^{2}-r^{3})\,dr={\frac {|\Delta P|\pi R^{4}}{8\mu \Delta x}}}
Startup of Poiseuille flow in a pipe[8][edit]
When a constant pressure gradient G = − d p / d x = constant {\displaystyle G=-dp/dx={\text{constant}}} is applied between two ends of a long pipe, the flow will not immediately obtain Poiseuille profile, rather it develops through time and reaches the Poiseuille profile at steady state. The Navier-Stokes equations reduce to
∂ u ∂ t = G ρ + ν ( ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r ) {\displaystyle {\frac {\partial u}{\partial t}}={\frac {G}{\rho }}+\nu \left({\frac {\partial ^{2}u}{\partial r^{2}}}+{\frac {1}{r}}{\frac {\partial u}{\partial r}}\right)}
with initial and boundary conditions,
u ( r , 0 ) = 0 , u ( R , t ) = 0. {\displaystyle u(r,0)=0,\quad u(R,t)=0.}
The velocity distribution is given by
u ( r , t ) = G 4 μ ( R 2 − r 2 ) − 2 G R 2 μ ∑ n = 1 ∞ 1 λ n 3 J o ( λ n r / R ) J 1 ( λ n ) e − λ n 2 ν t R 2 , J o ( λ n ) = 0 {\displaystyle u(r,t)={\frac {G}{4\mu }}(R^{2}-r^{2})-{\frac {2GR^{2}}{\mu }}\sum _{n=1}^{\infty }{\frac {1}{\lambda _{n}^{3}}}{\frac {J_{o}(\lambda _{n}r/R)}{J_{1}(\lambda _{n})}}e^{-\lambda _{n}^{2}{\frac {\nu t}{R^{2}}}},\quad J_{o}(\lambda _{n})=0}
where J o ( λ n r / R ) {\displaystyle J_{o}(\lambda _{n}r/R)} is the Bessel function of the first kind of order zero and λ n {\displaystyle \lambda _{n}} are the positive roots of this function and J 1 ( λ n ) {\displaystyle J_{1}(\lambda _{n})} is the Bessel function of the first kind of order one. As t → ∞ {\displaystyle t\rightarrow \infty } , Poiseuille solution is recovered.
Poiseuille flow in annular section[9][edit]
Poiseuille flow in annular section
If R 1 {\displaystyle R_{1}} is the inner cylinder radii and R 2 {\displaystyle R_{2}} is the outer cylinder radii, with applied pressure gradient between the two ends G = − d p / d x = constant {\displaystyle G=-dp/dx={\text{constant}}} , the velocity distribution and the volume flux through the annular pipe are
u ( r ) = G 4 μ ( R 1 2 − r 2 ) + G 4 μ ( R 2 2 − R 1 2 ) ln  ( r / R 1 ) ln  ( R 2 / R 1 ) , Q = G π 8 μ [ R 2 4 − R 1 4 − ( R 2 2 − R 1 2 ) 2 ln  R 2 / R 1 ] . {\displaystyle {\begin{aligned}u(r)&={\frac {G}{4\mu }}(R_{1}^{2}-r^{2})+{\frac {G}{4\mu }}(R_{2}^{2}-R_{1}^{2}){\frac {\ln(r/R_{1})}{\ln(R_{2}/R_{1})}},\\Q&={\frac {G\pi }{8\mu }}\left[R_{2}^{4}-R_{1}^{4}-{\frac {(R_{2}^{2}-R_{1}^{2})^{2}}{\ln R_{2}/R_{1}}}\right].\end{aligned}}}
When R 2 = R , R 1 = 0 {\displaystyle R_{2}=R,\ R_{1}=0} , the original problem is recovered.
Plane Poiseuille flow[edit]
Plane Poiseuille flow
Plane Poiseuille flow is flow created between two infinitely long parallel plates, separated by a distance h {\displaystyle h} with a constant pressure gradient G = − d p / d x = constant {\displaystyle G=-dp/dx={\text{constant}}} is applied in the direction of flow. The flow is essentially unidirectional because of infinite length. The Navier-Stokes equations reduce to
d 2 u d y 2 = − G μ {\displaystyle {\frac {d^{2}u}{dy^{2}}}=-{\frac {G}{\mu }}}
with no-slip condition on both walls
u ( 0 ) = 0 , u ( h ) = 0 {\displaystyle u(0)=0,\quad u(h)=0}
Therefore, the velocity distribution and the volume flow rate per unit length are
u ( y ) = G 2 μ y ( h − y ) , Q = G h 3 12 μ . {\displaystyle u(y)={\frac {G}{2\mu }}y(h-y),\quad Q={\frac {Gh^{3}}{12\mu }}.}
Poiseuille flow in non-circular cross-sections[10][edit]
Boussinesq[11] derived the velocity profile and volume flow rate in 1868 for rectangular channel and tubes of equilateral triangular cross-section and for elliptical cross-section. Proudman[12] derived the same for isosceles triangles in 1914. Let G = − d p / d x = constant {\displaystyle G=-dp/dx={\text{constant}}} be the constant pressure gradient acting in direction parallel to the motion.
