Question
1.Compare the energy at 15 C°, one ATM pressure contained in 1 m 2 of the following wind regimes
a.100 hours of 6 m/s(13.4 mph).
b.50 hours at 3 m/s plus 50 hours at 9 m/s.
c.Comment on which regime contains more energy
2.Find the density of air at 1 ATMand 30 °C (86 F).
a.Is there an increase or decrease in the density of air when you raise the temperature?In class examples from March 9, 2016
1.Find the density of air at 15 C° and an elevation of 2000 m.
2.An anemometer mounted at a height of 10 m above a surface with crops, hedges, and shrubs shows a wind speed of 5 m/s.
a.Estimate the wind speed and the specific power in the wind at a height of 50 m.
b.What is the power available in the wind at 50 m?
c.What is the power available in the wind at 10 m ?
3.How fast does a big turbine turn?
a.A 40 m, three bladed wind turbine produces 600 kW at a windspeed of 14 m/s. Under these conditions, at what rpm does the rotor turn when it operates with a TSR of 4.0?
b.What is the tip speed of the rotor?
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Q1) The cross sectional area of the given wind Regime: 1m2
(i) The total speed of the wind = 6m/s
Temperature of the wind (Air mass) = 150C
(Energy = 0.5* density* swept Area * Velocity3)
E=0.5*   (1.225) *1 * 63 = 132.3 W
(Note: Density assumed 1.225kg/m3)
For 100 hours of operations the energy available will be 132.3 * 100* 3600 = 47.628MJ
(2) Wind speed if 3m/s for 50 hours
Energy contained in 50 hours of wind = 0.5*1.225*1*33 *50*3600 = 2.976MJ
Wind speed if 9m/s for 50 hours
Energy contained = 80.37225 MJ
Obviously the wind regime at 9m/s working for 50 hours does have more energy than the remaining two regimes. However the exact amount of energy available from the wind turbine will depend on the operational efficiency and generator efficiency factors
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      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (306μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (113μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheMissed (207μs)
      • Illuminate\Database\Events\StatementPrepared (838μs)
      • Illuminate\Database\Events\QueryExecuted (979μs)
      • eloquent.retrieved: App\Models\SubjectCat (92μs)
      • Illuminate\Cache\Events\KeyWritten (306μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • creating: site.layouts.app (382μs)
      • composing: site.layouts.app (17μs)
      • creating: components.canonical (418μs)
      • composing: components.canonical (81μs)
      • creating: components.open-graph (142μs)
      • composing: components.open-graph (49μs)
      • creating: site.headers.header (217μs)
      • composing: site.headers.header (49μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • creating: components.footer (81μs)
      • composing: components.footer (75μs)
      • Illuminate\Cache\Events\CacheHit (660μs)
      • Illuminate\Cache\Events\CacheMissed (365μs)
      • Illuminate\Database\Events\StatementPrepared (851μs)
      • Illuminate\Database\Events\QueryExecuted (1.46ms)
      • eloquent.retrieved: App\Models\SubjectCat (110μs)
      • Illuminate\Cache\Events\KeyWritten (463μs)
      • Illuminate\Cache\Events\CacheHit (389μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (248μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (362μs)
      • Illuminate\Cache\Events\CacheHit (342μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • creating: components.forms.contact-us (319μs)
      • composing: components.forms.contact-us (191μs)
      • creating: components.forms.get-started (331μs)
      • composing: components.forms.get-started (84μs)
      • creating: components.forms.free-tool-download (104μs)
      • composing: components.forms.free-tool-download (63μs)
      • creating: components.forms.claim-free-worksheet (124μs)
      • composing: components.forms.claim-free-worksheet (67μs)
      • creating: components.forms.tutor-subscription-waitlist (141μs)
      • composing: components.forms.tutor-subscription-waitlist (71μs)
      • creating: components.forms.tutor-subscription-join (130μs)
      • composing: components.forms.tutor-subscription-join (66μs)
      • creating: components.forms.tutor-support (124μs)
      • composing: components.forms.tutor-support (153μs)
      • 311 x Illuminate\Cache\Events\CacheHit (16.64%)
        60.34ms
        20 x Illuminate\Database\Events\StatementPrepared (10.78%)
        39.10ms
        20 x Illuminate\Database\Events\QueryExecuted (6.86%)
        24.89ms
        11 x Illuminate\Cache\Events\KeyWritten (2.51%)
        9.09ms
        11 x Illuminate\Cache\Events\CacheMissed (1.95%)
        7.07ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.5%)
        1.81ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.29%)
        1.04ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.17%)
        627μs
        1 x Illuminate\Routing\Events\Routing (0.15%)
        550μs
        1 x creating: components.canonical (0.12%)
        418μs
        1 x creating: site.layouts.app (0.11%)
        382μs
        1 x eloquent.booting: App\Models\SubjectCat (0.09%)
        339μs
        1 x creating: components.forms.get-started (0.09%)
        331μs
        1 x creating: components.forms.contact-us (0.09%)
        319μs
        1 x creating: homework.show (0.08%)
        285μs
        1 x Illuminate\Routing\Events\RouteMatched (0.07%)
        263μs
        1 x creating: components.breadcrumbs (0.07%)
        263μs
        2 x eloquent.retrieved: App\Models\Subject (0.07%)
        250μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        227μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        219μs
        1 x creating: site.headers.header (0.06%)
        217μs
        1 x composing: components.forms.contact-us (0.05%)
        191μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        158μs
        1 x composing: components.forms.tutor-support (0.04%)
        153μs
        1 x creating: components.open-graph (0.04%)
        142μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.04%)
        141μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        130μs
        1 x creating: components.forms.tutor-subscription-join (0.04%)
        130μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        124μs
        1 x composing: components.breadcrumbs (0.03%)
        124μs
        1 x creating: components.forms.claim-free-worksheet (0.03%)
        124μs
        1 x creating: components.forms.tutor-support (0.03%)
        124μs
        1 x composing: homework.show (0.03%)
        120μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        107μs
        1 x creating: components.forms.free-tool-download (0.03%)
        104μs
        1 x composing: components.forms.get-started (0.02%)
        84μs
        1 x composing: components.canonical (0.02%)
        81μs
        1 x creating: components.footer (0.02%)
        81μs
        1 x composing: components.footer (0.02%)
        75μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        71μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        67μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        66μs
        1 x composing: components.forms.free-tool-download (0.02%)
        63μs
        1 x eloquent.booted: App\Models\Subject (0.02%)
        62μs
        1 x composing: components.open-graph (0.01%)
        49μs
        1 x composing: site.headers.header (0.01%)
        49μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        40μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        40μs
        1 x composing: site.layouts.app (0%)
        17μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated47.51ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '47664' limit 1
        21.06mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 47664
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (371)
        1.67mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (47664)
        1.27mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.31mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 47664 and `subject` = 371 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.39mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 47664
        • 1: 371
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (371)
        1.47mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47664 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.27mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47664
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47664 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.24mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47664
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 47664 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.06mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 47664
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.24mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.54mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.4mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.12mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.43mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.57mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.34mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.55mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          ihboqiqGADsp0Y66nugdGT8P0o6IaZALUZ6lOu0a
          utm_source
          direct
          redirectUrl
          /college-homework-library/Engineering/Energy-Systems-Engineering/47664
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Ene...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Engineering/Energy-Systems-Engineering/47664
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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