Name: flow depth and energy in open channels
Uploaded: 2025-03-26T15:04:03.000Z
Duration: 1 min 27 s
Channel: JoVE

يختلف تدفق القناة المفتوحة ، حيث تتدفق المياه بسطح حر ، عن تدفق القناة المغلقة بسبب تأثير الجاذبية والتأثيرات السطحية.  اعتبارات الطاقة ضرورية لفهم سلوك التدفق في الأنهار والقنوات والقنوات الهندسية. تختلف الطاقة المحددة للتدفق ، والتي تشمل إمكانات الجاذبية والطاقة الحركية ، باختلاف العمق والسرعة ويتم تمثيلها على أنها E. لأي معدل تدفق معين ، تنتج الطاقة المحددة عمقين محتملين حيث تكون الطاقة دون الحرجة عميقة وبطيئة ، بينما تكون فوق الحرجة ضحلة وسريعة. يصنف رقم Froude ، F r ، هذه الأنظمة. التدفق دون الحرج ، مع رقم فرود أقل من واحد ، مدفوع بالجاذبية ، في حين أن التدفق فوق الحرج ، مع رقم فرود أكبر من واحد ، مدفوع بالقصور الذاتي. يحدث التدفق الحرج عندما يكون رقم Froude واحدا ، مما يقلل من الطاقة على عمق حرج. يؤثر ميل القناة على تباين العمق. في التدفق المتغير تدريجيا ، يظهر تدرج العمق أن التدفقات دون الحرجة وفوق الحرجة تتكيف بشكل مختلف. بالنسبة للتدفق المنتظم ، يتم تثبيت العمق عندما يساوي المنحدر S 0 منحدر الاحتكاك S f . تعد مبادئ الطاقة هذه ضرورية لتصميم قنوات فعالة تتنبأ بسلوك التدفق عبر الأنظمة الهيدروليكية وتديره.

اعتبارات الطاقة في تدفق القناة المفتوحة

Energy Considerations in Open Channel Flow

يخضع تدفق القناة المفتوحة ، حيث يتدفق السائل بسطح حر معرض للغلاف الجوي ، بشكل أساسي لتأثيرات الجاذبية والسطح ، مما يميزه عن القناة المغلقة أو تدفق الأنابيب. في القنوات المفتوحة مثل الأنهار والقنوات والقنوات الاصطناعية ، يوفر تحليل الطاقة رؤى قيمة حول سلوك التدفق والعلاقة بين العمق والسرعة والمنحدر. <h3 style="margin-left:0in;">الطاقة المحددة وعمق التدفق</h3> في تدفق القناة المفتوحة، تجمع الطاقة المحددة، E، بين طاقة وضع الجاذبية المرتبطة بعمق السائل، والطاقة الحركية المرتبطة بسرعة التدفق. بالنسبة لمعدل تفريغ أو تدفق معين ، عادة ما يكون هناك عمقان محتملان ، يعرفان باسم أعماق بديلة ، حيث تظل الطاقة المحددة كما هي. أحدهما أعمق وأبطأ ، يعرف باسم subcritical ، والآخر ضحل وأسرع ، يعرف باسم فوق الحرج. التدفق دون الحرج ، بسرعة أقل ، له عمق ينتج عنه حركة هادئة مدفوعة بالجاذبية. في المقابل ، تهيمن قوى القصور الذاتي على التدفق فوق الحرج ، على عمق ضحل وسرعة عالية. <h3 style="margin-left:0in;">رقم فرود وتصنيف التدفق</h3> رقم فرود Fr هو مؤشر بلا أبعاد لأنظمة التدفق، ويمثل نسبة قوى القصور الذاتي إلى قوى الجاذبية في القناة. يتم تعريفه من خلال: <figure class="image image-style-align-center image_resized" style="display:table;margin-left:auto;margin-right:auto;width:12%;"> <img style="aspect-ratio:246/150;" src="https://cloudfront.jove.com/files/ftp_upload/18092/18092_Equation_PT_editor_18092.svg" alt="18092_Equation_PT.svg"> </figure> هنا ، V هي سرعة التدفق ، g هي تسارع الجاذبية ، و y هو العمق الهيدروليكي. يصنف رقم Froude أنظمة التدفق. يحدث التدفق دون الحرج عندما يكون Fr أقل من واحد، مما يشير إلى أن الجاذبية تحكم سلوك التدفق. التدفق فوق الحرج ، حيث يكون F r أكبر من واحد ، مدفوعا بالقصور الذاتي ، ويتحرك الماء بسرعة بعمق أقل. يمثل التدفق الحرج ، حيث F r يساوي واحدا ، يمثل شرط الحد الأدنى من الطاقة النوعية التي تحدث على عمق حرج. هذا الشرط الضروري ضروري لتصميم هياكل مثل السدود والمجاري التي تتحكم في انتقالات التدفق بين الحالات دون الحرجة وفوق الحرجة. <h3 style="margin-left:0in;">يلعب دور منحدر القناة </h3> أيضا دورا مهما في تحديد خصائص التدفق. في التدفق المتغير تدريجيا ، يؤثر منحدر القناة وهندسة السرير على كيفية تغير العمق على طول التدفق. على سبيل المثال ، يتم الحفاظ على التدفق دون الحرج في منحدر معتدل ، بينما يسود التدفق فوق الحرج عادة في منحدر حاد. في حالات التدفق المنتظم ، يستقر عمق التدفق عندما يتطابق منحدر قاع القناة S 0 مع منحدر الاحتكاك S f ، وهو ما يمثل التوازن بين قوى الجاذبية والاحتكاك. هذا العمق المنتظم أمر بالغ الأهمية في تصميم قنوات مستقرة وفعالة حيث يكون التدفق متسقا ويمكن التنبؤ به على مسافات طويلة. يعد فهم مبادئ وتصنيفات الطاقة هذه في تدفق القناة المفتوحة أمرا ضروريا للهندسة الهيدروليكية. إنه يتيح تنبؤات دقيقة لسلوك التدفق ، وتصميمات القنوات الفعالة ، والإدارة المحسنة للأنظمة الهيدروليكية عبر التطبيقات المختلفة.

Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, ...

energy-considerations-in-open-channel-flow

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Open Channel Flow

الجريان في القنوات المفتوحة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

flow depth and energy in open channels

Open channel flow involves water moving with a free surface exposed to the air. Rivers, canals, and artificial channels are common examples. In these systems, gravity and surface effects shape the flow more than the behavior seen in closed pipes. Energy analysis helps explain how depth, velocity, and slope work together.

Specific energy combines the potential energy from water depth and the kinetic energy from flow speed. For a given discharge, or flow rate, there are often two possible depths with the same specific energy. These are alternate depths. One is deeper and slower and is called subcritical flow. The other is shallower and faster and is called supercritical flow.

Subcritical flow moves more slowly and is usually tranquil. Gravity has the greater effect in this regime. Supercritical flow is shallow and fast. In this case, inertial forces matter more than gravity.

The Froude number is a dimensionless value that compares inertial forces to gravitational forces in the channel. It uses flow velocity, gravitational acceleration, and hydraulic depth. When the Froude number is less than one, the flow is subcritical. When it is greater than one, the flow is supercritical. When it equals one, the flow is critical. Critical flow occurs at critical depth and gives the minimum specific energy.

This critical condition matters in the design of weirs and spillways. These structures help control the shift between subcritical and supercritical flow. Channel slope also affects flow behavior. In gradually varied flow, the slope and bed shape help determine how depth changes along the channel.

A mild slope usually supports subcritical flow, while a steep slope often leads to supercritical flow. In uniform flow, the depth stays steady when the bed slope S0 matches the friction slope Sf. At that point, gravitational and frictional forces are balanced. This stable depth is important for channels that must carry flow in a predictable way over long distances.

Understanding these energy principles is important in hydraulic engineering. They help engineers predict flow behavior and design efficient channels. They also support better management of water systems in many real-world settings.

Flow Depth and Energy in Open Channels

energy considerations in open channel flow

Open channel flow involves water moving with a free surface exposed to the air. Rivers, canals, and artificial channels are common examples. In these systems, gravity and surface effects shape the flow more than the behavior seen in closed pipes. Energy analysis helps explain how depth, velocity, and slope work together. Specific energy combines the potential energy from water depth and the kinetic energy from flow speed. For a given discharge, or flow rate, there are often two possible depths...

uniform depth channel flow

Channel Slope and Flow Balance

Uniform depth channel flow keeps the water depth steady along an open channel. This idea is often used for irrigation canals and is also a useful approximation for rivers. The channel bottom slope must match the energy slope. That balance offsets the gravity energy lost to shear stress at the boundary, so the depth does not change along the channel length. In a constant cross-section channel, uniform flow means the depth and velocity stay consistent. Two key measures are the flow area and the...

