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Hydrodynamics

Hydrodynamics

Hydrodynamics is a major branch of the physics discipline which studies the motion of liquids. A fluid in its simplest definition, is a body of matter that can flow. A fluid can be considered a liquid, which has definite volume and free surface, or it can be considered a gas, which expands to fill a container. The main forces that allow fluids to move are pressure differences, surface stress, and gravity.

There are many types of fluid flow. Determining the type of flow is essential to solving a problem involving moving fluids. Fluid flow can either be laminar or turbulent. Laminar flow deals with slow moving fluids traveling in regular, smooth paths. Laminar flows have thin layers and move parallel to each other. Turbulent flow, on the other hand, is more irregular and the speed of the fluid continuously changes in strength and direction. For example, a river may be turbulent, though undercurrents may undergo little movement. The Reynolds number (Re) is a quantity without dimensions, which can be used to predict flow patterns through a ratio of inertial forces to viscous forces within a fluid.

Hydrodynamic problems can be addressed by applying one or more physical principles: continuity (mass conservation), momentum, and energy. Continuity is often the most basic of equation and is usually applied to reduce unknown variables. Mass is unable to be created or destroyed. Continuity states that the total mass entering the control volume must equal the total mass exiting the control volume. This statement is true of fluid flow that is steady or incompressible.

The principle of momentum is based on Newton’s Laws of Motion. Newton’s Second Law states that the acceleration of an object is dependent on the force acting upon the object and the mass of the object. A greater force causes an increased acceleration of the object, but an increased object mass decreases the acceleration of the object. Newton’s Third Law declares that the force that is exerted on a contained fluid is equal and opposing to the force exerted by the containment of the fluid.

Energy can simply be considered the capacity for doing work. Energy exists in three forms: potential energy, kinetic energy, and pressure energy. Kinetic energy is utilized by a moving body.  Potential energy is stored relative to its position. Pressure energy is stored in a fluid based on the force exerted on it. The pressure energy principle uses as an equation which is also known as the Bernoulli equation to analyze a hydrodynamic system. In other words, change of energy equals the work achieved plus the heat input. Bernoulli’s equation associates a relationship between height, pressure, and velocity at two points along a streamline. This equation should only be used for ideal fluids or fluids without changes in energy.

Scientists from many different fields make use of hydrodynamics. It is an important area of study for technological advances including rocket engines, oil pipelines, reservoir management, and air conditioning systems. It also provides a basis for studying weather patterns, tectonic plates, and even the circulation of blood in the human body.

 

To fulfill our tutoring mission of online education, our college homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of hydrodynamics. Our engineering tutors can help with all your projects, large or small, and we challenge you to find better online hydrodynamics tutoring anywhere.