The velocity and the volume flow rate in a rectangular channel of height 0 ≤ y ≤ h {\displaystyle 0\leq y\leq h} and width 0 ≤ z ≤ l {\displaystyle 0\leq z\leq l} are
u ( y , z ) = G 2 μ y ( h − y ) − 4 G h 2 μ π 3 ∑ n = 1 ∞ 1 ( 2 n − 1 ) 3 sinh  ( β n z ) + sinh  ( β n ( l − z ) ) sinh  ( β n l ) sin  ( β n y ) , β n = ( 2 n − 1 ) π h , Q = G h 3 l 12 μ − 16 G h 4 π 5 μ ∑ n = 1 ∞ 1 ( 2 n − 1 ) 5 cosh  ( β n l ) − 1 sinh  ( β n l ) . {\displaystyle {\begin{aligned}u(y,z)&={\frac {G}{2\mu }}y(h-y)-{\frac {4Gh^{2}}{\mu \pi ^{3}}}\sum _{n=1}^{\infty }{\frac {1}{(2n-1)^{3}}}{\frac {\sinh(\beta _{n}z)+\sinh(\beta _{n}(l-z))}{\sinh(\beta _{n}l)}}\sin(\beta _{n}y),\quad \beta _{n}={\frac {(2n-1)\pi }{h}},\\Q&={\frac {Gh^{3}l}{12\mu }}-{\frac {16Gh^{4}}{\pi ^{5}\mu }}\sum _{n=1}^{\infty }{\frac {1}{(2n-1)^{5}}}{\frac {\cosh(\beta _{n}l)-1}{\sinh(\beta _{n}l)}}.\end{aligned}}}
The velocity and the volume flow rate of tube with equilateral triangular cross-section of side length 2 h / 3 {\displaystyle 2h/{\sqrt {3}}} are
u ( y , z ) = − G 4 μ h ( y − h ) ( y 2 − 3 z 2 ) , Q = G h 4 60 3 μ . {\displaystyle {\begin{aligned}u(y,z)&=-{\frac {G}{4\mu h}}(y-h)(y^{2}-3z^{2}),\\Q&={\frac {Gh^{4}}{60{\sqrt {3}}\mu }}.\end{aligned}}}
The velocity and the volume flow rate in the right-angled isosceles triangle y = π , y ± z = 0 {\displaystyle y=\pi ,\ y\pm z=0} are
u ( y , z ) = G 2 μ ( y + z ) ( π − y ) − G π μ ∑ n = 1 ∞ 1 β n 3 sinh  ( 2 π β n ) { sinh  [ β n ( 2 π − y + z ) ] sin  [ β n ( y + z ) ] − sinh  [ β n ( y + z ) ] sin  [ β n ( y − z ) ] } , β n = n − 1 2 , Q = G π 4 12 μ − G 2 π μ ∑ n = 1 ∞ 1 β n 5 [ coth  ( 2 π β n ) + csc  ( 2 π β n ) ] . {\displaystyle {\begin{aligned}u(y,z)&={\frac {G}{2\mu }}(y+z)(\pi -y)-{\frac {G}{\pi \mu }}\sum _{n=1}^{\infty }{\frac {1}{\beta _{n}^{3}\sinh(2\pi \beta _{n})}}\{\sinh[\beta _{n}(2\pi -y+z)]\sin[\beta _{n}(y+z)]-\sinh[\beta _{n}(y+z)]\sin[\beta _{n}(y-z)]\},\quad \beta _{n}=n-{\frac {1}{2}},\\Q&={\frac {G\pi ^{4}}{12\mu }}-{\frac {G}{2\pi \mu }}\sum _{n=1}^{\infty }{\frac {1}{\beta _{n}^{5}}}[\coth(2\pi \beta _{n})+\csc(2\pi \beta _{n})].\end{aligned}}}
The velocity distribution for tubes of elliptical cross-section with semi-axis a {\displaystyle a} and b {\displaystyle b} is[8]
u ( y , z ) = G 2 μ ( 1 a 2 + 1 b 2 ) ( 1 − y 2 a 2 − z 2 b 2 ) , Q = π G a 3 b 3 4 μ ( a 2 + b 2 ) . {\displaystyle {\begin{aligned}u(y,z)&={\frac {G}{2\mu \left({\frac {1}{a^{2}}}+{\frac {1}{b^{2}}}\right)}}\left(1-{\frac {y^{2}}{a^{2}}}-{\frac {z^{2}}{b^{2}}}\right),\\Q&={\frac {\pi Ga^{3}b^{3}}{4\mu (a^{2}+b^{2})}}.\end{aligned}}}
Here, when a = b {\displaystyle a=b} , Poiseuille flow for circular pipe is recovered and when a → ∞ {\displaystyle a\rightarrow \infty } , plane Poiseuille flow is recovered.
