Name: hydraulic jump in a rectangular channel
Uploaded: 2025-03-26T15:04:36.000Z
Duration: 1 min 16 s
Channel: JoVE

يتدفق الماء عبر قناة مستطيلة بسرعة 6 أمتار في الثانية. عندما تغلق بوابة في نهاية القناة فجأة ، تنتقل موجة تسمى القفزة الهيدروليكية إلى اتجاه المنبع بسرعة 2 متر في الثانية.  أمام القفزة ، تجمع سرعة الموجة بين التدفق الأولي للقناة ، مما ينتج عنه سرعة فعالة في المنبع تبلغ 8 أمتار في الثانية. خلف القفزة ، يتدفق الماء بسرعة 2 متر في الثانية. نظرا لأن معدل التدفق يظل ثابتا ، فإن نسبة السرعة من المصب إلى المنبع هي 1: 4 ، وبالتالي فإن عمق المصب هو أربعة أضعاف عمق المنبع. لتحليل القفزة الهيدروليكية ، يتم حساب رقم Froude ، الذي يربط القصور الذاتي للتدفق بالجاذبية ،  على أنه سرعة المنبع مقسومة على الجذر التربيعي لتسارع الجاذبية مضروبا في عمق المنبع.  باستخدام هذا ، يتم تحديد عمق المنبع على أنه 0.652 متر. ينتج عن الضرب في أربعة عمق مصب يبلغ 2.61 متر. نتيجة لذلك ، يبلغ العمق أمام القفزة 0.65 متر ، وخلفها 2.61 متر.

القفزة الهيدروليكية: حل المشكلات

لتحليل قفزة هيدروليكية في قناة مستطيلة بسرعة تدفق تبلغ 6 أمتار في الثانية ، اتبع الخطوات التالية:<ol><li> احسب السرعة الفعالة في المنبع : عندما تغلق بوابة المصب ، تتشكل قفزة هيدروليكية ، تنتقل إلى المنبع بسرعة 2 متر في الثانية. تتحد سرعة الموجة هذه مع سرعة تدفق القناة الأولية ، مما يخلق سرعة فعالة في المنبع. </li><li>تحديد سرعات التدفق قبل وبعد القفزة الهيدروليكية : في اتجاه المنبع من القفزة الهيدروليكية ، تشمل سرعة التدفق الفعالة كلا من تدفق القناة وسرعة الموجة. في اتجاه مجرى النهر ، يتطابق التدفق مع سرعة الموجة ، وهي أبطأ من السرعة الأولية الأولية. </li><li>تحديد نسبة السرعة لحساب العمق : نظرا لأن معدل التدفق يظل ثابتا ، فإن نسبة سرعة المصب إلى المنبع تؤثر على عمق الماء. في هذا المثال، يبلغ عمق المصب أربعة أضعاف عمق المنبع. </li><li>احسب رقم Froude : يتم حساب رقم Froude ، الذي يقارن القصور الذاتي للتدفق بقوى الجاذبية ، باستخدام خصائص التدفق في المنبع. يساعد هذا الرقم في تحديد عمق المنبع. </li><li>تحديد عمق المنبع: احسب عمق المنبع من أسفل القناة إلى سطح الماء باستخدام سرعة المنبع ورقم فرود. </li><li>احسب عمق المصب: نظرا لأن عمق المصب هو أربعة أضعاف عمق المنبع ، يتم حساب هذه القيمة بناء على عمق المنبع. </li><li>تلخيص الأعماق عبر القفزة الهيدروليكية: تظهر النتائج أن عمق المياه قبل القفزة الهيدروليكية أقل عمقا بكثير من خلفها ، مما يعكس التغيرات في العمق بسبب ظروف التدفق وسلوك الموجة. </li></ol>توفر هذه الخطوات طريقة واضحة لتحليل القفزة الهيدروليكية ، وتوضح كيف تؤثر خصائص التدفق على عمق المياه عبر القناة.

To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream ...

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

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 after the hydraulic jump. Upstream of the jump, the velocity includes both the channel flow and the wave speed. Downstream, the flow matches the wave speed, which is slower than the original upstream flow.

The flow rate stays constant, so the velocity ratio helps determine the depth ratio. In this example, the downstream depth is four times the upstream depth. The Froude number is then calculated from the upstream flow. The Froude number compares flow inertia with gravitational forces, and it helps determine the upstream depth.

After the upstream depth is found, the downstream depth can be calculated from the four-to-one depth ratio. The result shows shallow water ahead of the hydraulic jump and deeper water behind it. This pattern reflects how flow conditions and wave motion change water depth across the channel.

Hydraulic Jump in a Rectangular Channel

energy considerations in open channel flow

energy-considerations-in-open-channel-flow

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...

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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

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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...

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Open Channel Depth Changes in GVF

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 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 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

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Weir Flow Rates and Channel Depth

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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

Use flow speed, wave speed, and the Froude number to compare water depth before and after a hydraulic jump in a rectangular channel.

Hydraulic Jump in a Rectangular Channel | 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

Hydraulic Jump in a Rectangular Channel

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