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      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • creating: components.tutors-card (1ms)
      • composing: components.tutors-card (66μs)
      • Illuminate\Database\Events\StatementPrepared (5.7ms)
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      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • creating: components.tutors-card (396μs)
      • composing: components.tutors-card (55μs)
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      • Illuminate\Database\Events\QueryExecuted (4.51ms)
      • Illuminate\Cache\Events\CacheHit (302μs)
      • Illuminate\Cache\Events\CacheHit (2.08ms)
      • Illuminate\Cache\Events\CacheHit (584μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
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      • Illuminate\Cache\Events\CacheHit (203μs)
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      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
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      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
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      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (12.31ms)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
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      • Illuminate\Cache\Events\CacheHit (175μs)
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      • Illuminate\Cache\Events\CacheHit (193μs)
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      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
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      • Illuminate\Cache\Events\CacheHit (196μs)
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      • Illuminate\Cache\Events\CacheHit (191μs)
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      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (8.26ms)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
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      • Illuminate\Cache\Events\CacheHit (1.14ms)
      • Illuminate\Cache\Events\CacheHit (825μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (151μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (155μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (8.36ms)
      • Illuminate\Cache\Events\CacheHit (2.88ms)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (364μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • creating: components.tutors-card (706μs)
      • composing: components.tutors-card (968μs)
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      • Illuminate\Cache\Events\CacheHit (703μs)
      • Illuminate\Cache\Events\CacheHit (11.87ms)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (156μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (255μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
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      • composing: site.blocks.subject-homework (25μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (205μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (124μs)
      • Illuminate\Database\Events\StatementPrepared (5.01ms)
      • Illuminate\Database\Events\QueryExecuted (1.42ms)
      • Illuminate\Database\Events\StatementPrepared (742μs)
      • Illuminate\Database\Events\QueryExecuted (1.34ms)
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      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (19μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
      • eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (10μs)
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      • eloquent.retrieved: App\Models\SubjectCat (85μs)
      • creating: components.homework-blocks (257μs)
      • composing: components.homework-blocks (127μs)
      • creating: site.blocks.reviews (1.05ms)
      • composing: site.blocks.reviews (36μs)
      • creating: site.blocks.submit-homework (164μs)
      • composing: site.blocks.submit-homework (20μs)
      • creating: site.blocks.faq (131μs)
      • composing: site.blocks.faq (19μs)
      • eloquent.booting: App\Models\Twill\TwillFaq (162μs)
      • eloquent.booted: App\Models\Twill\TwillFaq (171μs)
      • eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (265μs)
      • eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (67μs)
      • Illuminate\Database\Events\StatementPrepared (1.87ms)
      • Illuminate\Database\Events\QueryExecuted (1.91ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (122μs)
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      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (99μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (23μs)
      • creating: components.faq-item (153μs)
      • composing: components.faq-item (124μs)
      • Illuminate\Database\Events\StatementPrepared (1.9ms)
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      • eloquent.retrieved: App\Models\Twill\TwillFaq (101μs)
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      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (22μs)
      • creating: components.faq-item (94μs)
      • composing: components.faq-item (51μs)
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      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (75μs)
      • creating: components.faq-item (79μs)
      • composing: components.faq-item (51μs)
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      • creating: components.faq-item (72μs)
      • composing: components.faq-item (41μs)
      • creating: site.blocks.text-with-image (251μs)
      • composing: site.blocks.text-with-image (20μs)