Poiseuille's equation for compressible fluids[edit]
For a compressible fluid in a tube the volumetric flow rate and the linear velocity are not constant along the tube. The flow is usually expressed at outlet pressure. As fluid is compressed or expands, work is done and the fluid is heated or cooled. This means that the flow rate depends on the heat transfer to and from the fluid. For an ideal gas in the isothermal case, where the temperature of the fluid is permitted to equilibrate with its surroundings, and when the pressure difference between ends of the pipe is small, the volumetric flow rate at the pipe outlet is given by
Q = d V d t = v π R 2 = π R 4 ( P i − P o ) 8 μ L × P i + P o 2 P o = π R 4 16 μ L ( P i 2 − P o 2 P o ) {\displaystyle Q={\frac {dV}{dt}}=v\pi R^{2}={\frac {\pi R^{4}\left(P_{\mathrm {i} }-P_{\mathrm {o} }\right)}{8\mu L}}\times {\frac {P_{\mathrm {i} }+P_{\mathrm {o} }}{2P_{\mathrm {o} }}}={\frac {\pi R^{4}}{16\mu L}}\left({\frac {P_{\mathrm {i} }^{2}-P_{\mathrm {o} }^{2}}{P_{\mathrm {o} }}}\right)}
where:
Pi is inlet pressure
Po is outlet pressure
L is the length of tube
μ {\displaystyle \mu } is the viscosity
R is the radius
V is the volume of the fluid at outlet pressure
v is the velocity of the fluid at outlet pressure
This equation can be seen as Poiseuille's law with an extra correction factor Pi + Po/2Po expressing the average pressure relative to the outlet pressure.
Electrical circuits analogy[edit]
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Electricity was originally understood to be a kind of fluid. This hydraulic analogy is still conceptually useful for understanding circuits. This analogy is also used to study the frequency response of fluid-mechanical networks using circuit tools, in which case the fluid network is termed a hydraulic circuit.
Poiseuille's law corresponds to Ohm's law for electrical circuits, V = IR.
Since the net force acting on the fluid is equal to
Δ F = S Δ P , {\displaystyle \Delta F=S\Delta P,}
where S = πr2, i.e. ΔF = πr2 ΔP, then from Poiseuille's law
Δ P = 8 μ L Q π r 4 {\displaystyle \Delta P={\frac {8\mu LQ}{\pi r^{4}}}}
it follows that
Δ F = 8 μ L Q r 2 {\displaystyle \Delta F={\frac {8\mu LQ}{r^{2}}}} .
For electrical circuits, let n be the concentration of free charged particles (in m−3) and let q* be the charge of each particle (in coulombs). (For electrons, q* = e = 6981160000000000000♠1.6×10−19 C.)
Then nQ is the number of particles in the volume Q, and nQq* is their total charge. This is the charge that flows through the cross section per unit time, i.e. the current I. Therefore, I = nQq*. Consequently, Q = I/nq*, and
Δ F = 8 μ L I n r 2 q ∗ . {\displaystyle \Delta F={\frac {8\mu LI}{nr^{2}q^{*}}}.}
But ΔF = Eq, where q is the total charge in the volume of the tube. The volume of the tube is equal to πr2L, so the number of charged particles in this volume is equal to nπr2L, and their total charge is
q = n π r 2 L q ∗ . {\displaystyle q=n\pi r^{2}Lq^{*}.}
Now,
E = Δ F q = 8 μ I n 2 π r 4 ( q ∗ ) 2 . {\displaystyle E={\frac {\Delta F}{q}}={\frac {8\mu I}{n^{2}\pi r^{4}(q^{*})^{2}}}.}
Since the voltage V = EL, we get
V = 8 μ L I n 2 π r 4 ( q ∗ ) 2 . {\displaystyle V={\frac {8\mu LI}{n^{2}\pi r^{4}(q^{*})^{2}}}.}
This is exactly Ohm's law, where the resistance R = V/I is described by the formula
R = 8 μ L n 2 π r 4 ( q ∗ ) 2 {\displaystyle R={\frac {8\mu L}{n^{2}\pi r^{4}(q^{*})^{2}}}} .