uniform depth channel flow: problem solving

uniform-depth-channel-flow-problem-solving

Calculating Trapezoidal Channel Flow Rate

Calculating trapezoidal channel flow rate starts with the channel shape and the depth of flow. For a trapezoidal channel, identify the bottom width, side slope, and flow depth first. These values define the cross-section used in the calculation. Next, find the cross-sectional area for the flowing water. Use the depth of flow, the bottom width, and the side slope angle to determine area. Then calculate the wetted perimeter, which includes the bottom width and the sloped side lengths that touch...

gradually varying flow

Open Channel Depth Changes in GVF

Gradually varying flow in open channels describes water depth that changes slowly along a channel. The depth adjusts over distance as gravity, shear forces, and energy needs stay in balance. This creates a low rate of change in the water surface. Gradually varying flow is common in natural streams, rivers, and canals. In these settings, the depth shifts little by little over long distances. The slope of the channel bed, compared with the energy slope, helps determine how the flow behaves. A...

 rapidly varying flow

Hydraulic Jumps in Open Channels

Rapidly varying flow in open channels describes a sudden change in water depth over a short distance. The depth can change so quickly that the rate of change with distance is close to one. These flows are difficult to analyze exactly because they are transient and multi-dimensional. Approximate solutions with simplified models still give useful insight into how they behave. A common example is the hydraulic jump. In a hydraulic jump, fast and shallow water changes quickly into slower, deeper...

hydraulic jump

Flow Regimes and Energy in Hydraulic Jumps

Hydraulic jumps happen in open channels when fast, shallow water changes into slower, deeper water. This sudden rise in depth depends on the upstream Froude number, which compares flow speed to wave speed. A hydraulic jump can form only when the upstream flow is supercritical, with Fr greater than 1. If Fr is less than 1, the flow is already subcritical, and a jump cannot form. That is because the jump would require a negative head loss, which is not possible under thermodynamic principles.

hydraulic jump: problem solving

Hydraulic Jump in a Rectangular Channel

Hydraulic jump in a rectangular channel shows how flow speed and water depth change when a gate closes downstream. The jump travels upstream at 2 meters per second, so that wave speed is part of the calculation. The initial channel flow speed is 6 meters per second. To find the water depths on each side of the jump, first calculate the effective upstream velocity. This combines the flow moving through the channel with the upstream-moving wave. Next, identify the flow velocities before and...

weir

Weir Flow Measurement and Control

A weir is a hydraulic structure that partly blocks an open channel and helps control water flow. It also makes it possible to measure discharge, which is the amount of water moving past a point in a given time. Because of this, weirs are important in water resource management. Weirs are used in river flow regulation, irrigation systems, and flood control channels. They guide water to flow over or through the structure, which lets engineers estimate flow rates more accurately. This makes them...

weir: problem solving

Weir Flow Rates and Channel Depth

Weirs are hydraulic structures used to measure water flow in open channels. In a rectangular channel, they help calculate discharge, or the volume of water passing a point each second. The weir head is held at a fixed height above the channel bottom, which makes the math easier and lets students compare depth with flow rate. Three weir types are used in this setting: rectangular sharp-crested, triangular sharp-crested, and broad-crested. The rectangular sharp-crested weir depends on the weir...

underflow gates

Irrigation Canal Gate Flow Control

Underflow gates control water flow in irrigation canals. They help manage discharge so water moves where and when it is needed. The main underflow gate types are vertical gates, radial gates, and drum gates. Vertical gates move up and down. They create a free-flowing water jet. Radial gates pivot to regulate flow, and drum gates rotate for fine adjustments. Each design supports effective flow management in different canal settings. Downstream conditions change how water passes through an...

design example: design of an irrigation channel

design-example-design-of-an-irrigation-channel

Designing Trapezoidal Irrigation Channels

Trapezoidal irrigation channels are a common choice for moving water in farms and other water systems. Their flat bottom and sloping sides make them stable and easier to build than many other channel shapes. They are also cost-effective and efficient for carrying water. The channel size depends on the needed flow capacity and the site conditions. Designers choose the bottom width and the side slope ratio to match those demands. For unlined channels, the side slope is kept gentle to help...

key terms and concepts

Learn how specific energy, Froude number, flow depth, and channel slope classify open channel flow as subcritical, critical, or supercritical.

Flow Depth and Energy in Open Channels | 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

Flow Depth and Energy in Open Channels

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