      • creating: site.blocks.work-with-tutors (185μs)
      • composing: site.blocks.work-with-tutors (19μs)
      • creating: site.layouts.app (229μs)
      • composing: site.layouts.app (19μs)
      • creating: components.canonical (380μs)
      • composing: components.canonical (92μs)
      • creating: components.open-graph (275μs)
      • composing: components.open-graph (89μs)
      • creating: site.headers.header (344μs)
      • composing: site.headers.header (79μs)
      • Illuminate\Cache\Events\CacheHit (1.75ms)
      • creating: components.footer (81μs)
      • composing: components.footer (108μs)
      • Illuminate\Cache\Events\CacheHit (924μs)
      • Illuminate\Cache\Events\CacheHit (327μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (326μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (8.32ms)
      • Illuminate\Cache\Events\CacheHit (333μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • creating: components.forms.contact-us (305μs)
      • composing: components.forms.contact-us (200μs)
      • creating: components.forms.get-started (175μs)
      • composing: components.forms.get-started (82μs)
      • creating: components.forms.free-tool-download (133μs)
      • composing: components.forms.free-tool-download (73μs)
      • creating: components.forms.claim-free-worksheet (131μs)
      • composing: components.forms.claim-free-worksheet (72μs)
      • creating: components.forms.tutor-subscription-waitlist (130μs)
      • composing: components.forms.tutor-subscription-waitlist (72μs)
      • creating: components.forms.tutor-subscription-join (128μs)
      • composing: components.forms.tutor-subscription-join (72μs)
      • creating: components.forms.tutor-support (128μs)
      • composing: components.forms.tutor-support (72μs)
      • 436 x Illuminate\Cache\Events\CacheHit (23.19%)
        252ms
        24 x Illuminate\Database\Events\StatementPrepared (8.05%)
        87.64ms
        24 x Illuminate\Database\Events\QueryExecuted (4.62%)
        50.25ms
        1 x creating: site.blocks.subject-homework (1.18%)
        12.87ms
        1 x Illuminate\Cache\Events\CacheMissed (0.96%)
        10.50ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.49%)
        5.34ms
        6 x creating: components.tutors-card (0.37%)
        4.00ms
        6 x composing: components.tutors-card (0.12%)
        1.33ms
        2 x Illuminate\Database\Events\ConnectionEstablished (0.11%)
        1.23ms
        1 x creating: site.blocks.reviews (0.1%)
        1.05ms
        1 x Illuminate\Routing\Events\Routing (0.07%)
        767μs
        1 x Illuminate\Cache\Events\KeyWritten (0.04%)
        449μs
        4 x eloquent.retrieved: App\Models\Twill\TwillFaq (0.04%)
        446μs
        6 x eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (0.04%)
        404μs
        4 x creating: components.faq-item (0.04%)
        398μs
        1 x Illuminate\Routing\Events\RouteMatched (0.04%)
        396μs
        1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.04%)
        396μs
        1 x creating: components.canonical (0.03%)
        380μs
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        344μs
        1 x eloquent.booting: App\Models\User\Tutor (0.03%)
        328μs
        3 x eloquent.retrieved: App\Models\SubjectCat (0.03%)
        319μs
        1 x creating: site.blocks.how-it-works (0.03%)
        309μs
        1 x creating: components.forms.contact-us (0.03%)
        305μs
        1 x creating: components.open-graph (0.03%)
        275μs
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        1 x eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (0.02%)
        265μs
        1 x creating: components.homework-blocks (0.02%)
        257μs
        2 x eloquent.retrieved: App\Models\Subject (0.02%)
        256μs
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        251μs
        1 x creating: components.tutors-cards (0.02%)
        238μs
        6 x eloquent.retrieved: App\Models\User\Tutor (0.02%)
        237μs
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        229μs
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        229μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        221μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        205μs
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        200μs
        1 x eloquent.booted: App\Models\User\Tutor (0.02%)
        192μs
        1 x creating: site.blocks.work-with-tutors (0.02%)
        185μs
        1 x creating: components.forms.get-started (0.02%)
        175μs
        1 x eloquent.booted: App\Models\Twill\TwillFaq (0.02%)
        171μs
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        165μs
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        164μs
        1 x creating: site.blocks.submit-homework (0.02%)
        164μs
        1 x eloquent.booting: App\Models\Twill\TwillFaq (0.01%)
        162μs
        1 x creating: subjects.show (0.01%)
        152μs
        1 x eloquent.booting: App\Models\Meta (0.01%)
        151μs
        1 x creating: components.forms.free-tool-download (0.01%)
        133μs
        1 x creating: site.blocks.faq (0.01%)
        131μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        131μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        130μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        128μs
        1 x creating: components.forms.tutor-support (0.01%)
        128μs
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        127μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.01%)
        124μs
