Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 360720 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0452 1209400 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0452 1209400 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1228 4124320 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1242 4151984 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1250 4169696 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1252 4200216 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1263 4222936 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1263 4222936 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1785 4904616 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1823 5096768 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1829 5117696 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1949 5318872 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1950 5319128 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Velocity Potential

Velocity potential is used in fluid dynamics, when a fluid occupies a simply-connected region – no sources or sinks - and is irrotational, so the velocity fieldhas zero curl:

As a result,can be represented as the gradient of a scalar function:

in Cartesian coordinates. Given the velocity field we can find the velocity potential by integration.

The velocity potential is not unique. Ifis a constant thenis also a velocity potential forConversely, ifis a velocity potential forthenfor some constantIn other words, velocity potentials are unique up to a constant.

Example : Supposeshown below:

Example:Find the velocity potential.

These are all equal. Put the first and second equal. Thenare both functions ofonly and both are equal towhich is a function ofandsoandwhere is an arbitrary constant.

Add comment

Security code
Refresh