Name: laminar flow profile between parallel plates
Uploaded: 2025-02-13T15:43:26.000Z
Duration: 1 min 17 s
Channel: JoVE

يصف التدفق الرقائقي الثابت بين لوحين متوازيين حركة السوائل في قناة ضيقة ومحصورة ، وغالبا ما تستخدم لنمذجة أنظمة السوائل البسيطة.
بالنسبة للتدفق بين لوحين ثابتين ، يتم تبسيط معادلات Navier-Stokes حيث تختلف السرعة بشكل عمودي فقط على الألواح ، مع عدم وجود تسارع على طول اتجاه التدفق.
يؤدي هذا إلى ملف تعريف السرعة المكافئ ، حيث يتحرك السائل بشكل أسرع في المركز ويتباطأ إلى الصفر عند الصفائح بسبب الاحتكاك ، والمعروفة باسم حالة عدم الانزلاق.
يعتمد معدل التدفق بين الألواح على تدرج الضغط ولزوجة السوائل وفصل اللوحة ؛ توسيع الفجوة أو زيادة تدرج الضغط يعزز التدفق.
يرتبط متوسط سرعة التدفق أيضا بانخفاض الضغط ، حيث تبلغ السرعة القصوى في مركز القناة 1.5 ضعف متوسط السرعة.
يظل هذا التحليل صالحا فقط لأرقام رينولدز المنخفضة ، مما يشير إلى الظروف الصفيحية ، ويفشل في التدفقات المضطربة ذات رقم رينولدز العالي.
تشمل تطبيقات هذا التحليل قنوات الري وتدفق المياه الجوفية وأحواض الترسيب في محطات معالجة المياه ، حيث توجد ظروف رقائقية.

السريان المستقر والمنتظم بين لوحين متوازيين

Steady, Laminar Flow Between Parallel Plates

<div style="direction:rtl">يعد فهم السريان المستقر والمنتظم بين لوحين متوازيين أمر ضروري لتحليل وتصميم السريان في القنوات المستطيلة الضيقة، والتي توجد عادةً في أنظمة مختلفة لنقل المياه والصرف. تستنبط معادلات نافير-ستوكس سلوك حركة الموائع وعادةً ما يكون حلها صعبًا نظرا لكونها معادلات غير خطية. ومع ذلك، فإن تبسيطها ممكن في حالات معينة، مثل السريان المستقر بين لوحين متوازيين. في هذا السيناريو، يتم افتراض سريان مستقر ومنتظم لمائع غير قابل للانضغاط. بالنظر إلى لوحين افقيين متحاذيين على طول المحور السيني ومتباعدين بمسافة "2h"، يُفترض أن اتجاه حركة السائل متوازي مع المحور الصادي العمودي على اللوحين. هنا، تشير معادلة الاستمرارية إلى عدم وجود تغيير في السرعة على طول المحور السيني، ويتم تبسيط معادلات نافير-ستوكس على النحو التالي: <img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;"> لا تُظهر المعادلات في اتجاهي y وz أي تدرج في الضغط على طول هذه المحاور، مما يشير إلى أن الضغط يتغير هيدروستاتيكيًا في اتجاه y، مما يسمح للتكامل بانتاج مايلي: <img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;"> بالنسبة للالواح الموازية لتدرج في الضغط على طول المحور السيني، يتم تبسيط المعادلة: <img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;"> من خلال التكامل مرتين وتطبيق الشروط الاتية (u = 0 عند y = +h وy = -h)، نحصل على: <img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;"> يكشف هذا التعبير أن دالة السرعة تتغير عبر المسافة بين اللوحين معطية منحنى على شكل قطع مكافئ، مع أقصى سرعة عند y = 0، في منتصف المسافة بين اللوحين. يتم الحصول على معدل التدفق الحجمي المار عبر وحدة عرض للألواح من خلال تكامل دالة السرعة مع المسافة. إن فهم السريان المستقر بين الألواح المتوازية له تطبيقات عملية في تدفقات المياه الجوفية ومعالجة مياه الصرف الصحي وكذلك التزييت. على سبيل المثال، يمكن لهذا النموذج الحساب التقريبي لسريان الماء بين طبقات التربة، حيث يتحرك الماء بين جزيئات التربة مثل التدفق بين الألواح. تساعد معرفة معدل التدفق وتغير السرعات المهندسين على تصميم أنظمة صرف فعالة وكذلك التنبؤ بحركة المياه الجوفية.</div>

يصف التدفق الرقائقي الثابت بين لوحين متوازيين حركة السوائل في قناة ضيقة ومحصورة ، وغالبا ما تستخدم لنمذجة أنظمة السوائل البسيطة.
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Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Differential Analysis of Fluid Flow

التحليل التفاضلي لتدفق السوائل

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

laminar flow profile between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings.

The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem becomes simpler because the flow is steady, incompressible, and laminar. Two horizontal plates are placed along the x-axis, and the gap between them is 2h. The y-axis is perpendicular to the plates, and the fluid moves parallel to the plates.

With these assumptions, the continuity equation shows that the velocity does not change along the x-axis. The Navier-Stokes equations also simplify in the y and z directions. They show no pressure gradient along those axes, so pressure changes hydrostatically in the y-direction. After integration, the x-direction equation includes the pressure gradient along the plates.

Solving that equation requires integrating twice and applying the no-slip boundary conditions, where u = 0 at y = +h and y = -h. The result is a parabolic velocity profile across the gap. The fluid moves fastest at y = 0, the midpoint between the plates. The volumetric flow rate for a unit width of the plates is then found by integrating the velocity profile across the space.

This flow model has practical uses in groundwater flow, wastewater treatment, and lubrication. It can also represent water moving through soil layers, where the flow resembles movement between plates. Engineers use the velocity distribution and flow rate to help design drainage systems and predict groundwater movement.

Laminar Flow Profile Between Parallel Plates

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steady, laminar flow between parallel plates

Laminar flow between parallel plates shows how fluid moves through a narrow, flat channel. This model helps describe flow in water conveyance and drainage systems, where the space is limited and the motion stays orderly. It is also useful for analyzing flow in rectangular channels used in many engineering settings. The flow is studied with the Navier-Stokes equations, which govern fluid motion. These equations are often difficult to solve because they are nonlinear. In this case, the problem...

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key terms and concepts

Learn how steady laminar flow between parallel plates leads to a parabolic velocity profile, pressure-gradient behavior, and flow-rate calculations.

Laminar Flow Profile Between Parallel Plates | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Laminar Flow Profile Between Parallel Plates

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