        1 x eloquent.booting: App\Models\SubjectCat (0.01%)
        118μs
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        108μs
        1 x composing: components.tutors-cards (0.01%)
        105μs
        1 x composing: subjects.show (0.01%)
        104μs
        1 x creating: site.blocks.subject-tutors (0.01%)
        98μs
        1 x composing: components.canonical (0.01%)
        92μs
        1 x composing: components.open-graph (0.01%)
        89μs
        1 x composing: components.forms.get-started (0.01%)
        82μs
        1 x creating: components.footer (0.01%)
        81μs
        1 x eloquent.retrieved: App\Models\Meta (0.01%)
        79μs
        1 x composing: site.headers.header (0.01%)
        79μs
        1 x composing: components.forms.free-tool-download (0.01%)
        73μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        72μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        72μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        72μs
        1 x composing: components.forms.tutor-support (0.01%)
        72μs
        1 x eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (0.01%)
        67μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        64μs
        1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0.01%)
        59μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        57μs
        1 x eloquent.booted: App\Models\Meta (0%)
        54μs
        1 x composing: site.blocks.reviews (0%)
        36μs
        1 x composing: site.blocks.subject-homework (0%)
        25μs
        1 x composing: site.blocks.how-it-works (0%)
        22μs
        1 x composing: site.blocks.submit-homework (0%)
        20μs
        1 x composing: site.blocks.text-with-image (0%)
        20μs
        1 x composing: site.blocks.faq (0%)
        19μs
        1 x composing: site.blocks.work-with-tutors (0%)
        19μs
        1 x composing: site.layouts.app (0%)
        19μs
        1 x composing: site.blocks.subject-tutors (0%)
        18μs
      34 templates were rendered
      • 1x subjects.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.blocks.how-it-workshow-it-works.blade.phpblade
      • 1x site.blocks.subject-tutorssubject-tutors.blade.phpblade
      • 1x components.tutors-cardstutors-cards.blade.phpblade
      • 6x components.tutors-cardtutors-card.blade.phpblade
      • 1x site.blocks.subject-homeworksubject-homework.blade.phpblade
      • 1x components.homework-blockshomework-blocks.blade.phpblade
      • 1x site.blocks.reviewsreviews.blade.phpblade
      • 1x site.blocks.submit-homeworksubmit-homework.blade.phpblade
      • 1x site.blocks.faqfaq.blade.phpblade
      • 4x components.faq-itemfaq-item.blade.phpblade
      • 1x site.blocks.text-with-imagetext-with-image.blade.phpblade
      • 1x site.blocks.work-with-tutorswork-with-tutors.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 subjects/{categoryUri}/{subjectUri?}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\SubjectController@show
      namespace
      where
      as
      subjects.show
      file
      app/Http/Controllers/SubjectController.php:43-96
      24 statements were executed, 2 of which were duplicates, 22 unique. Show only duplicated116ms
      • Connection Establishedtwenty4_siteSubjectRepository.php#123
        Backtrace
        • 13. app/Repositories/SubjectRepository.php:123
        • 14. app/Http/Controllers/SubjectController.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `subjects` where `urlFriendlyTitle` = 'Hydrodynamics' limit 1
        10.17mstwenty4_siteSubjectRepository.php#123
        Bindings
        • 0: Hydrodynamics
        Backtrace
        • 15. app/Repositories/SubjectRepository.php:123
        • 16. app/Http/Controllers/SubjectController.php:54
        • 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
      • select * from `subject_cats` where `subject_cats`.`id` in (10)
        1mstwenty4_siteSubjectRepository.php#123
        Backtrace
        • 20. app/Repositories/SubjectRepository.php:123
        • 21. app/Http/Controllers/SubjectController.php:54
        • 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
      • select * from `meta` where `meta`.`id` = 3 limit 1
        930μstwenty4_siteMetaService.php#118
        Bindings
        • 0: 3
        Backtrace
        • 19. app/Services/MetaService.php:118
        • 20. app/Services/MetaService.php:108
        • 21. app/Services/MetaService.php:81
        • 22. app/Http/Controllers/SubjectController.php:89
        • 23. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • Connection Establishedtwenty4_siteTutorRepository.php#40
        Backtrace
        • 13. app/Repositories/TutorRepository.php:40
        • 14. app/View/Components/TutorsCards.php:28
        • 15. app/View/Components/TutorsCards.php:22
        • 17. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
      • select count(*) as aggregate from `users` where (`subjectsQualified` like '%|227|%' or `DSF_subjectsQualified` like '%|227|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'
        19.54mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|227|%
        • 1: %|227|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `users` where (`subjectsQualified` like '%|227|%' or `DSF_subjectsQualified` like '%|227|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 6 offset 0
        12.35mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|227|%
        • 1: %|227|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 2821 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        960μstwenty4_siteTutor.php#361