It follows that the resistance R is proportional to the length L of the resistor, which is true. However, it also follows that the resistance R is inversely proportional to the fourth power of the radius r, i.e. the resistance R is inversely proportional to the second power of the cross section area S = πr2 of the resistor, which is wrong according to the electrical analogy.
The correct relation is
R = ρ L S , {\displaystyle R={\frac {\rho L}{S}},}
where ρ is the specific resistance; i.e. the resistance R is inversely proportional to the cross section area S of the resistor.[13]
The reason why Poiseuille's law leads to a wrong formula for the resistance R is the difference between the fluid flow and the electric current. Electron gas is inviscid, so its velocity does not depend on the distance to the walls of the conductor. The resistance is due to the interaction between the flowing electrons and the atoms of the conductor. Therefore, Poiseuille's law and the hydraulic analogy are useful only within certain limits when applied to electricity.
Both Ohm's law and Poiseuille's law illustrate transport phenomena.
Medical applications – intravenous access and fluid delivery[edit]
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The Hagen–Poiseuille equation is useful in determining the flow rate of intravenous fluids that may be achieved using various sizes of peripheral and central cannulas. The equation states that flow rate is proportional to the radius to the fourth power, meaning that a small increase in the internal diameter of the cannula yields a significant increase in flow rate of IV fluids. The radius of IV cannulas is typically measured in "gauge", which is inversely proportional to the radius. Peripheral IV cannulas are typically available as (from large to small) 14G, 16G, 18G, 20G, 22G. As an example, the flow of a 14G cannula is typically twice that of a 16G, and ten times that of a 20G. It also states that flow is inversely proportional to length, meaning that longer lines have lower flow rates. This is important to remember as in an emergency, many clinicians favor shorter, larger catheters compared to longer, narrower catheters. While of less clinical importance, the change in pressure can be used to speed up flow rate by pressurizing the bag of fluid, squeezing the bag, or hanging the bag higher from the level of the cannula. It is also useful to understand that viscous fluids will flow slower (e.g. in blood transfusion).
See also[edit]
Couette flow
Darcy's law
Pulse
Wave
Hydraulic circuit
Notes[edit]
^ Jump up to: a b Sutera, Salvatore P.; Skalak, Richard (1993). "The History of Poiseuille's Law". Annual Review of Fluid Mechanics. 25: 1–19. Bibcode:1993AnRFM..25....1S. doi:10.1146/annurev.fl.25.010193.000245.
Jump up ^ István Szabó, ;;Geschichte der mechanischen Prinzipien und ihrer wichtigsten Anwendungen, Basel: Birkhäuser Verlag, 1979.
Jump up ^ Kirby, B. J. (2010). Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. Cambridge University Press. ISBN 978-0-521-11903-0.
Jump up ^ Bruus, H. (2007). Theoretical Microfluidics.
Jump up ^ "Poiseuille and his law" (PDF). pdfs.semanticscholar.org.
Jump up ^ Vogel, Steven (1981). Life in Moving Fluids: The Physical Biology of Flow. PWS Kent Publishers. ISBN 0871507498.
Jump up ^ Determinants of blood vessel resistance.
^ Jump up to: a b Batchelor, George Keith. An introduction to fluid dynamics. Cambridge university press, 2000.
Jump up ^ Rosenhead, Louis, ed. Laminar boundary layers. Clarendon Press, 1963.
Jump up ^ Drazin, Philip G., and Norman Riley. The Navier–Stokes equations: a classification of flows and exact solutions. No. 334. Cambridge University Press, 2006.
Jump up ^ Boussinesq, Joseph. "Mémoire sur l’influence des Frottements dans les Mouvements Réguliers des Fluids." J. Math. Pures Appl 13.2 (1868): 377-424.
Jump up ^ Proudman, J. "IV. Notes on the motion of viscous liquids in channels." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 28.163 (1914): 30-36.
Jump up ^ Fütterer, C. et al. "Injection and flow control system for microchannels" Lab-on-a-Chip (2004): 351-356.
References[edit]
Sutera, S. P.; Skalak, R. (1993). "The history of Poiseuille's law". Annual Review of Fluid Mechanics. 25: 1–19. Bibcode:1993AnRFM..25....1S. doi:10.1146/annurev.fl.25.010193.000245 .
Pfitzner, J (1976). "Poiseuille and his law". Anaesthesia. 31 (2) (published Mar 1976). pp. 273–5. doi:10.1111/j.1365-2044.1976.tb11804.x. PMID 779509 .
Bennett, C. O.; Myers, J. E. (1962). "Momentum, Heat, and Mass Transfer". McGraw-Hill .
External links[edit]
Poiseuille's law for power-law non-Newtonian fluid
Poiseuille's law in a slightly tapered tube
Hagen–Poiseuille equation calculator
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hagen–Poiseuille_equation&oldid=840490732"
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