        Bindings
        • 0: 2821
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 76351 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        14.88mstwenty4_siteTutor.php#361
        Bindings
        • 0: 76351
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `subject_cats` where `subject_cats`.`id` = 42 limit 1
        1.15mstwenty4_siteSubject.php#100
        Bindings
        • 0: 42
        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 `tutor_degrees` where `tutor_degrees`.`tutor_id` = 70589 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        5.76mstwenty4_siteTutor.php#361
        Bindings
        • 0: 70589
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 70780 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        12mstwenty4_siteTutor.php#361
        Bindings
        • 0: 70780
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 128085 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        5.49mstwenty4_siteTutor.php#361
        Bindings
        • 0: 128085
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 127971 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        3.25mstwenty4_siteTutor.php#361
        Bindings
        • 0: 127971
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select count(*) as aggregate from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 227 and `status` = 'published' and `price` > 0
        5.37mstwenty4_siteHomeworkBlocks.php#27
        Bindings
        • 0: 227
        • 1: published
        • 2: 0
        Backtrace
        • 15. app/View/Components/HomeworkBlocks.php:27
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.subject-homework:4
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 227 and `status` = 'published' and `price` > 0 order by `purchase_count` desc limit 6 offset 0
        1.49mstwenty4_siteHomeworkBlocks.php#27
        Bindings
        • 0: 227
        • 1: published
        • 2: 0
        Backtrace
        • 15. app/View/Components/HomeworkBlocks.php:27
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.subject-homework:4
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `subjects` where `subjects`.`id` in (227)
        1.24mstwenty4_siteHomeworkBlocks.php#27
        Backtrace
        • 20. app/View/Components/HomeworkBlocks.php:27
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.subject-homework:4
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `subject_cats` where `subject_cats`.`id` in (10)
        910μstwenty4_siteHomeworkBlocks.php#27
        Backtrace
        • 25. app/View/Components/HomeworkBlocks.php:27
        • 26. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 27. view::site.blocks.subject-homework:4
        • 29. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 30. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-homework-in-less-than-24-hours' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        1.93mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: can-you-help-me-with-my-homework-in-less-than-24-hours
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:7
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (1) and `twill_faq_slugs`.`deleted_at` is null
        5.49mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:7
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-examquiztest' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        1.57mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: can-you-help-me-with-my-examquiztest
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:24
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (2) and `twill_faq_slugs`.`deleted_at` is null
        7.06mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:24
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'how-much-will-it-cost' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        940μstwenty4_siteFaqItem.php#15
        Bindings
        • 0: how-much-will-it-cost
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:41
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (3) and `twill_faq_slugs`.`deleted_at` is null
        840μstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:41
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'what-kind-of-payments-do-you-accept' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        820μstwenty4_siteFaqItem.php#15
        Bindings
        • 0: what-kind-of-payments-do-you-accept
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:58
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (4) and `twill_faq_slugs`.`deleted_at` is null
        940μstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:58
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      App\Models\User\Tutor
      6Tutor.php
      App\Models\Twill\Slugs\TwillFaqSlug
      6TwillFaqSlug.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      5HomeworkLibrary.php
      App\Models\Twill\TwillFaq
      4TwillFaq.php
      App\Models\SubjectCat
      3SubjectCat.php
      App\Models\Subject
      2Subject.php
      App\Models\Meta
      1Meta.php
          _token
          qEzgMC7u2w4rwCg1EJlyhcvW2oKFQfCjTC4o82V8
          utm_source
          direct
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/subjects/Engineering/Hydrodynamics" ]
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /subjects/Engineering/Hydrodynamics
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-67f5d5c9-2c01654c6f2502374e948261" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "18.223.29.51" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
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